निम्नलिखित में से कौन-सी संख्या अपरिमेय है?
Which of the following numbers is irrational?
#real-numbers
#irrational-numbers
#square-root
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A (0.25)
B \(\sqrt{2}\)
C \(\frac{3}{4}\)
D (5)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{2}\)
Step 1
Concept
अपरिमेय संख्या को \(\frac{p}{q}\) के रूप में नहीं लिखा जा सकता। / An irrational number cannot be written as \(\frac{p}{q}\).
Step 2
Why this answer is correct
\(\sqrt{2}\) पूर्ण वर्ग का वर्गमूल नहीं है, इसलिए यह अपरिमेय है। / \(\sqrt{2}\) is not the square root of a perfect square, so it is irrational.
Step 3
Exam Tip
वर्गमूल में संख्या पूर्ण वर्ग न हो तो वह अक्सर अपरिमेय होती है। / If the number under a square root is not a perfect square, it is usually irrational.
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निम्नलिखित में से कौन-सी संख्या परिमेय है?
Which of the following numbers is rational?
#real-numbers
#rational-numbers
#irrational-numbers
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A \(\sqrt{3}\)
B \(\sqrt{5}\)
C \(\sqrt{9}\)
D \(\sqrt{7}\)
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Correct Answer
C. \(\sqrt{9}\)
Step 1
Concept
पूर्ण वर्ग का वर्गमूल परिमेय संख्या होता है। / The square root of a perfect square is rational.
Step 2
Why this answer is correct
(9) पूर्ण वर्ग है और \(\sqrt{9}=3\), इसलिए यह परिमेय है। / (9) is a perfect square and \(\sqrt{9}=3\), so it is rational.
Step 3
Exam Tip
वर्गमूल वाले प्रश्न में पहले देखें कि अंदर की संख्या पूर्ण वर्ग है या नहीं। / In square root questions, first check whether the number inside is a perfect square.
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\(\sqrt{16}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{16}\)?
#real-numbers
#square-root
#rational-number
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C ऋणात्मक संख्या / Negative number
D अपरिभाषित संख्या / Undefined number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
(16) एक पूर्ण वर्ग है। / (16) is a perfect square.
Step 2
Why this answer is correct
\(\sqrt{16}=4\), और (4) को \(\frac{4}{1}\) के रूप में लिखा जा सकता है। / \(\sqrt{16}=4\), and (4) can be written as \(\frac{4}{1}\).
Step 3
Exam Tip
जो संख्या भिन्न रूप में लिखी जा सके, वह परिमेय होती है। / A number that can be written as a fraction is rational.
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\(\sqrt{10}\) के बारे में सही कथन कौन-सा है?
Which statement about \(\sqrt{10}\) is correct?
#real-numbers
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#concept
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह पूर्णांक है / It is an integer
D यह शून्य है / It is zero
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
(10) पूर्ण वर्ग नहीं है। / (10) is not a perfect square.
Step 2
Why this answer is correct
इसलिए \(\sqrt{10}\) को ठीक-ठीक \(\frac{p}{q}\) के रूप में नहीं लिखा जा सकता। / So \(\sqrt{10}\) cannot be written exactly as \(\frac{p}{q}\).
Step 3
Exam Tip
बिना पूर्ण वर्ग वाली संख्या का वर्गमूल पहचानने में सावधानी रखें। / Be careful while identifying square roots of non-perfect squares.
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निम्नलिखित में से अपरिमेय संख्या का उदाहरण कौन-सा है?
Which of the following is an example of an irrational number?
#real-numbers
#irrational-numbers
#mcq
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A (0.75)
B \(\frac{11}{2}\)
C \(\sqrt{6}\)
D (8)
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Correct Answer
C. \(\sqrt{6}\)
Step 1
Concept
दशमलव (0.75), भिन्न और पूर्णांक परिमेय होते हैं। / (0.75), fractions, and integers are rational.
Step 2
Why this answer is correct
(6) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{6}\) अपरिमेय है। / (6) is not a perfect square, so \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
विकल्पों में पहले साफ परिमेय संख्याएँ हटाने से उत्तर जल्दी मिलता है। / In options, eliminate clear rational numbers first.
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कौन-सा दशमलव रूप अपरिमेय संख्या को दिखाता है?
Which decimal form represents an irrational number?
#real-numbers
#decimal-form
#irrational
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A समाप्त दशमलव / Terminating decimal
B आवर्ती दशमलव / Recurring decimal
C अनवसानी और अनावर्ती दशमलव / Non-terminating and non-recurring decimal
D शून्य दशमलव / Zero decimal
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Correct Answer
C. अनवसानी और अनावर्ती दशमलव / Non-terminating and non-recurring decimal
Step 1
Concept
परिमेय संख्या का दशमलव या तो समाप्त होता है या आवर्ती होता है। / A rational number has either a terminating or recurring decimal form.
Step 2
Why this answer is correct
अपरिमेय संख्या का दशमलव अनवसानी और अनावर्ती होता है। / An irrational number has a non-terminating and non-recurring decimal form.
Step 3
Exam Tip
दशमलव पहचान में आवर्ती और अनावर्ती का अंतर जरूर देखें। / While judging decimals, carefully check recurring and non-recurring patterns.
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\(0.3333\ldots\) किस प्रकार की संख्या है?
What type of number is \(0.3333\ldots\)?
#real-numbers
#recurring-decimal
#rational
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अपूर्ण संख्या / Incomplete number
D केवल प्राकृतिक संख्या / Only natural number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
\(0.3333\ldots\) में (3) बार-बार दोहराता है। / In \(0.3333\ldots\), the digit (3) repeats.
Step 2
Why this answer is correct
आवर्ती दशमलव परिमेय संख्या होता है। / A recurring decimal is rational.
Step 3
Exam Tip
बार-बार दोहरने वाला दशमलव देखकर उसे अपरिमेय न मानें। / Do not call a repeating decimal irrational.
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\(0.101001000100001\ldots\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(0.101001000100001\ldots\)?
#real-numbers
#non-recurring-decimal
#irrational
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A यह समाप्त दशमलव है / It is a terminating decimal
B यह आवर्ती दशमलव है / It is a recurring decimal
C यह अपरिमेय संख्या है / It is an irrational number
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
C. यह अपरिमेय संख्या है / It is an irrational number
Step 1
Concept
दिए गए दशमलव में अंकों का दोहराव निश्चित रूप से नहीं चल रहा है। / The digits do not repeat in a fixed recurring pattern.
Step 2
Why this answer is correct
यह अनवसानी और अनावर्ती दशमलव है, इसलिए अपरिमेय है। / It is non-terminating and non-recurring, so it is irrational.
Step 3
Exam Tip
लंबे दशमलव में दोहराव का साफ नियम न हो तो उसे ध्यान से पहचानें। / In long decimals, check whether there is a fixed repeating block.
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यदि (a) एक अशून्य परिमेय संख्या है और (b) एक अपरिमेय संख्या है, तो (ab) सामान्यतः कैसी संख्या होगी?
If (a) is a non-zero rational number and (b) is an irrational number, what type of number is (ab) generally?
#real-numbers
#irrational-product
#rational-number
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C हमेशा शून्य / Always zero
D हमेशा पूर्णांक / Always integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
अशून्य परिमेय संख्या से अपरिमेय संख्या को गुणा करने पर परिणाम अपरिमेय रहता है। / Multiplying an irrational number by a non-zero rational number keeps it irrational.
Step 2
Why this answer is correct
जैसे \(2 \times \sqrt{3}=2\sqrt{3}\), जो अपरिमेय है। / For example, \(2 \times \sqrt{3}=2\sqrt{3}\), which is irrational.
Step 3
Exam Tip
यहां अशून्य शर्त जरूरी है, क्योंकि शून्य से गुणा करने पर परिणाम (0) होगा। / The non-zero condition is important because multiplication by (0) gives (0).
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\(\sqrt{2}+3\) कैसी संख्या है?
What type of number is \(\sqrt{2}+3\)?
#real-numbers
#irrational-sum
#sqrt2
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C पूर्ण वर्ग / Perfect square
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{2}\) अपरिमेय है और (3) परिमेय है। / \(\sqrt{2}\) is irrational and (3) is rational.
Step 2
Why this answer is correct
परिमेय संख्या जोड़ने से अपरिमेय संख्या परिमेय नहीं बन जाती। / Adding a rational number does not make it rational.
Step 3
Exam Tip
अपरिमेय में कोई साधारण परिमेय संख्या जोड़ने पर परिणाम आम तौर पर अपरिमेय रहता है। / Adding a simple rational number to an irrational number generally keeps it irrational.
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\(\sqrt{2}+\sqrt{2}\) का सरल रूप किस प्रकार की संख्या है?
The simplified form of \(\sqrt{2}+\sqrt{2}\) is what type of number?
#real-numbers
#irrational-numbers
#radicals
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C शून्य / Zero
D ऋणात्मक पूर्णांक / Negative integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{2}+\sqrt{2}=2\sqrt{2}\)। / \(\sqrt{2}+\sqrt{2}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(\sqrt{2}\) अपरिमेय है और (2) अशून्य परिमेय है, इसलिए \(2\sqrt{2}\) अपरिमेय है। / \(\sqrt{2}\) is irrational and (2) is non-zero rational, so \(2\sqrt{2}\) is irrational.
Step 3
Exam Tip
समान वर्गमूलों को पहले जोड़कर सरल करें। / First simplify like radicals, then decide the type.
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\(\sqrt{5}\times\sqrt{5}\) का मान किस प्रकार की संख्या है?
What type of number is the value of \(\sqrt{5}\times\sqrt{5}\)?
#real-numbers
#irrational-product
#rational-result
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अनावर्ती दशमलव / Non-recurring decimal
D केवल ऋणात्मक संख्या / Only negative number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
किसी धनात्मक संख्या के वर्गमूल को उसी से गुणा करने पर वही संख्या मिलती है। / Multiplying a square root by itself gives the number inside the root.
Step 2
Why this answer is correct
\(\sqrt{5}\times\sqrt{5}=5\), और (5) परिमेय है। / \(\sqrt{5}\times\sqrt{5}=5\), and (5) is rational.
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता। / The product of two irrational numbers is not always irrational.
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\(\sqrt{7}\) और \(-\sqrt{7}\) का गुणनफल क्या होगा?
What is the product of \(\sqrt{7}\) and \(-\sqrt{7}\)?
#real-numbers
#square-root
#product
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A (7)
B (-7)
C \(\sqrt{14}\)
D (0)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\times\sqrt{7}=7\) होता है। / \(\sqrt{7}\times\sqrt{7}=7\).
Step 2
Why this answer is correct
एक ऋण चिह्न होने से गुणनफल (-7) होगा। / Because there is one negative sign, the product is (-7).
Step 3
Exam Tip
चिह्न और वर्गमूल दोनों पर ध्यान दें। / Pay attention to both the sign and the square root.
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कौन-सी संख्या अपरिमेय नहीं है?
Which number is not irrational?
#real-numbers
#irrational-numbers
#perfect-square
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A \(\sqrt{11}\)
B \(\sqrt{13}\)
C \(\sqrt{25}\)
D \(\sqrt{17}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{25}\)
Step 1
Concept
प्रश्न अपरिमेय नहीं पूछ रहा है, इसलिए परिमेय विकल्प खोजें। / The question asks for the number that is not irrational, so look for a rational option.
Step 2
Why this answer is correct
\(\sqrt{25}=5\), इसलिए यह परिमेय है। / \(\sqrt{25}=5\), so it is rational.
Step 3
Exam Tip
नकारात्मक शब्दों वाले प्रश्नों में जल्दबाजी न करें। / Be careful with negative wording in MCQs.
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\(\sqrt{12}\) को सरल करने पर कौन-सा रूप मिलता है?
Which form is obtained by simplifying \(\sqrt{12}\)?
#real-numbers
#radical-simplification
#irrational
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A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(6\sqrt{2}\)
D \(4\sqrt{3}\)
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Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(12=4 \times 3\) लिखें। / Write \(12=4 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{12}=\sqrt{4 \times 3}=2\sqrt{3}\)। / \(\sqrt{12}=\sqrt{4 \times 3}=2\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय पूर्ण वर्ग गुणनखंड बाहर निकालें। / While simplifying square roots, take the perfect square factor outside.
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\(\sqrt{18}\) का सरल अपरिमेय रूप कौन-सा है?
Which is the simplified irrational form of \(\sqrt{18}\)?
#real-numbers
#simplification
#square-root
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A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(9\sqrt{2}\)
D \(6\sqrt{3}\)
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Correct Answer
B. \(3\sqrt{2}\)
Step 1
Concept
\(18=9 \times 2\) है। / \(18=9 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{18}=\sqrt{9 \times 2}=3\sqrt{2}\)। / \(\sqrt{18}=\sqrt{9 \times 2}=3\sqrt{2}\).
Step 3
Exam Tip
सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनने से उत्तर जल्दी सरल होता है। / Choosing the largest perfect square factor makes simplification faster.
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\(\sqrt{3}\) के दशमलव विस्तार के बारे में सही कथन कौन-सा है?
Which statement is correct about the decimal expansion of \(\sqrt{3}\)?
#real-numbers
#decimal-expansion
#sqrt3
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A यह समाप्त होता है / It terminates
B यह आवर्ती है / It is recurring
C यह अनवसानी और अनावर्ती है / It is non-terminating and non-recurring
D यह (3) के बराबर है / It is equal to (3)
Explanation opens after your attempt
Correct Answer
C. यह अनवसानी और अनावर्ती है / It is non-terminating and non-recurring
Step 1
Concept
(3) पूर्ण वर्ग नहीं है। / (3) is not a perfect square.
Step 2
Why this answer is correct
\(\sqrt{3}\) अपरिमेय है, इसलिए इसका दशमलव अनवसानी और अनावर्ती होगा। / \(\sqrt{3}\) is irrational, so its decimal expansion is non-terminating and non-recurring.
Step 3
Exam Tip
अपरिमेय संख्या के दशमलव में कोई स्थिर दोहराव नहीं होता। / An irrational decimal has no fixed repeating pattern.
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यदि कोई संख्या \(\frac{p}{q}\) के रूप में नहीं लिखी जा सकती, जहाँ (p) और (q) पूर्णांक हैं तथा \(q \neq 0\), तो वह संख्या क्या कहलाती है?
If a number cannot be written as \(\frac{p}{q}\), where (p) and (q) are integers and \(q \neq 0\), what is it called?
#real-numbers
#definition
#irrational
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C सम संख्या / Even number
D विषम संख्या / Odd number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
परिमेय संख्या \(\frac{p}{q}\) के रूप में लिखी जा सकती है। / A rational number can be written in the form \(\frac{p}{q}\).
Step 2
Why this answer is correct
जो संख्या ऐसे रूप में नहीं लिखी जा सकती, वह अपरिमेय कहलाती है। / A number that cannot be written in this form is called irrational.
Step 3
Exam Tip
परिभाषा वाले प्रश्न में \(q \neq 0\) की शर्त याद रखें। / In definition questions, remember the condition \(q \neq 0\).
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निम्नलिखित में कौन-सा कथन सही है?
Which of the following statements is correct?
#real-numbers
#conceptual
#perfect-square
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A हर वर्गमूल अपरिमेय होता है / Every square root is irrational
B हर पूर्णांक अपरिमेय होता है / Every integer is irrational
C पूर्ण वर्ग का वर्गमूल परिमेय होता है / The square root of a perfect square is rational
D हर दशमलव अपरिमेय होता है / Every decimal is irrational
Explanation opens after your attempt
Correct Answer
C. पूर्ण वर्ग का वर्गमूल परिमेय होता है / The square root of a perfect square is rational
Step 1
Concept
पूर्ण वर्गों के वर्गमूल पूर्णांक होते हैं। / Square roots of perfect squares are integers.
Step 2
Why this answer is correct
जैसे \(\sqrt{36}=6\), इसलिए यह परिमेय है। / For example, \(\sqrt{36}=6\), so it is rational.
Step 3
Exam Tip
हर वर्गमूल को अपरिमेय मान लेना गलत है। / Do not assume every square root is irrational.
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\(\sqrt{2}\times\sqrt{8}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{8}\)?
#real-numbers
#radical-product
#rational-result
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A (4)
B \(\sqrt{10}\)
C \(2\sqrt{8}\)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\times\sqrt{8}=\sqrt{16}\)। / \(\sqrt{2}\times\sqrt{8}=\sqrt{16}\).
Step 2
Why this answer is correct
\(\sqrt{16}=4\), इसलिए मान परिमेय है। / \(\sqrt{16}=4\), so the value is rational.
Step 3
Exam Tip
वर्गमूलों को गुणा करते समय अंदर की संख्याएँ गुणा करें। / While multiplying square roots, multiply the numbers inside the roots.
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\(\sqrt{50}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{50}\)?
#real-numbers
#square-root
#simplification
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A \(5\sqrt{2}\)
B \(2\sqrt{5}\)
C \(10\sqrt{5}\)
D \(25\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(50=25 \times 2\) लिखें। / Write \(50=25 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{50}=\sqrt{25 \times 2}=5\sqrt{2}\)। / \(\sqrt{50}=\sqrt{25 \times 2}=5\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग गुणनखंड से वर्गमूल सरल करना आसान होता है। / A larger perfect square factor makes square-root simplification easier.
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\(2+\sqrt{5}\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(2+\sqrt{5}\)?
#real-numbers
#irrational-sum
#sqrt5
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह (7) के बराबर है / It is equal to (7)
D यह पूर्ण वर्ग है / It is a perfect square
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
(2) परिमेय है और \(\sqrt{5}\) अपरिमेय है। / (2) is rational and \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
परिमेय और अपरिमेय का योग अपरिमेय होता है। / The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
ऐसे प्रश्नों में दोनों भागों की प्रकृति अलग-अलग पहचानें। / In such questions, identify the nature of both parts separately.
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\(\sqrt{11}-\sqrt{11}\) का मान किस प्रकार की संख्या है?
What type of number is the value of \(\sqrt{11}-\sqrt{11}\)?
#real-numbers
#irrational-difference
#rational-result
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C धनात्मक अपरिमेय / Positive irrational
D अनवसानी दशमलव / Non-terminating decimal
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
किसी संख्या में से वही संख्या घटाने पर (0) मिलता है। / Subtracting a number from itself gives (0).
Step 2
Why this answer is correct
\(\sqrt{11}-\sqrt{11}=0\), और (0) परिमेय है। / \(\sqrt{11}-\sqrt{11}=0\), and (0) is rational.
Step 3
Exam Tip
दो अपरिमेय संख्याओं का अंतर हमेशा अपरिमेय नहीं होता। / The difference of two irrational numbers is not always irrational.
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\(\frac{\sqrt{3}}{2}\) कैसी संख्या है?
What type of number is \(\frac{\sqrt{3}}{2}\)?
#real-numbers
#irrational-division
#sqrt3
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{3}\) अपरिमेय है। / \(\sqrt{3}\) is irrational.
Step 2
Why this answer is correct
इसे अशून्य परिमेय संख्या (2) से भाग देने पर भी परिणाम अपरिमेय रहता है। / Dividing it by the non-zero rational number (2) still gives an irrational number.
Step 3
Exam Tip
अपरिमेय संख्या को अशून्य परिमेय से गुणा या भाग करने पर सामान्यतः अपरिमेय परिणाम मिलता है। / Multiplying or dividing an irrational number by a non-zero rational number generally keeps it irrational.
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\(\sqrt{4}+\sqrt{9}\) का मान क्या है?
What is the value of \(\sqrt{4}+\sqrt{9}\)?
#real-numbers
#square-root
#rational-number
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A (5)
B \(\sqrt{13}\)
C (13)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{4}=2\) और \(\sqrt{9}=3\)। / \(\sqrt{4}=2\) and \(\sqrt{9}=3\).
Step 2
Why this answer is correct
दोनों को जोड़ने पर (2+3=5) मिलता है। / Adding them gives (2+3=5).
Step 3
Exam Tip
पूर्ण वर्गों के वर्गमूल पहले अलग-अलग निकालें। / First find the square roots of perfect squares separately.
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कौन-सा विकल्प अपरिमेय संख्या की सही पहचान बताता है?
Which option gives the correct identification of an irrational number?
#real-numbers
#irrational-definition
#decimal
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A जिसका दशमलव समाप्त हो / Its decimal terminates
B जिसका दशमलव आवर्ती हो / Its decimal recurs
C जिसका दशमलव अनवसानी और अनावर्ती हो / Its decimal is non-terminating and non-recurring
D जो हमेशा ऋणात्मक हो / It is always negative
Explanation opens after your attempt
Correct Answer
C. जिसका दशमलव अनवसानी और अनावर्ती हो / Its decimal is non-terminating and non-recurring
Step 1
Concept
अपरिमेय संख्या का दशमलव खत्म नहीं होता। / The decimal of an irrational number does not terminate.
Step 2
Why this answer is correct
उसमें कोई निश्चित दोहराव भी नहीं होता। / It also does not repeat in a fixed pattern.
Step 3
Exam Tip
दशमलव विस्तार देखकर अपरिमेय संख्या पहचानना आसान हो जाता है। / Decimal expansion is a useful way to identify irrational numbers.
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\(\sqrt{49}\) और \(\sqrt{50}\) में से कौन-सी संख्या अपरिमेय है?
Which of \(\sqrt{49}\) and \(\sqrt{50}\) is irrational?
#real-numbers
#perfect-square
#irrational
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A \(\sqrt{49}\)
B \(\sqrt{50}\)
C दोनों परिमेय हैं / Both are rational
D दोनों पूर्णांक हैं / Both are integers
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{50}\)
Step 1
Concept
(49) पूर्ण वर्ग है, इसलिए \(\sqrt{49}=7\) परिमेय है। / (49) is a perfect square, so \(\sqrt{49}=7\) is rational.
Step 2
Why this answer is correct
(50) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{50}\) अपरिमेय है। / (50) is not a perfect square, so \(\sqrt{50}\) is irrational.
Step 3
Exam Tip
पास-पास की संख्याओं में भी पूर्ण वर्ग पहचानना जरूरी है। / Even for nearby numbers, check perfect squares carefully.
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\(\sqrt{2}\) और \(\sqrt{8}\) का योग किसके बराबर है?
What is the sum of \(\sqrt{2}\) and \(\sqrt{8}\)?
#real-numbers
#radical-addition
#irrational
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A \(3\sqrt{2}\)
B (10)
C \(\sqrt{10}\)
D \(2\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) है। / \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल करें। / Simplify radicals before adding them.
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\(\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{27}\)?
#real-numbers
#simplify-radicals
#irrational
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A \(3\sqrt{3}\)
B \(9\sqrt{3}\)
C \(2\sqrt{7}\)
D \(\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(27=9 \times 3\) लिखें। / Write \(27=9 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{27}=\sqrt{9 \times 3}=3\sqrt{3}\)। / \(\sqrt{27}=\sqrt{9 \times 3}=3\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल में पूर्ण वर्ग (9) दिखे तो उसे बाहर (3) के रूप में निकालें। / When (9) appears as a factor inside a square root, take it out as (3).
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कौन-सा कथन गलत है?
Which statement is false?
#real-numbers
#false-statement
#irrational
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A \(\sqrt{2}\) अपरिमेय है / \(\sqrt{2}\) is irrational
B \(\sqrt{4}\) परिमेय है / \(\sqrt{4}\) is rational
C हर अपरिमेय संख्या पूर्णांक होती है / Every irrational number is an integer
D (0.5) परिमेय है / (0.5) is rational
Explanation opens after your attempt
Correct Answer
C. हर अपरिमेय संख्या पूर्णांक होती है / Every irrational number is an integer
Step 1
Concept
अपरिमेय संख्या पूर्णांक नहीं होती, क्योंकि पूर्णांक \(\frac{p}{q}\) रूप में लिखे जा सकते हैं। / Irrational numbers are not integers because integers can be written in the form \(\frac{p}{q}\).
Step 2
Why this answer is correct
इसलिए हर अपरिमेय संख्या को पूर्णांक कहना गलत है। / So saying every irrational number is an integer is false.
Step 3
Exam Tip
गलत कथन वाले प्रश्न में हर विकल्प को अलग-अलग जांचें। / In false-statement questions, check every option separately.
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\(\sqrt{45}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{45}\)?
#real-numbers
#square-root
#simplification
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A \(3\sqrt{5}\)
B \(5\sqrt{3}\)
C \(9\sqrt{5}\)
D (15)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{5}\)
Step 1
Concept
\(45=9 \times 5\) है। / \(45=9 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{45}=\sqrt{9 \times 5}=3\sqrt{5}\)। / \(\sqrt{45}=\sqrt{9 \times 5}=3\sqrt{5}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड पहचानना वर्गमूल सरलीकरण की कुंजी है। / Identifying the perfect square factor is the key to simplifying square roots.
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यदि \(x=\sqrt{2}\), तो \(x^2\) का मान क्या होगा?
If \(x=\sqrt{2}\), what is the value of \(x^2\)?
#real-numbers
#square-root
#irrational
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A (2)
B \(\sqrt{2}\)
C (4)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(x=\sqrt{2}\) दिया है। / We are given \(x=\sqrt{2}\).
Step 2
Why this answer is correct
(x-2 =\(\sqrt{2}\)2 =2)। / (x-2 =\(\sqrt{2}\)2 =2).
Step 3
Exam Tip
वर्गमूल का वर्ग करने पर अंदर की संख्या मिलती है। / Squaring a square root gives the number inside it.
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\(\sqrt{3}\times\sqrt{12}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{12}\)?
#real-numbers
#irrational-product
#rational-result
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A (6)
B \(\sqrt{15}\)
C \(3\sqrt{12}\)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{12}=\sqrt{36}\)। / \(\sqrt{3}\times\sqrt{12}=\sqrt{36}\).
Step 2
Why this answer is correct
\(\sqrt{36}=6\), इसलिए परिणाम परिमेय है। / \(\sqrt{36}=6\), so the result is rational.
Step 3
Exam Tip
कभी-कभी दो अपरिमेय संख्याओं का गुणनफल परिमेय हो सकता है। / Sometimes the product of two irrational numbers can be rational.
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निम्नलिखित में से कौन-सा युग्म दोनों अपरिमेय संख्याओं का है?
Which pair contains two irrational numbers?
#real-numbers
#irrational-pair
#mcq
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A \(2,\sqrt{3}\)
B \(\sqrt{5},\sqrt{7}\)
C \(\sqrt{9},\sqrt{11}\)
D \(\frac{1}{2},\sqrt{13}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{5},\sqrt{7}\)
Step 1
Concept
\(\sqrt{5}\) और \(\sqrt{7}\) दोनों में अंदर की संख्या पूर्ण वर्ग नहीं है। / In \(\sqrt{5}\) and \(\sqrt{7}\), the numbers inside the roots are not perfect squares.
Step 2
Why this answer is correct
इसलिए दोनों अपरिमेय हैं। / Hence both are irrational.
Step 3
Exam Tip
युग्म वाले प्रश्न में दोनों संख्याओं की जांच जरूरी है। / In pair questions, check both numbers, not just one.
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\(\sqrt{20}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{20}\)?
#real-numbers
#radical-simplification
#sqrt20
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A \(2\sqrt{5}\)
B \(5\sqrt{2}\)
C \(4\sqrt{5}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{5}\)
Step 1
Concept
\(20=4 \times 5\) है। / \(20=4 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{20}=\sqrt{4 \times 5}=2\sqrt{5}\)। / \(\sqrt{20}=\sqrt{4 \times 5}=2\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल के अंदर पूर्ण वर्ग को बाहर निकालें और बाकी अंदर रहने दें। / Take the perfect square outside the root and leave the remaining factor inside.
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\(\frac{1}{\sqrt{2}}\) किस प्रकार की संख्या है?
What type of number is \(\frac{1}{\sqrt{2}}\)?
#real-numbers
#irrational-number
#rationalisation
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{2}\) अपरिमेय है। / \(\sqrt{2}\) is irrational.
Step 2
Why this answer is correct
\(\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\), जो अपरिमेय है। / \(\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\), which is irrational.
Step 3
Exam Tip
हर में वर्गमूल हो तो परिमेयकरण करके पहचानना आसान होता है। / When a square root is in the denominator, rationalising helps identify the number.
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कौन-सा विकल्प परिमेय और अपरिमेय संख्या के योग का सही परिणाम बताता है?
Which option correctly describes the sum of a rational and an irrational number?
#real-numbers
#rational-irrational-sum
#concept
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A हमेशा परिमेय / Always rational
B हमेशा अपरिमेय / Always irrational
C हमेशा शून्य / Always zero
D हमेशा पूर्णांक / Always integer
Explanation opens after your attempt
Correct Answer
B. हमेशा अपरिमेय / Always irrational
Step 1
Concept
परिमेय संख्या को जोड़ने से अपरिमेय भाग खत्म नहीं होता। / Adding a rational number does not remove the irrational part.
Step 2
Why this answer is correct
जैसे \(4+\sqrt{2}\) अपरिमेय है। / For example, \(4+\sqrt{2}\) is irrational.
Step 3
Exam Tip
परिमेय और अपरिमेय का योग याद रखने योग्य नियम है। / The sum of a rational and an irrational number is an important rule to remember.
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\(\sqrt{2}+\sqrt{3}\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{2}+\sqrt{3}\)?
#real-numbers
#radicals
#irrational-sum
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह (5) है / It is (5)
D यह \(\sqrt{5}\) है / It is \(\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
\(\sqrt{2}\) और \(\sqrt{3}\) दोनों अपरिमेय हैं। / Both \(\sqrt{2}\) and \(\sqrt{3}\) are irrational.
Step 2
Why this answer is correct
उनका योग \(\sqrt{5}\) नहीं होता; \(\sqrt{2}+\sqrt{3}\) अपरिमेय रहता है। / Their sum is not \(\sqrt{5}\); \(\sqrt{2}+\sqrt{3}\) remains irrational.
Step 3
Exam Tip
अलग-अलग वर्गमूलों को सीधे अंदर की संख्याएँ जोड़कर न लिखें। / Do not add the numbers inside different square roots directly.
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\(\sqrt{2}\times\sqrt{3}\) किसके बराबर है?
What is \(\sqrt{2}\times\sqrt{3}\) equal to?
#real-numbers
#radical-product
#irrational
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A \(\sqrt{5}\)
B \(\sqrt{6}\)
C (6)
D \(2\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{6}\)
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / While multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{3}=\sqrt{6}\), जो अपरिमेय है। / \(\sqrt{2}\times\sqrt{3}=\sqrt{6}\), which is irrational.
Step 3
Exam Tip
गुणा में अंदर की संख्याएँ गुणा करें, जोड़ नहीं। / In multiplication, multiply the inside numbers; do not add them.
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\(\sqrt{72}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{72}\)?
#real-numbers
#square-root
#simplification
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A \(6\sqrt{2}\)
B \(8\sqrt{2}\)
C \(3\sqrt{8}\)
D \(2\sqrt{18}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{2}\)
Step 1
Concept
\(72=36 \times 2\) लिखें। / Write \(72=36 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{72}=\sqrt{36 \times 2}=6\sqrt{2}\)। / \(\sqrt{72}=\sqrt{36 \times 2}=6\sqrt{2}\).
Step 3
Exam Tip
सबसे बड़ा पूर्ण वर्ग गुणनखंड लेने से अंतिम रूप साफ मिलता है। / Taking the largest perfect square factor gives a cleaner final form.
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निम्नलिखित में से कौन-सी संख्या (3) और (4) के बीच है और अपरिमेय है?
Which of the following numbers lies between (3) and (4) and is irrational?
#real-numbers
#irrational-between-numbers
#square-root
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A \(\sqrt{10}\)
B \(\sqrt{16}\)
C \(\sqrt{9}\)
D (3.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{10}\)
Step 1
Concept
(9<10<16), इसलिए \(3<\sqrt{10}<4\)। / Since (9<10<16), we get \(3<\sqrt{10}<4\).
Step 2
Why this answer is correct
(10) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{10}\) अपरिमेय है। / (10) is not a perfect square, so \(\sqrt{10}\) is irrational.
Step 3
Exam Tip
दो पूर्ण वर्गों के बीच की संख्या का वर्गमूल अंतराल बताता है। / Use nearby perfect squares to locate square roots.
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\(2\sqrt{3}\) किस प्रकार की संख्या है?
What type of number is \(2\sqrt{3}\)?
#real-numbers
#irrational-number
#coefficient
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C पूर्णांक / Integer
D सम संख्या / Even number
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
\(\sqrt{3}\) अपरिमेय है। / \(\sqrt{3}\) is irrational.
Step 2
Why this answer is correct
(2) अशून्य परिमेय संख्या है, इसलिए \(2\sqrt{3}\) अपरिमेय रहेगा। / (2) is a non-zero rational number, so \(2\sqrt{3}\) remains irrational.
Step 3
Exam Tip
बाहर का गुणांक देखकर संख्या को परिमेय न मानें। / Do not call a radical rational just because it has a coefficient outside.
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\(\sqrt{32}\) को सरल कीजिए।
Simplify \(\sqrt{32}\).
#real-numbers
#radical-simplification
#sqrt32
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A \(4\sqrt{2}\)
B \(2\sqrt{8}\)
C \(8\sqrt{2}\)
D \(16\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{2}\)
Step 1
Concept
\(32=16 \times 2\) है। / \(32=16 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{32}=\sqrt{16 \times 2}=4\sqrt{2}\)। / \(\sqrt{32}=\sqrt{16 \times 2}=4\sqrt{2}\).
Step 3
Exam Tip
उत्तर को पूरी तरह सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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\(\sqrt{2}\) का निकटतम मान कौन-सा है?
Which is the nearest value of \(\sqrt{2}\)?
#real-numbers
#approximation
#sqrt2
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A (1.41)
B (2.00)
C (1.00)
D (1.73)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\) का दशमलव मान लगभग (1.414) होता है। / The decimal value of \(\sqrt{2}\) is about (1.414).
Step 2
Why this answer is correct
दिए गए विकल्पों में (1.41) सबसे निकट है। / Among the given options, (1.41) is the closest.
Step 3
Exam Tip
कुछ सामान्य वर्गमूलों के लगभग मान याद रखने से अनुमान आसान होता है। / Remembering approximate values of common square roots helps in estimation.
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\(\sqrt{3}\) का निकटतम मान कौन-सा है?
Which is the nearest value of \(\sqrt{3}\)?
#real-numbers
#approximation
#sqrt3
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A (1.22)
B (1.73)
C (2.24)
D (3.00)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\) का मान लगभग (1.732) होता है। / The value of \(\sqrt{3}\) is approximately (1.732).
Step 2
Why this answer is correct
इसलिए (1.73) सबसे निकट विकल्प है। / So (1.73) is the closest option.
Step 3
Exam Tip
अनुमान वाले प्रश्न में पहले देखें कि संख्या किन पूर्ण वर्गों के बीच है। / In estimation questions, first see between which perfect squares the number lies.
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कौन-सी संख्या \(\sqrt{5}\) के सबसे निकट है?
Which number is closest to \(\sqrt{5}\)?
#real-numbers
#approximation
#sqrt5
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A (2.24)
B (1.41)
C (3.16)
D (5.00)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\) का मान लगभग (2.236) है। / The value of \(\sqrt{5}\) is about (2.236).
Step 2
Why this answer is correct
(2.24) इस मान के सबसे निकट है। / (2.24) is the closest value.
Step 3
Exam Tip
निकटतम मान चुनते समय केवल पूर्णांक सीमा पर निर्भर न रहें। / While choosing nearest values, do not depend only on integer boundaries.
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\(\sqrt{2}\) और \(\sqrt{3}\) के बीच कौन-सी संख्या स्थित है?
Which number lies between \(\sqrt{2}\) and \(\sqrt{3}\)?
#real-numbers
#comparison
#irrational-numbers
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A (1.5)
B (2)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\approx 1.414\) और \(\sqrt{3}\approx 1.732\)। / \(\sqrt{2}\approx 1.414\) and \(\sqrt{3}\approx 1.732\).
Step 2
Why this answer is correct
(1.5) इन दोनों के बीच आता है। / (1.5) lies between these two values.
Step 3
Exam Tip
वर्गमूलों के बीच संख्या चुनने में लगभग मान मदद करते हैं। / Approximate values help in comparing square roots.
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\(\sqrt{64}\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{64}\)?
#real-numbers
#perfect-square
#rational
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A यह अपरिमेय है / It is irrational
B यह (8) है और परिमेय है / It is (8) and rational
C यह (32) है / It is (32)
D यह अनवसानी दशमलव है / It is a non-terminating decimal
Explanation opens after your attempt
Correct Answer
B. यह (8) है और परिमेय है / It is (8) and rational
Step 1
Concept
(64) पूर्ण वर्ग है। / (64) is a perfect square.
Step 2
Why this answer is correct
\(\sqrt{64}=8\), इसलिए यह परिमेय संख्या है। / \(\sqrt{64}=8\), so it is rational.
Step 3
Exam Tip
बड़े पूर्ण वर्गों के वर्गमूल भी परिमेय हो सकते हैं। / Square roots of larger perfect squares can also be rational.
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यदि (n) पूर्ण वर्ग नहीं है, तो \(\sqrt{n}\) सामान्यतः कैसी संख्या होती है?
If (n) is not a perfect square, what type of number is \(\sqrt{n}\) generally?
#real-numbers
#irrational-rule
#square-root
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A परिमेय संख्या / Rational number
B अपरिमेय संख्या / Irrational number
C हमेशा शून्य / Always zero
D हमेशा पूर्णांक / Always integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय संख्या / Irrational number
Step 1
Concept
पूर्ण वर्ग का वर्गमूल पूर्णांक होता है। / The square root of a perfect square is an integer.
Step 2
Why this answer is correct
यदि (n) पूर्ण वर्ग नहीं है, तो \(\sqrt{n}\) परिमेय नहीं होता। / If (n) is not a perfect square, \(\sqrt{n}\) is not rational.
Step 3
Exam Tip
यह नियम कक्षा दस के अपरिमेय संख्या प्रश्नों में बहुत उपयोगी है। / This rule is very useful in Class 10 irrational number questions.
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\(\sqrt{75}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{75}\)?
#real-numbers
#simplify-radicals
#irrational
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A \(5\sqrt{3}\)
B \(3\sqrt{5}\)
C \(25\sqrt{3}\)
D \(15\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{3}\)
Step 1
Concept
\(75=25 \times 3\) लिखें। / Write \(75=25 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{75}=\sqrt{25 \times 3}=5\sqrt{3}\)। / \(\sqrt{75}=\sqrt{25 \times 3}=5\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल को सरल करते समय अंदर की संख्या को पूर्ण वर्ग और बाकी गुणनखंड में तोड़ें। / While simplifying a square root, split the inside number into a perfect square and the remaining factor.
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निम्नलिखित में से कौन-सी संख्या अपरिमेय है?
Which of the following numbers is irrational?
#real-numbers
#irrational-numbers
#square-root
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A \(\sqrt{15}\)
B \(\sqrt{16}\)
C (0.125)
D \(\frac{7}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{15}\)
Step 1
Concept
अपरिमेय संख्या को ठीक-ठीक भिन्न रूप में नहीं लिखा जा सकता। / An irrational number cannot be written exactly as a fraction.
Step 2
Why this answer is correct
(15) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{15}\) अपरिमेय है। / (15) is not a perfect square, so \(\sqrt{15}\) is irrational.
Step 3
Exam Tip
वर्गमूल वाले विकल्पों में अंदर की संख्या पूर्ण वर्ग है या नहीं, पहले यही देखें। / For square-root options, first check whether the number inside is a perfect square.
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\(\sqrt{81}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{81}\)?
#real-numbers
#rational-number
#perfect-square
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अनावर्ती दशमलव / Non-recurring decimal
D ऋणात्मक संख्या / Negative number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
(81) एक पूर्ण वर्ग है। / (81) is a perfect square.
Step 2
Why this answer is correct
\(\sqrt{81}=9\), और (9) को \(\frac{9}{1}\) लिखा जा सकता है। / \(\sqrt{81}=9\), and (9) can be written as \(\frac{9}{1}\).
Step 3
Exam Tip
पूर्ण वर्ग का वर्गमूल हमेशा परिमेय होता है। / The square root of a perfect square is always rational.
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कौन-सा दशमलव अपरिमेय संख्या को दर्शाता है?
Which decimal represents an irrational number?
#real-numbers
#decimal-expansion
#irrational
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A \(0.272727\ldots\)
B (0.4)
C \(0.1234567891011\ldots\)
D (2.75)
Explanation opens after your attempt
Correct Answer
C. \(0.1234567891011\ldots\)
Step 1
Concept
समाप्त या आवर्ती दशमलव परिमेय होते हैं। / Terminating or recurring decimals are rational.
Step 2
Why this answer is correct
\(0.1234567891011\ldots\) में कोई निश्चित दोहराव नहीं है, इसलिए यह अनवसानी और अनावर्ती है। / \(0.1234567891011\ldots\) has no fixed repeating pattern, so it is non-terminating and non-recurring.
Step 3
Exam Tip
अपरिमेय दशमलव पहचानने के लिए दोहराव का नियम जांचें। / To identify an irrational decimal, check for a repeating rule.
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\(\sqrt{28}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{28}\)?
#real-numbers
#radical-simplification
#sqrt28
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A \(2\sqrt{7}\)
B \(7\sqrt{2}\)
C \(4\sqrt{7}\)
D \(14\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
\(28=4 \times 7\) लिखें। / Write \(28=4 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\)। / \(\sqrt{28}=\sqrt{4 \times 7}=2\sqrt{7}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय पूर्ण वर्ग गुणनखंड को बाहर निकालें। / While simplifying a square root, take the perfect square factor outside.
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\(\sqrt{2}\times\sqrt{18}\) का मान क्या होगा?
What is the value of \(\sqrt{2}\times\sqrt{18}\)?
#real-numbers
#radical-product
#rational-result
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A (6)
B \(\sqrt{20}\)
C \(2\sqrt{18}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा होती हैं। / When multiplying square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\)। / \(\sqrt{2}\times\sqrt{18}=\sqrt{36}=6\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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निम्नलिखित में से कौन-सा विकल्प परिमेय है?
Which of the following options is rational?
#real-numbers
#rational-number
#square-root
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A \(\sqrt{19}\)
B \(\sqrt{21}\)
C \(\sqrt{100}\)
D \(\sqrt{30}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{100}\)
Step 1
Concept
परिमेय विकल्प खोजने के लिए पूर्ण वर्ग का वर्गमूल देखें। / To find the rational option, look for the square root of a perfect square.
Step 2
Why this answer is correct
(100) पूर्ण वर्ग है और \(\sqrt{100}=10\)। / (100) is a perfect square and \(\sqrt{100}=10\).
Step 3
Exam Tip
\(\sqrt{n}\) में यदि (n) पूर्ण वर्ग हो, तो उत्तर परिमेय होगा। / In \(\sqrt{n}\), if (n) is a perfect square, the value is rational.
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\(\sqrt{2}+5\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{2}+5\)?
#real-numbers
#irrational-sum
#sqrt2
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A यह परिमेय है / It is rational
B यह अपरिमेय है / It is irrational
C यह (7) है / It is (7)
D यह पूर्णांक है / It is an integer
Explanation opens after your attempt
Correct Answer
B. यह अपरिमेय है / It is irrational
Step 1
Concept
\(\sqrt{2}\) अपरिमेय है और (5) परिमेय है। / \(\sqrt{2}\) is irrational and (5) is rational.
Step 2
Why this answer is correct
परिमेय संख्या जोड़ने से अपरिमेय भाग समाप्त नहीं होता। / Adding a rational number does not remove the irrational part.
Step 3
Exam Tip
परिमेय और अपरिमेय का योग सामान्यतः अपरिमेय होता है। / The sum of a rational and an irrational number is generally irrational.
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\(\sqrt{48}\) को सरल करने पर क्या मिलेगा?
What do we get after simplifying \(\sqrt{48}\)?
#real-numbers
#simplify-radicals
#irrational
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A \(4\sqrt{3}\)
B \(3\sqrt{4}\)
C \(6\sqrt{2}\)
D \(8\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(48=16 \times 3\) है। / \(48=16 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{48}=\sqrt{16 \times 3}=4\sqrt{3}\)। / \(\sqrt{48}=\sqrt{16 \times 3}=4\sqrt{3}\).
Step 3
Exam Tip
सबसे बड़ा पूर्ण वर्ग लेने से सरल रूप सही और छोटा मिलता है। / Using the largest perfect square gives the simplest form.
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किस संख्या का दशमलव विस्तार समाप्त होता है?
Which number has a terminating decimal expansion?
#real-numbers
#terminating-decimal
#rational
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A \(\sqrt{5}\)
B \(\frac{3}{8}\)
C \(\sqrt{11}\)
D \(\sqrt{13}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{8}\)
Step 1
Concept
समाप्त दशमलव वाली संख्या परिमेय होती है। / A number with a terminating decimal is rational.
Step 2
Why this answer is correct
\(\frac{3}{8}=0.375\), इसलिए इसका दशमलव समाप्त होता है। / \(\frac{3}{8}=0.375\), so its decimal terminates.
Step 3
Exam Tip
भिन्न के हर में केवल (2) और (5) के गुणनखंड हों तो दशमलव समाप्त होता है। / If the denominator has only factors (2) and (5), the decimal terminates.
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\(\sqrt{7}+\sqrt{7}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{7}+\sqrt{7}\)?
#real-numbers
#radical-addition
#irrational
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A \(2\sqrt{7}\)
B \(\sqrt{14}\)
C \(7\sqrt{2}\)
D (14)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{7}\)
Step 1
Concept
समान वर्गमूलों को समान पद की तरह जोड़ा जाता है। / Like radicals are added like like terms.
Step 2
Why this answer is correct
\(\sqrt{7}+\sqrt{7}=2\sqrt{7}\)। / \(\sqrt{7}+\sqrt{7}=2\sqrt{7}\).
Step 3
Exam Tip
जोड़ में अंदर की संख्याएँ जोड़कर \(\sqrt{14}\) नहीं लिखना चाहिए। / In addition, do not add the numbers inside roots to write \(\sqrt{14}\).
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\(\sqrt{7}-\sqrt{7}\) का मान क्या है?
What is the value of \(\sqrt{7}-\sqrt{7}\)?
#real-numbers
#irrational-difference
#zero
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A (0)
B \(\sqrt{14}\)
C (7)
D \(2\sqrt{7}\)
Explanation opens after your attempt
Step 1
Concept
किसी संख्या में से वही संख्या घटाने पर शून्य मिलता है। / Subtracting a number from itself gives zero.
Step 2
Why this answer is correct
\(\sqrt{7}-\sqrt{7}=0\), और (0) परिमेय है। / \(\sqrt{7}-\sqrt{7}=0\), and (0) is rational.
Step 3
Exam Tip
अपरिमेय संख्याओं के साथ भी सामान्य घटाव नियम लागू होता है। / Normal subtraction rules also apply to irrational numbers.
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\(\sqrt{2}\) और \(\sqrt{5}\) के गुणनफल की प्रकृति क्या है?
What is the nature of the product of \(\sqrt{2}\) and \(\sqrt{5}\)?
#real-numbers
#irrational-product
#sqrt10
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{2}\times\sqrt{5}=\sqrt{10}\)। / \(\sqrt{2}\times\sqrt{5}=\sqrt{10}\).
Step 2
Why this answer is correct
(10) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{10}\) अपरिमेय है। / (10) is not a perfect square, so \(\sqrt{10}\) is irrational.
Step 3
Exam Tip
गुणन के बाद बने वर्गमूल की अंदर की संख्या जांचें। / After multiplication, check the number inside the new root.
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निम्नलिखित में से कौन-सा कथन सत्य है?
Which of the following statements is true?
#real-numbers
#true-statement
#irrational
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A हर अपरिमेय संख्या ऋणात्मक होती है / Every irrational number is negative
B हर परिमेय संख्या अपरिमेय होती है / Every rational number is irrational
C \(\sqrt{n}\) अपरिमेय हो सकता है जब (n) पूर्ण वर्ग न हो / \(\sqrt{n}\) can be irrational when (n) is not a perfect square
D हर दशमलव पूर्णांक होता है / Every decimal is an integer
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{n}\) अपरिमेय हो सकता है जब (n) पूर्ण वर्ग न हो / \(\sqrt{n}\) can be irrational when (n) is not a perfect square
Step 1
Concept
यदि (n) पूर्ण वर्ग नहीं है, तो \(\sqrt{n}\) परिमेय नहीं होता। / If (n) is not a perfect square, \(\sqrt{n}\) is not rational.
Step 2
Why this answer is correct
जैसे \(\sqrt{6}\) अपरिमेय है। / For example, \(\sqrt{6}\) is irrational.
Step 3
Exam Tip
सत्य कथन में उदाहरण लगाकर जांच करना आसान रहता है। / Testing a statement with an example makes it easier to judge.
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\(\sqrt{98}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{98}\)?
#real-numbers
#sqrt98
#simplification
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A \(7\sqrt{2}\)
B \(2\sqrt{7}\)
C \(14\sqrt{2}\)
D \(49\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{2}\)
Step 1
Concept
\(98=49 \times 2\) है। / \(98=49 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{98}=\sqrt{49 \times 2}=7\sqrt{2}\)। / \(\sqrt{98}=\sqrt{49 \times 2}=7\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (49) को पहचानना सरलीकरण में मदद करता है। / Recognising larger perfect squares like (49) helps in simplification.
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\(\sqrt{3}\) और \(\sqrt{12}\) का योग क्या है?
What is the sum of \(\sqrt{3}\) and \(\sqrt{12}\)?
#real-numbers
#radical-addition
#sqrt3
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A \(3\sqrt{3}\)
B \(\sqrt{15}\)
C \(4\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\) है। / \(\sqrt{12}=2\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)। / \(\sqrt{3}+2\sqrt{3}=3\sqrt{3}\).
Step 3
Exam Tip
जोड़ से पहले वर्गमूलों को समान रूप में बदलें। / Before adding, convert radicals into like terms if possible.
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कौन-सी संख्या (4) और (5) के बीच स्थित अपरिमेय संख्या है?
Which number is an irrational number lying between (4) and (5)?
#real-numbers
#irrational-between-numbers
#sqrt17
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A \(\sqrt{17}\)
B \(\sqrt{16}\)
C \(\sqrt{25}\)
D (4.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{17}\)
Step 1
Concept
(16<17<25), इसलिए \(4<\sqrt{17}<5\)। / Since (16<17<25), \(4<\sqrt{17}<5\).
Step 2
Why this answer is correct
(17) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{17}\) अपरिमेय है। / (17) is not a perfect square, so \(\sqrt{17}\) is irrational.
Step 3
Exam Tip
अंतराल वाले प्रश्न में पास के पूर्ण वर्गों का उपयोग करें। / Use nearby perfect squares in interval questions.
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\(\frac{\sqrt{5}}{5}\) कैसी संख्या है?
What type of number is \(\frac{\sqrt{5}}{5}\)?
#real-numbers
#irrational-division
#sqrt5
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{5}\) अपरिमेय है। / \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
अशून्य परिमेय संख्या (5) से भाग देने पर यह अपरिमेय ही रहती है। / Dividing it by the non-zero rational number (5) keeps it irrational.
Step 3
Exam Tip
हर में परिमेय संख्या होने से पूरा पद परिमेय नहीं हो जाता। / A rational denominator alone does not make the whole expression rational.
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निम्नलिखित में से कौन-सा युग्म एक परिमेय और एक अपरिमेय संख्या का है?
Which pair has one rational and one irrational number?
#real-numbers
#rational-irrational-pair
#mcq
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A \(3,\sqrt{6}\)
B \(\sqrt{2},\sqrt{3}\)
C \(5,\frac{7}{2}\)
D \(\sqrt{4},\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(3,\sqrt{6}\)
Step 1
Concept
(3) परिमेय है। / (3) is rational.
Step 2
Why this answer is correct
\(\sqrt{6}\) अपरिमेय है क्योंकि (6) पूर्ण वर्ग नहीं है। / \(\sqrt{6}\) is irrational because (6) is not a perfect square.
Step 3
Exam Tip
युग्म में दोनों संख्याओं को अलग-अलग पहचानें। / In a pair, identify each number separately.
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\(\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{125}\)?
#real-numbers
#square-root
#simplification
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A \(5\sqrt{5}\)
B \(25\sqrt{5}\)
C \(3\sqrt{5}\)
D \(5\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{5}\)
Step 1
Concept
\(125=25 \times 5\) लिखें। / Write \(125=25 \times 5\).
Step 2
Why this answer is correct
\(\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5}\)। / \(\sqrt{125}=\sqrt{25 \times 5}=5\sqrt{5}\).
Step 3
Exam Tip
पूर्ण वर्ग (25) को बाहर (5) के रूप में निकालें। / Take the perfect square (25) outside as (5).
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\(\sqrt{6}+\sqrt{6}+\sqrt{6}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{6}+\sqrt{6}+\sqrt{6}\)?
#real-numbers
#like-radicals
#addition
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A \(3\sqrt{6}\)
B \(\sqrt{18}\)
C \(6\sqrt{3}\)
D (18)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{6}\)
Step 1
Concept
तीन समान अपरिमेय पद जोड़े जा रहे हैं। / Three like irrational terms are being added.
Step 2
Why this answer is correct
\(\sqrt{6}+\sqrt{6}+\sqrt{6}=3\sqrt{6}\)। / \(\sqrt{6}+\sqrt{6}+\sqrt{6}=3\sqrt{6}\).
Step 3
Exam Tip
समान वर्गमूलों को गुणांक की तरह गिनें। / Count like radicals as coefficients.
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\(\sqrt{45}-\sqrt{20}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{45}-\sqrt{20}\)?
#real-numbers
#radical-subtraction
#sqrt5
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A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(\sqrt{25}\)
D \(3\sqrt{25}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\)। / \(\sqrt{45}=3\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\).
Step 2
Why this answer is correct
\(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\)। / \(3\sqrt{5}-2\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को सरल करें। / Simplify both radicals before subtracting.
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\(\sqrt{2}\) का वर्ग किस प्रकार की संख्या है?
What type of number is the square of \(\sqrt{2}\)?
#real-numbers
#square-of-irrational
#rational-result
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A अपरिमेय / Irrational
B परिमेय / Rational
C अनवसानी अनावर्ती / Non-terminating non-recurring
D ऋणात्मक / Negative
Explanation opens after your attempt
Correct Answer
B. परिमेय / Rational
Step 1
Concept
(\(\sqrt{2}\)2 =2)। / (\(\sqrt{2}\)2 =2).
Step 2
Why this answer is correct
(2) परिमेय संख्या है क्योंकि इसे \(\frac{2}{1}\) लिखा जा सकता है। / (2) is rational because it can be written as \(\frac{2}{1}\).
Step 3
Exam Tip
अपरिमेय संख्या का वर्ग कभी-कभी परिमेय हो सकता है। / The square of an irrational number can sometimes be rational.
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यदि \(x=\sqrt{5}\), तो (5x) कैसी संख्या होगी?
If \(x=\sqrt{5}\), what type of number is (5x)?
#real-numbers
#irrational-product
#coefficient
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A परिमेय / Rational
B अपरिमेय / Irrational
C शून्य / Zero
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(x=\sqrt{5}\) अपरिमेय है। / \(x=\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
\(5x=5\sqrt{5}\), और (5) अशून्य परिमेय है। / \(5x=5\sqrt{5}\), and (5) is a non-zero rational number.
Step 3
Exam Tip
अपरिमेय संख्या को अशून्य परिमेय से गुणा करने पर परिणाम अपरिमेय रहता है। / Multiplying an irrational number by a non-zero rational number keeps it irrational.
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कौन-सा विकल्प अपरिमेय संख्या नहीं है?
Which option is not an irrational number?
#real-numbers
#not-irrational
#perfect-square
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A \(\sqrt{22}\)
B \(\sqrt{36}\)
C \(\sqrt{26}\)
D \(\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{36}\)
Step 1
Concept
प्रश्न अपरिमेय नहीं पूछ रहा है, इसलिए परिमेय संख्या खोजें। / The question asks for the number that is not irrational, so find the rational one.
Step 2
Why this answer is correct
\(\sqrt{36}=6\), जो परिमेय है। / \(\sqrt{36}=6\), which is rational.
Step 3
Exam Tip
ऐसे प्रश्नों में नकारात्मक भाषा को ध्यान से पढ़ें। / Read negative wording carefully in MCQs.
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\(\sqrt{8}+\sqrt{18}\) का सरल रूप क्या होगा?
What is the simplified form of \(\sqrt{8}+\sqrt{18}\)?
#real-numbers
#radical-addition
#simplification
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A \(5\sqrt{2}\)
B \(2\sqrt{26}\)
C \(\sqrt{26}\)
D \(10\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\) और \(\sqrt{18}=3\sqrt{2}\)। / \(\sqrt{8}=2\sqrt{2}\) and \(\sqrt{18}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\)। / \(2\sqrt{2}+3\sqrt{2}=5\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only after they become like radicals.
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निम्नलिखित में से कौन-सा कथन गलत है?
Which of the following statements is false?
#real-numbers
#false-statement
#perfect-square
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A \(0.121212\ldots\) परिमेय है / \(0.121212\ldots\) is rational
B \(\sqrt{23}\) अपरिमेय है / \(\sqrt{23}\) is irrational
C \(\sqrt{49}\) अपरिमेय है / \(\sqrt{49}\) is irrational
D \(\frac{5}{6}\) परिमेय है / \(\frac{5}{6}\) is rational
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{49}\) अपरिमेय है / \(\sqrt{49}\) is irrational
Step 1
Concept
\(\sqrt{49}=7\) होता है। / \(\sqrt{49}=7\).
Step 2
Why this answer is correct
(7) परिमेय है, इसलिए \(\sqrt{49}\) को अपरिमेय कहना गलत है। / (7) is rational, so saying \(\sqrt{49}\) is irrational is false.
Step 3
Exam Tip
गलत कथन चुनते समय पूर्ण वर्गों को जरूर जांचें। / While choosing a false statement, check perfect squares carefully.
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\(\sqrt{150}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{150}\)?
#real-numbers
#sqrt150
#radical-simplification
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A \(5\sqrt{6}\)
B \(6\sqrt{5}\)
C \(10\sqrt{15}\)
D \(15\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{6}\)
Step 1
Concept
\(150=25 \times 6\) लिखें। / Write \(150=25 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\)। / \(\sqrt{150}=\sqrt{25 \times 6}=5\sqrt{6}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर बाकी गुणनखंड अंदर छोड़ें। / Take the perfect square factor outside and leave the remaining factor inside.
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\(\sqrt{5}\times\sqrt{20}\) का मान क्या होगा?
What is the value of \(\sqrt{5}\times\sqrt{20}\)?
#real-numbers
#radical-product
#rational-result
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A (10)
B \(\sqrt{25}\)
C \(5\sqrt{20}\)
D \(\sqrt{1000}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{5}\times\sqrt{20}=\sqrt{100}\)। / \(\sqrt{5}\times\sqrt{20}=\sqrt{100}\).
Step 2
Why this answer is correct
\(\sqrt{100}=10\), जो परिमेय संख्या है। / \(\sqrt{100}=10\), which is rational.
Step 3
Exam Tip
गुणन में पहले अंदर की संख्याओं का गुणन करें। / In multiplication, first multiply the numbers inside the roots.
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कौन-सी संख्या (5) और (6) के बीच स्थित है?
Which number lies between (5) and (6)?
#real-numbers
#comparison
#irrational-between
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A \(\sqrt{30}\)
B \(\sqrt{25}\)
C \(\sqrt{36}\)
D (6.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{30}\)
Step 1
Concept
(25<30<36), इसलिए \(5<\sqrt{30}<6\)। / Since (25<30<36), \(5<\sqrt{30}<6\).
Step 2
Why this answer is correct
(30) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{30}\) अपरिमेय है। / (30) is not a perfect square, so \(\sqrt{30}\) is irrational.
Step 3
Exam Tip
वर्गमूल की स्थिति जानने के लिए नजदीकी पूर्ण वर्ग देखें। / Use nearby perfect squares to locate a square root.
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\(\sqrt{200}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{200}\)?
#real-numbers
#sqrt200
#simplification
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A \(10\sqrt{2}\)
B \(20\sqrt{5}\)
C \(2\sqrt{100}\)
D \(100\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{2}\)
Step 1
Concept
\(200=100 \times 2\) है। / \(200=100 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{200}=\sqrt{100 \times 2}=10\sqrt{2}\)। / \(\sqrt{200}=\sqrt{100 \times 2}=10\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग (100) को पहचानने से उत्तर जल्दी मिलता है। / Recognising a large perfect square like (100) gives the answer quickly.
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\(\sqrt{3}+2\sqrt{3}\) किसके बराबर है?
What is \(\sqrt{3}+2\sqrt{3}\) equal to?
#real-numbers
#like-radicals
#addition
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A \(3\sqrt{3}\)
B \(2\sqrt{6}\)
C \(\sqrt{9}\)
D \(5\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{3}\)
Step 1
Concept
दोनों पदों में \(\sqrt{3}\) समान है। / Both terms have the same radical \(\sqrt{3}\).
Step 2
Why this answer is correct
\(1\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)। / \(1\sqrt{3}+2\sqrt{3}=3\sqrt{3}\).
Step 3
Exam Tip
समान वर्गमूलों में केवल गुणांक जोड़ें। / For like radicals, add only the coefficients.
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\(\sqrt{2}\) का लगभग मान किसके सबसे निकट है?
The approximate value of \(\sqrt{2}\) is closest to which number?
#real-numbers
#approximation
#sqrt2
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A (1.41)
B (1.90)
C (2.41)
D (0.41)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\) का मान लगभग (1.414) है। / The value of \(\sqrt{2}\) is about (1.414).
Step 2
Why this answer is correct
दिए गए विकल्पों में (1.41) सबसे निकट है। / Among the given options, (1.41) is closest.
Step 3
Exam Tip
सामान्य वर्गमूलों के लगभग मान याद रखने से तुलना आसान होती है। / Remembering approximate values of common roots helps in comparison.
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\(\sqrt{10}\) का मान किन दो पूर्णांकों के बीच होगा?
Between which two integers does \(\sqrt{10}\) lie?
#real-numbers
#comparison
#sqrt10
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A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
C. (3) और (4) / (3) and (4)
Step 1
Concept
(9<10<16) है।
Step 2
Why this answer is correct
इसलिए \(\sqrt{9}<\sqrt{10}<\sqrt{16}\), यानी \(3<\sqrt{10}<4\)। / So \(\sqrt{9}<\sqrt{10}<\sqrt{16}\), meaning \(3<\sqrt{10}<4\).
Step 3
Exam Tip
वर्गमूल की सीमा के लिए पास के पूर्ण वर्गों का उपयोग करें। / Use nearby perfect squares to find the range of a square root.
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\(\sqrt{63}\) को सरल कीजिए।
Simplify \(\sqrt{63}\).
#real-numbers
#sqrt63
#radical-simplification
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A \(3\sqrt{7}\)
B \(7\sqrt{3}\)
C \(9\sqrt{7}\)
D (21)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{7}\)
Step 1
Concept
\(63=9 \times 7\) है। / \(63=9 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\)। / \(\sqrt{63}=\sqrt{9 \times 7}=3\sqrt{7}\).
Step 3
Exam Tip
(9) जैसे पूर्ण वर्ग को बाहर निकालना याद रखें। / Remember to take a perfect square like (9) outside the root.
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यदि \(y=\sqrt{11}\), तो \(y^2\) का मान क्या होगा?
If \(y=\sqrt{11}\), what is the value of \(y^2\)?
#real-numbers
#square-root
#square
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A (11)
B \(\sqrt{11}\)
C (121)
D (22)
Explanation opens after your attempt
Step 1
Concept
\(y=\sqrt{11}\) है। / \(y=\sqrt{11}\).
Step 2
Why this answer is correct
(y-2 =\(\sqrt{11}\)2 =11)। / (y-2 =\(\sqrt{11}\)2 =11).
Step 3
Exam Tip
वर्गमूल का वर्ग करने पर मूल संख्या मिलती है। / Squaring a square root gives the original number inside it.
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कौन-सा विकल्प दो अपरिमेय संख्याओं का ऐसा गुणनफल दिखाता है जो परिमेय है?
Which option shows a product of two irrational numbers that is rational?
#real-numbers
#irrational-product
#rational-result
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A \(\sqrt{3}\times\sqrt{3}\)
B \(\sqrt{2}\times\sqrt{5}\)
C \(\sqrt{7}\times\sqrt{11}\)
D \(\sqrt{5}\times\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\times\sqrt{3}\)
Step 1
Concept
\(\sqrt{3}\) अपरिमेय है। / \(\sqrt{3}\) is irrational.
Step 2
Why this answer is correct
\(\sqrt{3}\times\sqrt{3}=3\), जो परिमेय है। / \(\sqrt{3}\times\sqrt{3}=3\), which is rational.
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता। / The product of two irrational numbers is not always irrational.
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\(\sqrt{5}+0\) किसके बराबर है?
What is \(\sqrt{5}+0\) equal to?
#real-numbers
#zero-property
#irrational
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A \(\sqrt{5}\)
B (5)
C (0)
D \(\sqrt{0}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
शून्य जोड़ने से संख्या नहीं बदलती। / Adding zero does not change a number.
Step 2
Why this answer is correct
\(\sqrt{5}+0=\sqrt{5}\), जो अपरिमेय है। / \(\sqrt{5}+0=\sqrt{5}\), which is irrational.
Step 3
Exam Tip
शून्य के साथ भी संख्या की मूल प्रकृति समझें। / Even with zero, understand the original nature of the number.
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\(\sqrt{6}\) का दशमलव विस्तार कैसा होगा?
What kind of decimal expansion does \(\sqrt{6}\) have?
#real-numbers
#decimal-expansion
#sqrt6
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A समाप्त / Terminating
B आवर्ती / Recurring
C अनवसानी और अनावर्ती / Non-terminating and non-recurring
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. अनवसानी और अनावर्ती / Non-terminating and non-recurring
Step 1
Concept
(6) पूर्ण वर्ग नहीं है। / (6) is not a perfect square.
Step 2
Why this answer is correct
इसलिए \(\sqrt{6}\) अपरिमेय है और इसका दशमलव अनवसानी अनावर्ती होगा। / So \(\sqrt{6}\) is irrational and its decimal is non-terminating and non-recurring.
Step 3
Exam Tip
अपरिमेय संख्या में स्थिर दोहराव नहीं होता। / An irrational number has no fixed repeating pattern.
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\(\sqrt{90}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{90}\)?
#real-numbers
#sqrt90
#simplification
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A \(3\sqrt{10}\)
B \(9\sqrt{10}\)
C \(10\sqrt{9}\)
D \(5\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{10}\)
Step 1
Concept
\(90=9 \times 10\) लिखें। / Write \(90=9 \times 10\).
Step 2
Why this answer is correct
\(\sqrt{90}=\sqrt{9 \times 10}=3\sqrt{10}\)। / \(\sqrt{90}=\sqrt{9 \times 10}=3\sqrt{10}\).
Step 3
Exam Tip
पूर्ण वर्ग को बाहर निकालकर शेष भाग अंदर रखें। / Take the perfect square outside and keep the remaining part inside.
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कौन-सी संख्या \(\sqrt{12}\) के बराबर है?
Which number is equal to \(\sqrt{12}\)?
#real-numbers
#equivalent-radicals
#sqrt12
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A \(2\sqrt{3}\)
B \(3\sqrt{2}\)
C \(4\sqrt{3}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{3}\)
Step 1
Concept
\(12=4 \times 3\) है। / \(12=4 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{12}=2\sqrt{3}\)। / \(\sqrt{12}=2\sqrt{3}\).
Step 3
Exam Tip
बराबर रूप पहचानने के लिए वर्गमूल को सरल करना जरूरी है। / To identify an equivalent form, simplify the square root first.
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\(\sqrt{5}\) और \(-\sqrt{5}\) का योग क्या है?
What is the sum of \(\sqrt{5}\) and \(-\sqrt{5}\)?
#real-numbers
#opposites
#irrational
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A (0)
B (5)
C (-5)
D \(2\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
दोनों पद एक-दूसरे के विपरीत हैं। / The two terms are opposites of each other.
Step 2
Why this answer is correct
(\sqrt{5}+\(-\sqrt{5}\)=0)। / (\sqrt{5}+\(-\sqrt{5}\)=0).
Step 3
Exam Tip
विपरीत पदों का योग हमेशा शून्य होता है। / The sum of opposite terms is always zero.
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यदि (a) अपरिमेय है और (r) अशून्य परिमेय है, तो (ra) किस प्रकार की संख्या होगी?
If (a) is irrational and (r) is a non-zero rational number, what type of number is (ra)?
#real-numbers
#irrational-rule
#nonzero-rational
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A परिमेय / Rational
B अपरिमेय / Irrational
C हमेशा शून्य / Always zero
D हमेशा प्राकृतिक / Always natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
अशून्य परिमेय गुणक अपरिमेयता को समाप्त नहीं करता। / A non-zero rational multiplier does not remove irrationality.
Step 2
Why this answer is correct
जैसे \(3\sqrt{2}\) अपरिमेय है। / For example, \(3\sqrt{2}\) is irrational.
Step 3
Exam Tip
यहां अशून्य शर्त जरूरी है क्योंकि शून्य से गुणा करने पर परिणाम शून्य होगा। / The non-zero condition is important because multiplying by zero gives zero.
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\(\sqrt{112}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{112}\)?
#real-numbers
#sqrt112
#radical-simplification
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A \(4\sqrt{7}\)
B \(7\sqrt{4}\)
C \(8\sqrt{7}\)
D \(16\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{7}\)
Step 1
Concept
\(112=16 \times 7\) है। / \(112=16 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\)। / \(\sqrt{112}=\sqrt{16 \times 7}=4\sqrt{7}\).
Step 3
Exam Tip
सरलीकरण में अंदर बची संख्या को फिर पूर्ण वर्ग के लिए जांचें। / After simplification, check that the remaining number has no perfect square factor.
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निम्नलिखित में कौन-सा अपरिमेय संख्या का दशमलव रूप हो सकता है?
Which of the following can be the decimal form of an irrational number?
#real-numbers
#decimal-form
#irrational
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A \(0.6666\ldots\)
B (0.2500)
C \(1.41421356\ldots\) बिना निश्चित दोहराव / \(1.41421356\ldots\) with no fixed repetition
D (3.000)
Explanation opens after your attempt
Correct Answer
C. \(1.41421356\ldots\) बिना निश्चित दोहराव / \(1.41421356\ldots\) with no fixed repetition
Step 1
Concept
आवर्ती या समाप्त दशमलव परिमेय होते हैं। / Recurring or terminating decimals are rational.
Step 2
Why this answer is correct
बिना निश्चित दोहराव वाला अनवसानी दशमलव अपरिमेय हो सकता है। / A non-terminating decimal without fixed repetition can be irrational.
Step 3
Exam Tip
केवल लंबा दशमलव देखकर नहीं, दोहराव देखकर निर्णय लें। / Do not judge only by length; check for repetition.
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\(\sqrt{147}\) को सरल कीजिए।
Simplify \(\sqrt{147}\).
#real-numbers
#sqrt147
#simplification
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A \(7\sqrt{3}\)
B \(3\sqrt{7}\)
C \(21\sqrt{3}\)
D \(49\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{3}\)
Step 1
Concept
\(147=49 \times 3\) लिखें। / Write \(147=49 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{147}=\sqrt{49 \times 3}=7\sqrt{3}\)। / \(\sqrt{147}=\sqrt{49 \times 3}=7\sqrt{3}\).
Step 3
Exam Tip
पूर्ण वर्ग (49) को पहचानना यहां मुख्य कदम है। / Recognising the perfect square (49) is the main step here.
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\(\sqrt{2}\times\sqrt{32}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{32}\)?
#real-numbers
#radical-product
#sqrt64
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A (8)
B \(\sqrt{34}\)
C (16)
D \(4\sqrt{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{2}\times\sqrt{32}=\sqrt{64}\)। / \(\sqrt{2}\times\sqrt{32}=\sqrt{64}\).
Step 2
Why this answer is correct
\(\sqrt{64}=8\), इसलिए परिणाम परिमेय है। / \(\sqrt{64}=8\), so the result is rational.
Step 3
Exam Tip
गुणन में वर्गमूलों के अंदर की संख्याएँ गुणा करें। / In multiplication, multiply the numbers inside the square roots.
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\(\sqrt{3}\) का लगभग मान कौन-सा है?
What is the approximate value of \(\sqrt{3}\)?
#real-numbers
#approximation
#sqrt3
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A (1.73)
B (1.31)
C (2.73)
D (3.14)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\) का मान लगभग (1.732) है। / \(\sqrt{3}\) is approximately (1.732).
Step 2
Why this answer is correct
इसलिए (1.73) सबसे सही निकट मान है। / So (1.73) is the closest correct value.
Step 3
Exam Tip
अनुमान के लिए सामान्य वर्गमूलों के मान याद रखें। / For estimation, remember common square-root values.
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कौन-सा विकल्प \(\sqrt{24}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{24}\)?
#real-numbers
#sqrt24
#simplification
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A \(2\sqrt{6}\)
B \(4\sqrt{6}\)
C \(6\sqrt{2}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{6}\)
Step 1
Concept
\(24=4 \times 6\) है। / \(24=4 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{24}=\sqrt{4 \times 6}=2\sqrt{6}\)। / \(\sqrt{24}=\sqrt{4 \times 6}=2\sqrt{6}\).
Step 3
Exam Tip
यदि अंदर (6) बचे तो वह आगे सरल नहीं होगा क्योंकि (6) में पूर्ण वर्ग गुणनखंड नहीं है। / If (6) remains inside, it cannot be simplified further because it has no perfect square factor.
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\(\sqrt{13}\) का मान किन दो पूर्णांकों के बीच है?
Between which two integers does \(\sqrt{13}\) lie?
#real-numbers
#comparison
#sqrt13
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A (2) और (3) / (2) and (3)
B (3) और (4) / (3) and (4)
C (4) और (5) / (4) and (5)
D (5) और (6) / (5) and (6)
Explanation opens after your attempt
Correct Answer
B. (3) और (4) / (3) and (4)
Step 1
Concept
(9<13<16) है।
Step 2
Why this answer is correct
इसलिए \(3<\sqrt{13}<4\)। / Therefore, \(3<\sqrt{13}<4\).
Step 3
Exam Tip
वर्गमूल की तुलना के लिए पास के पूर्ण वर्ग बहुत उपयोगी होते हैं। / Nearby perfect squares are very useful for comparing square roots.
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निम्नलिखित में से कौन-सा परिणाम अपरिमेय है?
Which of the following results is irrational?
#real-numbers
#irrational-result
#radicals
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A \(\sqrt{2}+\sqrt{8}\)
B \(\sqrt{4}+\sqrt{9}\)
C \(\sqrt{5}\times\sqrt{5}\)
D \(\sqrt{16}-\sqrt{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}+\sqrt{8}\)
Step 1
Concept
\(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\)। / \(\sqrt{2}+\sqrt{8}=\sqrt{2}+2\sqrt{2}=3\sqrt{2}\).
Step 2
Why this answer is correct
\(3\sqrt{2}\) अपरिमेय है। / \(3\sqrt{2}\) is irrational.
Step 3
Exam Tip
विकल्पों में परिणाम निकालकर ही संख्या की प्रकृति तय करें। / In options, simplify the result before deciding its nature.
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निम्नलिखित में से कौन-सी संख्या अपरिमेय है?
Which of the following numbers is irrational?
#real-numbers
#irrational-numbers
#square-root
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A \(\sqrt{14}\)
B \(\sqrt{121}\)
C \(\frac{9}{11}\)
D (0.625)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{14}\)
Step 1
Concept
अपरिमेय संख्या को \(\frac{p}{q}\) के रूप में ठीक-ठीक नहीं लिखा जा सकता। / An irrational number cannot be written exactly in the form \(\frac{p}{q}\).
Step 2
Why this answer is correct
(14) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{14}\) अपरिमेय है। / (14) is not a perfect square, so \(\sqrt{14}\) is irrational.
Step 3
Exam Tip
वर्गमूल में अंदर की संख्या पूर्ण वर्ग है या नहीं, पहले यही जांचें। / In square-root questions, first check whether the number inside is a perfect square.
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\(\sqrt{121}\) किस प्रकार की संख्या है?
What type of number is \(\sqrt{121}\)?
#real-numbers
#rational-number
#perfect-square
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A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अनवसानी अनावर्ती दशमलव / Non-terminating non-recurring decimal
D ऋणात्मक संख्या / Negative number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
(121) एक पूर्ण वर्ग है। / (121) is a perfect square.
Step 2
Why this answer is correct
\(\sqrt{121}=11\), और (11) को \(\frac{11}{1}\) के रूप में लिखा जा सकता है। / \(\sqrt{121}=11\), and (11) can be written as \(\frac{11}{1}\).
Step 3
Exam Tip
पूर्ण वर्गों के वर्गमूल परिमेय होते हैं। / Square roots of perfect squares are rational.
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कौन-सा दशमलव अपरिमेय संख्या का रूप हो सकता है?
Which decimal can represent an irrational number?
#real-numbers
#decimal-expansion
#irrational
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A \(0.5555\ldots\)
B (0.875)
C \(0.01001000100001\ldots\)
D (4.000)
Explanation opens after your attempt
Correct Answer
C. \(0.01001000100001\ldots\)
Step 1
Concept
समाप्त और आवर्ती दशमलव परिमेय होते हैं। / Terminating and recurring decimals are rational.
Step 2
Why this answer is correct
\(0.01001000100001\ldots\) में निश्चित दोहराव नहीं है, इसलिए यह अनवसानी और अनावर्ती है। / \(0.01001000100001\ldots\) has no fixed repeating pattern, so it is non-terminating and non-recurring.
Step 3
Exam Tip
दशमलव में केवल लंबाई नहीं, दोहराव का नियम देखना जरूरी है। / For decimals, check the repetition pattern, not just the length.
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\(\sqrt{108}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{108}\)?
#real-numbers
#radical-simplification
#sqrt108
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A \(3\sqrt{12}\)
B \(6\sqrt{3}\)
C \(9\sqrt{2}\)
D \(12\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(6\sqrt{3}\)
Step 1
Concept
\(108=36 \times 3\) लिखें। / Write \(108=36 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\)। / \(\sqrt{108}=\sqrt{36 \times 3}=6\sqrt{3}\).
Step 3
Exam Tip
वर्गमूल सरल करते समय सबसे बड़ा पूर्ण वर्ग गुणनखंड चुनना अच्छा रहता है। / While simplifying a square root, choosing the largest perfect square factor is helpful.
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\(\sqrt{7}+4\) के बारे में सही कथन कौन-सा है?
Which statement is correct about \(\sqrt{7}+4\)?
#real-numbers
#irrational-sum
#sqrt7
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A यह परिमेय है / It is rational
B यह पूर्णांक है / It is an integer
C यह अपरिमेय है / It is irrational
D यह शून्य है / It is zero
Explanation opens after your attempt
Correct Answer
C. यह अपरिमेय है / It is irrational
Step 1
Concept
\(\sqrt{7}\) अपरिमेय है और (4) परिमेय है। / \(\sqrt{7}\) is irrational and (4) is rational.
Step 2
Why this answer is correct
परिमेय संख्या जोड़ने से अपरिमेय भाग समाप्त नहीं होता। / Adding a rational number does not remove the irrational part.
Step 3
Exam Tip
परिमेय और अपरिमेय संख्या का योग सामान्यतः अपरिमेय होता है। / The sum of a rational and an irrational number is generally irrational.
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\(\sqrt{2}\times\sqrt{50}\) का मान क्या है?
What is the value of \(\sqrt{2}\times\sqrt{50}\)?
#real-numbers
#radical-product
#rational-result
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A (5)
B (10)
C \(\sqrt{52}\)
D (25)
Explanation opens after your attempt
Step 1
Concept
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / In multiplication of square roots, multiply the numbers inside.
Step 2
Why this answer is correct
\(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\)। / \(\sqrt{2}\times\sqrt{50}=\sqrt{100}=10\).
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल कभी-कभी परिमेय हो सकता है। / The product of two irrational numbers can sometimes be rational.
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निम्नलिखित में से कौन-सा विकल्प परिमेय संख्या है?
Which of the following options is a rational number?
#real-numbers
#rational-number
#square-root
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A \(\sqrt{37}\)
B \(\sqrt{41}\)
C \(\sqrt{144}\)
D \(\sqrt{58}\)
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Correct Answer
C. \(\sqrt{144}\)
Step 1
Concept
परिमेय विकल्प के लिए पूर्ण वर्ग का वर्गमूल खोजें। / To find the rational option, look for the square root of a perfect square.
Step 2
Why this answer is correct
(144) पूर्ण वर्ग है और \(\sqrt{144}=12\)। / (144) is a perfect square and \(\sqrt{144}=12\).
Step 3
Exam Tip
पूर्ण वर्ग पहचानने से ऐसे प्रश्न बहुत जल्दी हल होते हैं। / Recognising perfect squares makes such questions very quick.
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\(\sqrt{3}+\sqrt{27}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{3}+\sqrt{27}\)?
#real-numbers
#radical-addition
#sqrt3
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A \(4\sqrt{3}\)
B \(3\sqrt{3}\)
C \(\sqrt{30}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{3}\)
Step 1
Concept
\(\sqrt{27}=3\sqrt{3}\) होता है। / \(\sqrt{27}=3\sqrt{3}\).
Step 2
Why this answer is correct
\(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\)। / \(\sqrt{3}+3\sqrt{3}=4\sqrt{3}\).
Step 3
Exam Tip
जोड़ने से पहले वर्गमूलों को सरल करके समान रूप बनाएं। / Before adding, simplify radicals and make them like terms.
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किस संख्या का दशमलव विस्तार आवर्ती है?
Which number has a recurring decimal expansion?
#real-numbers
#recurring-decimal
#rational
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A \(\sqrt{2}\)
B \(\frac{5}{6}\)
C \(\sqrt{29}\)
D \(\sqrt{31}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{5}{6}\)
Step 1
Concept
\(\frac{5}{6}\) परिमेय संख्या है। / \(\frac{5}{6}\) is a rational number.
Step 2
Why this answer is correct
इसका दशमलव \(0.8333\ldots\) के रूप में आवर्ती होता है। / Its decimal form is \(0.8333\ldots\), which is recurring.
Step 3
Exam Tip
परिमेय संख्याओं का दशमलव समाप्त या आवर्ती होता है। / Rational numbers have decimal expansions that are either terminating or recurring.
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\(\sqrt{11}+\sqrt{11}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{11}+\sqrt{11}\)?
#real-numbers
#like-radicals
#addition
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A \(\sqrt{22}\)
B \(11\sqrt{2}\)
C \(2\sqrt{11}\)
D (22)
Explanation opens after your attempt
Correct Answer
C. \(2\sqrt{11}\)
Step 1
Concept
दोनों पद समान वर्गमूल वाले हैं। / Both terms have the same square root.
Step 2
Why this answer is correct
\(\sqrt{11}+\sqrt{11}=2\sqrt{11}\)। / \(\sqrt{11}+\sqrt{11}=2\sqrt{11}\).
Step 3
Exam Tip
समान वर्गमूलों में अंदर की संख्याएँ नहीं, केवल गुणांक जोड़े जाते हैं। / For like radicals, add only the coefficients, not the numbers inside the roots.
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\(\sqrt{19}-\sqrt{19}\) का मान क्या है?
What is the value of \(\sqrt{19}-\sqrt{19}\)?
#real-numbers
#irrational-difference
#zero
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A (19)
B (0)
C \(2\sqrt{19}\)
D \(\sqrt{38}\)
Explanation opens after your attempt
Step 1
Concept
किसी संख्या में से वही संख्या घटाने पर (0) मिलता है। / Subtracting a number from itself gives (0).
Step 2
Why this answer is correct
इसलिए \(\sqrt{19}-\sqrt{19}=0\), जो परिमेय है। / So \(\sqrt{19}-\sqrt{19}=0\), which is rational.
Step 3
Exam Tip
अपरिमेय पदों पर भी सामान्य घटाव नियम लागू होता है। / Ordinary subtraction rules also apply to irrational terms.
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\(\sqrt{3}\times\sqrt{75}\) का मान क्या है?
What is the value of \(\sqrt{3}\times\sqrt{75}\)?
#real-numbers
#radical-product
#rational-result
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A (15)
B \(\sqrt{78}\)
C \(3\sqrt{75}\)
D (75)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\times\sqrt{75}=\sqrt{225}\)। / \(\sqrt{3}\times\sqrt{75}=\sqrt{225}\).
Step 2
Why this answer is correct
\(\sqrt{225}=15\), इसलिए परिणाम परिमेय है। / \(\sqrt{225}=15\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद यदि अंदर की संख्या पूर्ण वर्ग बन जाए, तो उत्तर परिमेय हो सकता है। / If the number inside becomes a perfect square after multiplication, the answer can be rational.
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कौन-सा कथन सत्य है?
Which statement is true?
#real-numbers
#true-statement
#perfect-square
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A हर अनवसानी दशमलव अपरिमेय होता है / Every non-terminating decimal is irrational
B हर आवर्ती दशमलव अपरिमेय होता है / Every recurring decimal is irrational
C पूर्ण वर्ग का वर्गमूल परिमेय होता है / The square root of a perfect square is rational
D हर अपरिमेय संख्या शून्य होती है / Every irrational number is zero
Explanation opens after your attempt
Correct Answer
C. पूर्ण वर्ग का वर्गमूल परिमेय होता है / The square root of a perfect square is rational
Step 1
Concept
पूर्ण वर्गों के वर्गमूल पूर्णांक होते हैं। / Square roots of perfect squares are integers.
Step 2
Why this answer is correct
जैसे \(\sqrt{49}=7\), इसलिए यह परिमेय है। / For example, \(\sqrt{49}=7\), so it is rational.
Step 3
Exam Tip
कथन वाले प्रश्नों में उदाहरण लगाकर सत्यता जांचना आसान होता है। / In statement-based questions, using an example helps check the truth.
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\(\sqrt{242}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{242}\)?
#real-numbers
#sqrt242
#radical-simplification
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A \(11\sqrt{2}\)
B \(2\sqrt{121}\)
C \(22\sqrt{2}\)
D \(121\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(11\sqrt{2}\)
Step 1
Concept
\(242=121 \times 2\) है। / \(242=121 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\)। / \(\sqrt{242}=\sqrt{121 \times 2}=11\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग जैसे (121) को पहचानना सरलीकरण में बहुत उपयोगी है। / Recognising large perfect squares like (121) is very useful in simplification.
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\(\sqrt{5}+\sqrt{45}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{5}+\sqrt{45}\)?
#real-numbers
#radical-addition
#sqrt5
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A \(4\sqrt{5}\)
B \(10\sqrt{5}\)
C \(\sqrt{50}\)
D \(3\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\(\sqrt{45}=3\sqrt{5}\) है। / \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\)। / \(\sqrt{5}+3\sqrt{5}=4\sqrt{5}\).
Step 3
Exam Tip
वर्गमूल जोड़ते समय समान वर्गमूल बनने तक सरल करें। / While adding radicals, simplify them until like radicals appear.
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कौन-सी संख्या (6) और (7) के बीच स्थित अपरिमेय संख्या है?
Which number is an irrational number between (6) and (7)?
#real-numbers
#irrational-between-numbers
#sqrt45
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A \(\sqrt{35}\)
B \(\sqrt{40}\)
C \(\sqrt{45}\)
D \(\sqrt{49}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{45}\)
Step 1
Concept
(36<45<49), इसलिए \(6<\sqrt{45}<7\)। / Since (36<45<49), \(6<\sqrt{45}<7\).
Step 2
Why this answer is correct
(45) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{45}\) अपरिमेय है। / (45) is not a perfect square, so \(\sqrt{45}\) is irrational.
Step 3
Exam Tip
अंतराल वाले प्रश्नों में पास के पूर्ण वर्गों का उपयोग करें। / In interval questions, use nearby perfect squares.
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\(\frac{\sqrt{7}}{3}\) कैसी संख्या है?
What type of number is \(\frac{\sqrt{7}}{3}\)?
#real-numbers
#irrational-division
#sqrt7
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A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृतिक / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
\(\sqrt{7}\) अपरिमेय है। / \(\sqrt{7}\) is irrational.
Step 2
Why this answer is correct
इसे अशून्य परिमेय संख्या (3) से भाग देने पर परिणाम अपरिमेय रहता है। / Dividing it by the non-zero rational number (3) keeps the result irrational.
Step 3
Exam Tip
अशून्य परिमेय से भाग करने पर अपरिमेयता समाप्त नहीं होती। / Division by a non-zero rational number does not remove irrationality.
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कौन-सा युग्म एक परिमेय और एक अपरिमेय संख्या से बना है?
Which pair is made of one rational and one irrational number?
#real-numbers
#rational-irrational-pair
#mcq
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A \(\sqrt{6},\sqrt{10}\)
B \(8,\sqrt{15}\)
C \(\sqrt{16},\sqrt{25}\)
D \(\frac{2}{3},0.75\)
Explanation opens after your attempt
Correct Answer
B. \(8,\sqrt{15}\)
Step 1
Concept
(8) परिमेय संख्या है। / (8) is rational.
Step 2
Why this answer is correct
\(\sqrt{15}\) अपरिमेय है क्योंकि (15) पूर्ण वर्ग नहीं है। / \(\sqrt{15}\) is irrational because (15) is not a perfect square.
Step 3
Exam Tip
युग्म वाले प्रश्न में दोनों संख्याओं की प्रकृति अलग-अलग जांचें। / In pair questions, check the nature of both numbers separately.
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\(\sqrt{175}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{175}\)?
#real-numbers
#sqrt175
#simplification
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A \(25\sqrt{7}\)
B \(7\sqrt{5}\)
C \(5\sqrt{7}\)
D (35)
Explanation opens after your attempt
Correct Answer
C. \(5\sqrt{7}\)
Step 1
Concept
\(175=25 \times 7\) लिखें। / Write \(175=25 \times 7\).
Step 2
Why this answer is correct
\(\sqrt{175}=\sqrt{25 \times 7}=5\sqrt{7}\)। / \(\sqrt{175}=\sqrt{25 \times 7}=5\sqrt{7}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड को बाहर और बाकी संख्या को अंदर रखें। / Take the perfect square factor outside and keep the remaining number inside.
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\(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}\)?
#real-numbers
#like-radicals
#addition
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A \(4\sqrt{10}\)
B \(\sqrt{40}\)
C \(10\sqrt{4}\)
D (40)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{10}\)
Step 1
Concept
चार समान वर्गमूल पद जोड़े जा रहे हैं। / Four like radical terms are being added.
Step 2
Why this answer is correct
\(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}=4\sqrt{10}\)। / \(\sqrt{10}+\sqrt{10}+\sqrt{10}+\sqrt{10}=4\sqrt{10}\).
Step 3
Exam Tip
समान वर्गमूलों को जोड़ते समय केवल गुणांक जोड़ें। / When adding like radicals, add only the coefficients.
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\(\sqrt{80}-\sqrt{45}\) का सरल रूप क्या होगा?
What will be the simplified form of \(\sqrt{80}-\sqrt{45}\)?
#real-numbers
#radical-subtraction
#sqrt5
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A \(\sqrt{5}\)
B \(5\sqrt{5}\)
C \(7\sqrt{5}\)
D \(\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\)
Step 1
Concept
\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\)। / \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\).
Step 2
Why this answer is correct
\(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\)। / \(4\sqrt{5}-3\sqrt{5}=\sqrt{5}\).
Step 3
Exam Tip
घटाने से पहले दोनों वर्गमूलों को पूरी तरह सरल करें। / Before subtracting, simplify both radicals completely.
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\(\sqrt{13}\) का वर्ग किसके बराबर है?
The square of \(\sqrt{13}\) is equal to what?
#real-numbers
#square-root
#square
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A (169)
B \(\sqrt{13}\)
C (13)
D (26)
Explanation opens after your attempt
Step 1
Concept
वर्गमूल का वर्ग करने पर अंदर की संख्या मिलती है। / Squaring a square root gives the number inside it.
Step 2
Why this answer is correct
(\(\sqrt{13}\)2 =13)। / (\(\sqrt{13}\)2 =13).
Step 3
Exam Tip
(\(\sqrt{a}\)2 =a) को सीधे लागू करें। / Apply (\(\sqrt{a}\)2 =a) directly.
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यदि \(x=\sqrt{6}\), तो (2x) किस प्रकार की संख्या होगी?
If \(x=\sqrt{6}\), what type of number is (2x)?
#real-numbers
#irrational-product
#coefficient
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A परिमेय / Rational
B पूर्णांक / Integer
C अपरिमेय / Irrational
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
C. अपरिमेय / Irrational
Step 1
Concept
\(x=\sqrt{6}\) अपरिमेय है। / \(x=\sqrt{6}\) is irrational.
Step 2
Why this answer is correct
\(2x=2\sqrt{6}\), और (2) अशून्य परिमेय संख्या है। / \(2x=2\sqrt{6}\), and (2) is a non-zero rational number.
Step 3
Exam Tip
अपरिमेय संख्या को अशून्य परिमेय से गुणा करने पर परिणाम अपरिमेय रहता है। / Multiplying an irrational number by a non-zero rational number keeps it irrational.
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कौन-सा विकल्प अपरिमेय संख्या नहीं है?
Which option is not an irrational number?
#real-numbers
#not-irrational
#perfect-square
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A \(\sqrt{46}\)
B \(\sqrt{64}\)
C \(\sqrt{57}\)
D \(\sqrt{62}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{64}\)
Step 1
Concept
प्रश्न अपरिमेय नहीं पूछ रहा है, इसलिए परिमेय संख्या खोजें। / The question asks for the number that is not irrational, so look for a rational number.
Step 2
Why this answer is correct
\(\sqrt{64}=8\), जो परिमेय है। / \(\sqrt{64}=8\), which is rational.
Step 3
Exam Tip
ऐसे प्रश्नों में नकारात्मक शब्दों को ध्यान से पढ़ें। / Read negative wording carefully in such questions.
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\(\sqrt{32}+\sqrt{128}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{32}+\sqrt{128}\)?
#real-numbers
#radical-addition
#simplification
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A \(12\sqrt{2}\)
B \(16\sqrt{2}\)
C \(8\sqrt{2}\)
D \(\sqrt{160}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(\sqrt{32}=4\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\)। / \(\sqrt{32}=4\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\).
Step 2
Why this answer is correct
\(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\)। / \(4\sqrt{2}+8\sqrt{2}=12\sqrt{2}\).
Step 3
Exam Tip
समान वर्गमूल बनने पर ही उन्हें जोड़ा जा सकता है। / Radicals can be added only when they become like radicals.
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निम्नलिखित में से कौन-सा कथन गलत है?
Which of the following statements is false?
#real-numbers
#false-statement
#perfect-square
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A \(\sqrt{10}\) अपरिमेय है / \(\sqrt{10}\) is irrational
B \(0.454545\ldots\) परिमेय है / \(0.454545\ldots\) is rational
C \(\sqrt{169}\) अपरिमेय है / \(\sqrt{169}\) is irrational
D \(\frac{8}{5}\) परिमेय है / \(\frac{8}{5}\) is rational
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{169}\) अपरिमेय है / \(\sqrt{169}\) is irrational
Step 1
Concept
(169) पूर्ण वर्ग है। / (169) is a perfect square.
Step 2
Why this answer is correct
\(\sqrt{169}=13\), जो परिमेय है, इसलिए इसे अपरिमेय कहना गलत है। / \(\sqrt{169}=13\), which is rational, so calling it irrational is false.
Step 3
Exam Tip
गलत कथन चुनते समय पूर्ण वर्गों को जरूर पहचानें। / While choosing a false statement, identify perfect squares carefully.
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\(\sqrt{300}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{300}\)?
#real-numbers
#sqrt300
#radical-simplification
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A \(10\sqrt{3}\)
B \(3\sqrt{10}\)
C \(30\sqrt{10}\)
D \(100\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{3}\)
Step 1
Concept
\(300=100 \times 3\) लिखें। / Write \(300=100 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\)। / \(\sqrt{300}=\sqrt{100 \times 3}=10\sqrt{3}\).
Step 3
Exam Tip
(100) जैसा पूर्ण वर्ग दिखे तो उसे बाहर (10) के रूप में निकालें। / When you see a perfect square like (100), take it outside as (10).
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\(\sqrt{7}\times\sqrt{28}\) का मान क्या होगा?
What is the value of \(\sqrt{7}\times\sqrt{28}\)?
#real-numbers
#radical-product
#rational-result
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A (14)
B \(\sqrt{35}\)
C \(7\sqrt{28}\)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\times\sqrt{28}=\sqrt{196}\)। / \(\sqrt{7}\times\sqrt{28}=\sqrt{196}\).
Step 2
Why this answer is correct
\(\sqrt{196}=14\), इसलिए मान परिमेय है। / \(\sqrt{196}=14\), so the value is rational.
Step 3
Exam Tip
वर्गमूलों के गुणन में अंदर की संख्याएँ गुणा करें। / When multiplying square roots, multiply the numbers inside.
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कौन-सी संख्या (7) और (8) के बीच स्थित है?
Which number lies between (7) and (8)?
#real-numbers
#comparison
#irrational-between
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A \(\sqrt{50}\)
B \(\sqrt{55}\)
C \(\sqrt{64}\)
D \(\sqrt{49}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{55}\)
Step 1
Concept
(49<55<64), इसलिए \(7<\sqrt{55}<8\)। / Since (49<55<64), \(7<\sqrt{55}<8\).
Step 2
Why this answer is correct
(55) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{55}\) अपरिमेय है। / (55) is not a perfect square, so \(\sqrt{55}\) is irrational.
Step 3
Exam Tip
वर्गमूल की स्थिति पास के पूर्ण वर्गों से आसानी से मिलती है। / Nearby perfect squares help locate a square root easily.
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\(\sqrt{288}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\sqrt{288}\)?
#real-numbers
#sqrt288
#simplification
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A \(12\sqrt{2}\)
B \(24\sqrt{2}\)
C \(8\sqrt{6}\)
D \(144\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(12\sqrt{2}\)
Step 1
Concept
\(288=144 \times 2\) है। / \(288=144 \times 2\).
Step 2
Why this answer is correct
\(\sqrt{288}=\sqrt{144 \times 2}=12\sqrt{2}\)। / \(\sqrt{288}=\sqrt{144 \times 2}=12\sqrt{2}\).
Step 3
Exam Tip
बड़े पूर्ण वर्ग का उपयोग करने से उत्तर सीधे सरल रूप में मिलता है। / Using a large perfect square gives the simplified form directly.
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\(\sqrt{7}+2\sqrt{7}\) किसके बराबर है?
What is \(\sqrt{7}+2\sqrt{7}\) equal to?
#real-numbers
#like-radicals
#addition
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A \(2\sqrt{14}\)
B \(3\sqrt{7}\)
C \(\sqrt{21}\)
D \(7\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{7}\)
Step 1
Concept
दोनों पदों में \(\sqrt{7}\) समान है। / Both terms contain the same radical \(\sqrt{7}\).
Step 2
Why this answer is correct
\(1\sqrt{7}+2\sqrt{7}=3\sqrt{7}\)। / \(1\sqrt{7}+2\sqrt{7}=3\sqrt{7}\).
Step 3
Exam Tip
समान वर्गमूलों में केवल बाहर के गुणांक जोड़ें। / For like radicals, add only the outside coefficients.
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\(\sqrt{7}\) का लगभग मान किसके सबसे निकट है?
The approximate value of \(\sqrt{7}\) is closest to which number?
#real-numbers
#approximation
#sqrt7
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A (2.24)
B (2.65)
C (3.16)
D (1.73)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{7}\) का मान लगभग (2.646) है। / The value of \(\sqrt{7}\) is about (2.646).
Step 2
Why this answer is correct
दिए गए विकल्पों में (2.65) सबसे निकट है। / Among the options, (2.65) is closest.
Step 3
Exam Tip
अनुमान में पास के पूर्ण वर्ग (4) और (9) से सीमा समझें। / For estimation, use nearby perfect squares (4) and (9) to understand the range.
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\(\sqrt{26}\) का मान किन दो पूर्णांकों के बीच होगा?
Between which two integers does \(\sqrt{26}\) lie?
#real-numbers
#comparison
#sqrt26
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A (4) और (5) / (4) and (5)
B (5) और (6) / (5) and (6)
C (6) और (7) / (6) and (7)
D (7) और (8) / (7) and (8)
Explanation opens after your attempt
Correct Answer
B. (5) और (6) / (5) and (6)
Step 1
Concept
(25<26<36) है।
Step 2
Why this answer is correct
इसलिए \(\sqrt{25}<\sqrt{26}<\sqrt{36}\), यानी \(5<\sqrt{26}<6\)। / So \(\sqrt{25}<\sqrt{26}<\sqrt{36}\), meaning \(5<\sqrt{26}<6\).
Step 3
Exam Tip
वर्गमूल की सीमा के लिए पास के पूर्ण वर्ग देखें। / To find the range of a square root, look at nearby perfect squares.
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\(\sqrt{192}\) को सरल कीजिए।
Simplify \(\sqrt{192}\).
#real-numbers
#sqrt192
#radical-simplification
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A \(8\sqrt{3}\)
B \(4\sqrt{12}\)
C \(16\sqrt{3}\)
D \(12\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(8\sqrt{3}\)
Step 1
Concept
\(192=64 \times 3\) है। / \(192=64 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\)। / \(\sqrt{192}=\sqrt{64 \times 3}=8\sqrt{3}\).
Step 3
Exam Tip
उत्तर को पूरा सरल करने के लिए सबसे बड़ा पूर्ण वर्ग बाहर निकालें। / To fully simplify the answer, take out the largest perfect square.
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यदि \(y=\sqrt{17}\), तो \(y^2\) का मान क्या होगा?
If \(y=\sqrt{17}\), what is the value of \(y^2\)?
#real-numbers
#square-root
#square
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A (34)
B (289)
C (17)
D \(\sqrt{17}\)
Explanation opens after your attempt
Step 1
Concept
\(y=\sqrt{17}\) दिया है। / We are given \(y=\sqrt{17}\).
Step 2
Why this answer is correct
(y-2 =\(\sqrt{17}\)2 =17)। / (y-2 =\(\sqrt{17}\)2 =17).
Step 3
Exam Tip
वर्गमूल का वर्ग करने पर अंदर की संख्या ही मिलती है। / Squaring a square root gives the number inside it.
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कौन-सा विकल्प दो अपरिमेय संख्याओं का ऐसा गुणनफल है जो परिमेय बनता है?
Which option is a product of two irrational numbers that becomes rational?
#real-numbers
#irrational-product
#rational-result
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A \(\sqrt{5}\times\sqrt{5}\)
B \(\sqrt{2}\times\sqrt{7}\)
C \(\sqrt{3}\times\sqrt{11}\)
D \(\sqrt{6}\times\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{5}\times\sqrt{5}\)
Step 1
Concept
\(\sqrt{5}\) अपरिमेय है। / \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
\(\sqrt{5}\times\sqrt{5}=5\), जो परिमेय है। / \(\sqrt{5}\times\sqrt{5}=5\), which is rational.
Step 3
Exam Tip
दो अपरिमेय संख्याओं का गुणनफल हमेशा अपरिमेय नहीं होता। / The product of two irrational numbers is not always irrational.
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\(\sqrt{11}+0\) किसके बराबर है?
What is \(\sqrt{11}+0\) equal to?
#real-numbers
#zero-property
#irrational
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A (11)
B (0)
C \(\sqrt{11}\)
D \(\sqrt{0}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{11}\)
Step 1
Concept
शून्य जोड़ने से संख्या का मान नहीं बदलता। / Adding zero does not change the value of a number.
Step 2
Why this answer is correct
\(\sqrt{11}+0=\sqrt{11}\), जो अपरिमेय है। / \(\sqrt{11}+0=\sqrt{11}\), which is irrational.
Step 3
Exam Tip
शून्य के साथ भी मूल संख्या की प्रकृति पहचानें। / Even with zero, identify the nature of the original number.
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\(\sqrt{21}\) का दशमलव विस्तार कैसा होगा?
What kind of decimal expansion does \(\sqrt{21}\) have?
#real-numbers
#decimal-expansion
#sqrt21
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A समाप्त / Terminating
B आवर्ती / Recurring
C अनवसानी और अनावर्ती / Non-terminating and non-recurring
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
C. अनवसानी और अनावर्ती / Non-terminating and non-recurring
Step 1
Concept
(21) पूर्ण वर्ग नहीं है। / (21) is not a perfect square.
Step 2
Why this answer is correct
इसलिए \(\sqrt{21}\) अपरिमेय है और इसका दशमलव अनवसानी अनावर्ती होगा। / So \(\sqrt{21}\) is irrational and its decimal expansion is non-terminating and non-recurring.
Step 3
Exam Tip
अपरिमेय संख्या में कोई निश्चित आवर्ती समूह नहीं होता। / An irrational number has no fixed recurring block.
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\(\sqrt{135}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{135}\)?
#real-numbers
#sqrt135
#simplification
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A \(5\sqrt{27}\)
B \(3\sqrt{15}\)
C \(9\sqrt{15}\)
D \(15\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(3\sqrt{15}\)
Step 1
Concept
\(135=9 \times 15\) लिखें। / Write \(135=9 \times 15\).
Step 2
Why this answer is correct
\(\sqrt{135}=\sqrt{9 \times 15}=3\sqrt{15}\)। / \(\sqrt{135}=\sqrt{9 \times 15}=3\sqrt{15}\).
Step 3
Exam Tip
अंदर बची संख्या में पूर्ण वर्ग गुणनखंड न हो, तब रूप सरल माना जाता है। / The form is simplified when the remaining number inside has no perfect square factor.
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कौन-सी संख्या \(\sqrt{75}\) के बराबर है?
Which number is equal to \(\sqrt{75}\)?
#real-numbers
#equivalent-radicals
#sqrt75
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A \(3\sqrt{5}\)
B \(5\sqrt{3}\)
C (15)
D \(25\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(5\sqrt{3}\)
Step 1
Concept
\(75=25 \times 3\) है। / \(75=25 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{75}=5\sqrt{3}\)। / \(\sqrt{75}=5\sqrt{3}\).
Step 3
Exam Tip
बराबर रूप पहचानने के लिए पहले वर्गमूल को सरल करें। / To identify an equivalent form, simplify the square root first.
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\(\sqrt{13}\) और \(-\sqrt{13}\) का योग क्या है?
What is the sum of \(\sqrt{13}\) and \(-\sqrt{13}\)?
#real-numbers
#opposite-terms
#zero
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A (0)
B (13)
C (-13)
D \(2\sqrt{13}\)
Explanation opens after your attempt
Step 1
Concept
ये दोनों पद एक-दूसरे के विपरीत हैं। / The two terms are opposites of each other.
Step 2
Why this answer is correct
(\sqrt{13}+\(-\sqrt{13}\)=0)। / (\sqrt{13}+\(-\sqrt{13}\)=0).
Step 3
Exam Tip
विपरीत पदों का योग हमेशा शून्य होता है। / The sum of opposite terms is always zero.
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यदि (a) अपरिमेय है और (r) अशून्य परिमेय है, तो \(\frac{a}{r}\) कैसी संख्या होगी?
If (a) is irrational and (r) is a non-zero rational number, what type of number is \(\frac{a}{r}\)?
#real-numbers
#irrational-rule
#division
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A परिमेय / Rational
B अपरिमेय / Irrational
C हमेशा शून्य / Always zero
D हमेशा पूर्णांक / Always integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
अशून्य परिमेय संख्या से भाग करने पर अपरिमेयता समाप्त नहीं होती। / Dividing by a non-zero rational number does not remove irrationality.
Step 2
Why this answer is correct
जैसे \(\frac{\sqrt{2}}{5}\) अपरिमेय है। / For example, \(\frac{\sqrt{2}}{5}\) is irrational.
Step 3
Exam Tip
यहां \(r\neq0\) शर्त जरूरी है क्योंकि शून्य से भाग संभव नहीं होता। / The condition \(r\neq0\) is necessary because division by zero is not possible.
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\(\sqrt{275}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{275}\)?
#real-numbers
#sqrt275
#radical-simplification
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A \(5\sqrt{11}\)
B \(11\sqrt{5}\)
C \(25\sqrt{11}\)
D (55)
Explanation opens after your attempt
Correct Answer
A. \(5\sqrt{11}\)
Step 1
Concept
\(275=25 \times 11\) है। / \(275=25 \times 11\).
Step 2
Why this answer is correct
\(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\)। / \(\sqrt{275}=\sqrt{25 \times 11}=5\sqrt{11}\).
Step 3
Exam Tip
पूर्ण वर्ग गुणनखंड बाहर निकालकर उत्तर को सरल बनाएं। / Take the perfect square factor outside to simplify the answer.
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निम्नलिखित में से कौन-सा अपरिमेय संख्या का दशमलव रूप हो सकता है?
Which of the following can be the decimal form of an irrational number?
#real-numbers
#decimal-form
#irrational
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A \(2.3333\ldots\)
B (5.125)
C \(1.01011011101111\ldots\) बिना निश्चित दोहराव / \(1.01011011101111\ldots\) with no fixed repetition
D (9.0)
Explanation opens after your attempt
Correct Answer
C. \(1.01011011101111\ldots\) बिना निश्चित दोहराव / \(1.01011011101111\ldots\) with no fixed repetition
Step 1
Concept
आवर्ती या समाप्त दशमलव परिमेय होते हैं। / Recurring or terminating decimals are rational.
Step 2
Why this answer is correct
बिना निश्चित दोहराव वाला अनवसानी दशमलव अपरिमेय हो सकता है। / A non-terminating decimal with no fixed repetition can be irrational.
Step 3
Exam Tip
दोहराव का नियम न दिखे तो संख्या की प्रकृति ध्यान से जांचें। / If no repeating rule is visible, examine the number carefully.
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\(\sqrt{243}\) को सरल कीजिए।
Simplify \(\sqrt{243}\).
#real-numbers
#sqrt243
#simplification
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A \(3\sqrt{27}\)
B \(9\sqrt{3}\)
C \(27\sqrt{3}\)
D \(81\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(9\sqrt{3}\)
Step 1
Concept
\(243=81 \times 3\) लिखें। / Write \(243=81 \times 3\).
Step 2
Why this answer is correct
\(\sqrt{243}=\sqrt{81 \times 3}=9\sqrt{3}\)। / \(\sqrt{243}=\sqrt{81 \times 3}=9\sqrt{3}\).
Step 3
Exam Tip
बड़ा पूर्ण वर्ग चुनने से उत्तर एक ही चरण में सरल हो जाता है। / Choosing a larger perfect square simplifies the answer in one step.
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\(\sqrt{6}\times\sqrt{54}\) का मान क्या है?
What is the value of \(\sqrt{6}\times\sqrt{54}\)?
#real-numbers
#radical-product
#rational-result
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A (18)
B \(\sqrt{60}\)
C \(6\sqrt{54}\)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\times\sqrt{54}=\sqrt{324}\)। / \(\sqrt{6}\times\sqrt{54}=\sqrt{324}\).
Step 2
Why this answer is correct
\(\sqrt{324}=18\), इसलिए परिणाम परिमेय है। / \(\sqrt{324}=18\), so the result is rational.
Step 3
Exam Tip
गुणन के बाद अंदर की संख्या पूर्ण वर्ग बन सकती है, इसे जरूर जांचें। / After multiplication, check whether the inside number has become a perfect square.
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\(\sqrt{11}\) का लगभग मान कौन-सा है?
What is the approximate value of \(\sqrt{11}\)?
#real-numbers
#approximation
#sqrt11
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A (2.24)
B (3.32)
C (4.12)
D (5.11)
Explanation opens after your attempt
Step 1
Concept
(9<11<16), इसलिए \(\sqrt{11}\) (3) और (4) के बीच होगा। / Since (9<11<16), \(\sqrt{11}\) lies between (3) and (4).
Step 2
Why this answer is correct
इसका लगभग मान (3.316) है, इसलिए (3.32) निकट है। / Its approximate value is (3.316), so (3.32) is close.
Step 3
Exam Tip
अनुमान में पहले पूर्ण वर्गों से सीमा तय करें। / In estimation, first set the range using perfect squares.
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कौन-सा विकल्प \(\sqrt{216}\) का सरल रूप है?
Which option is the simplified form of \(\sqrt{216}\)?
#real-numbers
#sqrt216
#simplification
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A \(6\sqrt{6}\)
B \(9\sqrt{6}\)
C \(12\sqrt{3}\)
D \(36\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(6\sqrt{6}\)
Step 1
Concept
\(216=36 \times 6\) है। / \(216=36 \times 6\).
Step 2
Why this answer is correct
\(\sqrt{216}=\sqrt{36 \times 6}=6\sqrt{6}\)। / \(\sqrt{216}=\sqrt{36 \times 6}=6\sqrt{6}\).
Step 3
Exam Tip
अंदर बचे (6) में कोई पूर्ण वर्ग गुणनखंड नहीं है, इसलिए रूप सरल है। / The remaining (6) has no perfect square factor, so the form is simplified.
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\(\sqrt{39}\) का मान किन दो पूर्णांकों के बीच है?
Between which two integers does \(\sqrt{39}\) lie?
#real-numbers
#comparison
#sqrt39
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A (4) और (5) / (4) and (5)
B (5) और (6) / (5) and (6)
C (6) और (7) / (6) and (7)
D (7) और (8) / (7) and (8)
Explanation opens after your attempt
Correct Answer
C. (6) और (7) / (6) and (7)
Step 1
Concept
(36<39<49) है।
Step 2
Why this answer is correct
इसलिए \(6<\sqrt{39}<7\)। / Therefore, \(6<\sqrt{39}<7\).
Step 3
Exam Tip
वर्गमूल की तुलना के लिए पास के पूर्ण वर्ग सबसे अच्छे संकेत देते हैं। / Nearby perfect squares give the best clues for comparing square roots.
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निम्नलिखित में से कौन-सा परिणाम अपरिमेय है?
Which of the following results is irrational?
#real-numbers
#irrational-result
#radicals
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A \(\sqrt{9}+\sqrt{16}\)
B \(\sqrt{7}+\sqrt{28}\)
C \(\sqrt{12}\times\sqrt{3}\)
D \(\sqrt{25}-\sqrt{4}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{7}+\sqrt{28}\)
Step 1
Concept
\(\sqrt{28}=2\sqrt{7}\), इसलिए \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\)। / \(\sqrt{28}=2\sqrt{7}\), so \(\sqrt{7}+\sqrt{28}=3\sqrt{7}\).
Step 2
Why this answer is correct
\(3\sqrt{7}\) अपरिमेय है क्योंकि \(\sqrt{7}\) अपरिमेय है। / \(3\sqrt{7}\) is irrational because \(\sqrt{7}\) is irrational.
Step 3
Exam Tip
विकल्पों में परिणाम की प्रकृति तय करने से पहले सरलीकरण करें। / In options, simplify first before deciding the nature of the result.
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