100 results found for "number-864" in Class 10.
संख्या 864 का सही अभाज्य गुणनखंडन क्या है?
What is the correct prime factorisation of 864?
#prime-factorisation
#number-864
#medium
A \(2^5\times3^3\)
B \(2^4\times3^3\)
C \(32\times27\)
D \(2^5\times27\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^3\)
Step 1
Concept
Write \(864=32\times27\).
Step 2
Why this answer is correct
\(32=2^5\) and \(27=3^3\), so \(864=2^5\times3^3\).
Step 3
Exam Tip
It is necessary to convert 32 and 27 into prime powers. चरण 1: \(864=32\times27\) लिखें। चरण 2: \(32=2^5\) और \(27=3^3\), इसलिए \(864=2^5\times3^3\)। चरण 3: 32 और 27 को अभाज्य घातों में बदलना जरूरी है।
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एक आयत की लंबाई चौड़ाई से (12) सेमी अधिक है और क्षेत्रफल (864) वर्ग सेमी है। लंबाई क्या है?
A rectangle has length (12) cm more than its breadth and area (864) square cm. What is the length?
#quadratic equations
#rectangle
#dimension
A (24) सेमी / (24) cm
B (32) सेमी / (32) cm
C (36) सेमी / (36) cm
D (48) सेमी / (48) cm
Explanation opens after your attempt
Correct Answer
C. (36) सेमी / (36) cm
Step 1
Concept
If breadth is (x), then (x(x+12)=864), giving (x=24). Hence the length is (36) cm.
Step 2
Why this answer is correct
The correct answer is C. (36) सेमी / (36) cm. If breadth is (x), then (x(x+12)=864), giving (x=24). Hence the length is (36) cm.
Step 3
Exam Tip
चौड़ाई (x) हो तो (x(x+12)=864), जिससे (x=24) है। अतः लंबाई (36) सेमी है।
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एक आयताकार छत की लंबाई चौड़ाई से (22) मीटर अधिक है और क्षेत्रफल (864) वर्ग मीटर है। चौड़ाई क्या है?
A rectangular roof has length (22) m more than its breadth and area (864) square m. What is its breadth?
#quadratic equations
#rectangle
#roof
A (18) मीटर / (18) m
B (20) मीटर / (20) m
C (24) मीटर / (24) m
D (36) मीटर / (36) m
Explanation opens after your attempt
Correct Answer
A. (18) मीटर / (18) m
Step 1
Concept
Taking breadth as (x), (x(x+22)=864), giving (x=18). Avoid wrong checking and verify the correct product.
Step 2
Why this answer is correct
The correct answer is A. (18) मीटर / (18) m. Taking breadth as (x), (x(x+22)=864), giving (x=18). Avoid wrong checking and verify the correct product.
Step 3
Exam Tip
चौड़ाई (x) लेने पर (x(x+22)=864), जिससे (x=18) मिलता है। अंत में \(18 \times 40=720\) जैसी गलत जाँच से बचें और सही गुणनफल जाँचें।
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किस संख्या का अभाज्य गुणनखंडन \(2^5\times3^3\) है?
Which number has prime factorisation \(2^5\times3^3\)?
#evaluate-factorisation
#number-864
#medium
A 864
B 432
C 1728
D 1296
Explanation opens after your attempt
Step 1
Concept
Calculate \(2^5=32\) and \(3^3=27\).
Step 2
Why this answer is correct
\(32\times27=864\).
Step 3
Exam Tip
Simplify both powers separately. चरण 1: \(2^5=32\) और \(3^3=27\) निकालें। चरण 2: \(32\times27=864\)। चरण 3: दोनों घातों को अलग-अलग सरल करें।
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संख्या रेखा पर \(-\frac{17}{5}\) किस मिश्र संख्या के बराबर स्थान पर होगा?
At which mixed number position will \(-\frac{17}{5}\) lie on the number line?
#polynomials
#number-line
#negative-mixed-number
#medium
A \(3+\frac{2}{5}\)
B \(-3-\frac{2}{5}\)
C \(-4-\frac{2}{5}\)
D \(-2-\frac{3}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(-3-\frac{2}{5}\)
Step 1
Concept
\(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
Step 2
Why this answer is correct
The correct answer is B. \(-3-\frac{2}{5}\). \(-\frac{17}{5}=-3-\frac{2}{5}\), so it lies between (-4) and (-3). In exams, keep the sign of a negative mixed number correct.
Step 3
Exam Tip
\(-\frac{17}{5}=-3-\frac{2}{5}\), इसलिए यह (-4) और (-3) के बीच है। परीक्षा में ऋणात्मक मिश्र संख्या का चिह्न ठीक रखें।
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संख्या रेखा पर \(\frac{13}{4}\) को किस मिश्र संख्या के रूप में दिखाया जाएगा?
How will \(\frac{13}{4}\) be shown as a mixed number on the number line?
#polynomials
#number-line
#mixed-number
#medium
A \(3+\frac{1}{4}\)
B \(3+\frac{3}{4}\)
C \(4+\frac{1}{3}\)
D \(2+\frac{3}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(3+\frac{1}{4}\)
Step 1
Concept
\(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
Step 2
Why this answer is correct
The correct answer is A. \(3+\frac{1}{4}\). \(\frac{13}{4}=3+\frac{1}{4}\), so it lies one-fourth after (3). In exams, convert an improper fraction into a mixed number.
Step 3
Exam Tip
\(\frac{13}{4}=3+\frac{1}{4}\), इसलिए यह (3) के बाद एक चौथाई पर होगा। परीक्षा में विषम भिन्न को मिश्र संख्या में बदलें।
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संख्या रेखा पर \(\frac{5}{4}\) को मिश्र संख्या के रूप में कहां रखा जाएगा?
Where will \(\frac{5}{4}\) be placed as a mixed number on the number line?
#polynomials
#number-line
#mixed-number
#class-10
A \(1+\frac{1}{4}\)
B \(1+\frac{3}{4}\)
C \(2+\frac{1}{4}\)
D \(\frac{4}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(1+\frac{1}{4}\)
Step 1
Concept
\(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
Step 2
Why this answer is correct
The correct answer is A. \(1+\frac{1}{4}\). \(\frac{5}{4}=1+\frac{1}{4}\), so it is one-fourth after (1). In exams, convert an improper fraction into mixed form.
Step 3
Exam Tip
\(\frac{5}{4}=1+\frac{1}{4}\), इसलिए यह (1) के बाद एक चौथाई भाग पर है। परीक्षा में अपूर्ण भिन्न को मिश्र रूप में बदलें।
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एक दो अंकों की संख्या में अंकों का योग (12) है। उस संख्या और उलटी संख्या का गुणनफल (4032) है। मूल संख्या कौन-सी हो सकती है?
A two-digit number has digit sum (12). The product of the number and its reversed number is (4032). Which can be the original number?
#quadratic equations
#digit problem
#reverse number
A (39)
B (48)
C (57)
D (66)
Explanation opens after your attempt
Step 1
Concept
The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.
Step 2
Why this answer is correct
The correct answer is B. (48). The reverse of (48) is (84), and \(48 \times 84=4032\). In digit problems, checking the reversed number is essential.
Step 3
Exam Tip
(48) की उलटी संख्या (84) है और \(48 \times 84=4032\)। अंकों की समस्याओं में उलटी संख्या भी जाँचना जरूरी है।
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किस संख्या की (0) से दूरी \( \sqrt{41} \) है और वह (0) के बाईं ओर है?
Which number has distance \( \sqrt{41} \) from (0) and lies to the left of (0) on the number line?
#number-line
#distance-from-zero
#negative-root
A \( \sqrt{41} \)
B \( -\sqrt{41} \)
C (41)
D ( -41 )
Explanation opens after your attempt
Correct Answer
B. \( -\sqrt{41} \)
Step 1
Concept
The point on the left is negative and its distance is \( \sqrt{41} \). Therefore the number is \( -\sqrt{41} \).
Step 2
Why this answer is correct
The correct answer is B. \( -\sqrt{41} \). The point on the left is negative and its distance is \( \sqrt{41} \). Therefore the number is \( -\sqrt{41} \).
Step 3
Exam Tip
बाईं ओर का बिंदु ऋणात्मक होगा और दूरी \( \sqrt{41} \) है। इसलिए संख्या \( -\sqrt{41} \) है।
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संख्या रेखा पर \(0.7272272227\ldots\) किस प्रकार की संख्या है?
What type of number is \(0.7272272227\ldots\) on the number line?
#number-line
#irrational-decimal
#classification
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
This decimal is non-terminating and non-repeating, so it is irrational. Check whether the decimal pattern truly repeats or not.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating, so it is irrational. Check whether the decimal pattern truly repeats or not.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है, इसलिए अपरिमेय है। दशमलव पैटर्न सच में दोहरता है या नहीं, यह जाँचें।
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किस संख्या की (0) से दूरी \( \sqrt{26} \) है और वह (0) के दाईं ओर है?
Which number has distance \( \sqrt{26} \) from (0) and lies to the right of (0) on the number line?
#number-line
#distance-from-zero
#positive-root
A \( -\sqrt{26} \)
B \( \sqrt{26} \)
C (26)
D ( -26 )
Explanation opens after your attempt
Correct Answer
B. \( \sqrt{26} \)
Step 1
Concept
The point on the right is positive and its distance is \( \sqrt{26} \). Therefore the number is \( \sqrt{26} \).
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{26} \). The point on the right is positive and its distance is \( \sqrt{26} \). Therefore the number is \( \sqrt{26} \).
Step 3
Exam Tip
दाईं ओर का बिंदु धनात्मक होगा और दूरी \( \sqrt{26} \) है। इसलिए संख्या \( \sqrt{26} \) है।
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संख्या रेखा पर \(0.6161161116\ldots\) किस प्रकार की संख्या है?
What type of number is \(0.6161161116\ldots\) on the number line?
#number-line
#irrational-decimal
#classification
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
This decimal is non-terminating and non-repeating, so it is irrational. Check carefully whether the pattern repeats or not.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating, so it is irrational. Check carefully whether the pattern repeats or not.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है, इसलिए अपरिमेय है। पैटर्न दोहराव वाला है या नहीं, इसे ध्यान से देखें।
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किस संख्या की (0) से दूरी संख्या रेखा पर \( \sqrt{17} \) है और वह (0) के बाईं ओर है?
Which number has distance \( \sqrt{17} \) from (0) and lies to the left of (0) on the number line?
#number-line
#distance-from-zero
#negative-root
A \( -\sqrt{17} \)
B \( \sqrt{17} \)
C (17)
D ( -17 )
Explanation opens after your attempt
Correct Answer
A. \( -\sqrt{17} \)
Step 1
Concept
The point on the left is negative and its distance is \( \sqrt{17} \). Therefore the number is \( -\sqrt{17} \).
Step 2
Why this answer is correct
The correct answer is A. \( -\sqrt{17} \). The point on the left is negative and its distance is \( \sqrt{17} \). Therefore the number is \( -\sqrt{17} \).
Step 3
Exam Tip
बाईं ओर का बिंदु ऋणात्मक होगा और दूरी \( \sqrt{17} \) है। इसलिए संख्या \( -\sqrt{17} \) है।
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संख्या रेखा पर \(0.2727727772\ldots\) किस प्रकार की संख्या है?
What type of number is \(0.2727727772\ldots\) on the number line?
#number-line
#irrational-decimal
#classification
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C पूर्णांक / Integer
D प्राकृतिक संख्या / Natural number
Explanation opens after your attempt
Correct Answer
A. अपरिमेय संख्या / Irrational number
Step 1
Concept
This decimal is non-terminating and non-repeating. Hence it is an irrational number on the number line.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating. Hence it is an irrational number on the number line.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है। इसलिए यह संख्या रेखा पर अपरिमेय संख्या है।
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कौन सी संख्या \( \sqrt{8} \) और (3) के बीच संख्या रेखा पर स्थित है?
Which number lies between \( \sqrt{8} \) and (3) on the number line?
#number-line
#between-numbers
#square-roots
A (2.9)
B (2.7)
C (3.1)
D (2)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.
Step 2
Why this answer is correct
The correct answer is A. (2.9). \( \sqrt{8}\approx2.828\), so (2.9) lies between it and (3). First estimate the irrational number.
Step 3
Exam Tip
\( \sqrt{8}\approx2.828\), इसलिए (2.9) उसके और (3) के बीच है। पहले अपरिमेय संख्या का अनुमान करें।
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किस संख्या को संख्या रेखा पर \(\sqrt{25}-\sqrt{4}\) के रूप में दर्शाया जा सकता है?
Which number can be represented as \(\sqrt{25}-\sqrt{4}\) on the number line?
#polynomials
#number-line
#simplification
#perfect-square
A (3)
B (7)
C (21)
D \(\sqrt{21}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
Step 3
Exam Tip
\(\sqrt{25}=5\) और \(\sqrt{4}=2\), इसलिए \(\sqrt{25}-\sqrt{4}=3\)। पूर्ण वर्गों को तुरंत सरल करें।
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संख्या रेखा पर कौन-सी संख्या \(\sqrt{9.61}\) के बराबर है?
Which number is equal to \(\sqrt{9.61}\) on the number line?
#polynomials
#number-line
#decimal-square-root
#perfect-decimal-square
A (3.1)
B (3.01)
C (3.001)
D (9.61)
Explanation opens after your attempt
Step 1
Concept
Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.
Step 2
Why this answer is correct
The correct answer is A. (3.1). Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.
Step 3
Exam Tip
क्योंकि \(3.1^2=9.61\), इसलिए \(\sqrt{9.61}=3.1\)। दशमलव वर्गों को सावधानी से गुणा करें।
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यदि (A) संख्या रेखा पर \(\sqrt{18}\) है, तो (A) किसके सबसे निकट होगा?
If (A) is \(\sqrt{18}\) on the number line, to which number is (A) closest?
#polynomials
#number-line
#surd
#approximation
A (4.24)
B (3.24)
C (5.24)
D (6.24)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}=3\sqrt{2}\approx4.242\), so (4.24) is closest. Simplification makes estimation easier.
Step 2
Why this answer is correct
The correct answer is A. (4.24). \(\sqrt{18}=3\sqrt{2}\approx4.242\), so (4.24) is closest. Simplification makes estimation easier.
Step 3
Exam Tip
\(\sqrt{18}=3\sqrt{2}\approx4.242\), इसलिए (4.24) सबसे निकट है। सरलीकरण अनुमान को आसान बनाता है।
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कौन-सी संख्या रेखा पर \(\sqrt{6}\) के सबसे निकट है?
Which number is closest to \(\sqrt{6}\) on the number line?
#polynomials
#number-line
#approximation
#square-root
A (2.45)
B (2.10)
C (2.90)
D (3.20)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.
Step 2
Why this answer is correct
The correct answer is A. (2.45). \(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.
Step 3
Exam Tip
\(\sqrt{6}\approx2.449\), इसलिए (2.45) सबसे निकट है। निकटता के लिए अनुमानित मान से अंतर जाँचें।
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संख्या रेखा पर कौन-सी संख्या (1) से छोटी और (0) से बड़ी अपरिमेय संख्या है?
Which number is irrational and lies between (0) and (1) on the number line?
#polynomials
#number-line
#irrational-between-zero-one
A \(\frac{\sqrt{2}}{2}\)
B \(\frac{1}{2}\)
C \(\frac{3}{4}\)
D (1)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{2}}{2}\)
Step 1
Concept
\(\frac{\sqrt{2}}{2}\) is irrational and its value lies between (0) and (1). An irrational divided by a non-zero rational remains irrational.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{2}}{2}\). \(\frac{\sqrt{2}}{2}\) is irrational and its value lies between (0) and (1). An irrational divided by a non-zero rational remains irrational.
Step 3
Exam Tip
\(\frac{\sqrt{2}}{2}\) अपरिमेय है और इसका मान (0) और (1) के बीच है। अपरिमेय संख्या को परिमेय से भाग देने पर शून्येतर परिमेय के लिए अपरिमेय ही रहती है।
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किस दशमलव संख्या का स्थान संख्या रेखा पर \(\frac{13}{8}\) के बराबर है?
Which decimal number has the same position as \(\frac{13}{8}\) on the number line?
#polynomials
#number-line
#decimal
#fraction-conversion
A (1.625)
B (1.375)
C (1.75)
D (1.875)
Explanation opens after your attempt
Correct Answer
A. (1.625)
Step 1
Concept
\(\frac{13}{8}=1.625\), so both represent the same point. Convert the fraction into a decimal to identify position.
Step 2
Why this answer is correct
The correct answer is A. (1.625). \(\frac{13}{8}=1.625\), so both represent the same point. Convert the fraction into a decimal to identify position.
Step 3
Exam Tip
\(\frac{13}{8}=1.625\), इसलिए दोनों एक ही बिंदु दर्शाते हैं। भिन्न को दशमलव में बदलकर स्थान पहचानें।
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किस संख्या को संख्या रेखा पर (0) और (1) के ठीक बीच में दर्शाया जाता है?
Which number is represented exactly midway between (0) and (1) on the number line?
#polynomials
#number-line
#rational-numbers
#midpoint
A \(\frac{1}{2}\)
B \(\frac{1}{3}\)
C \(\frac{2}{3}\)
D \(\frac{3}{4}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
The midpoint of (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). To find a midpoint on a number line, take the average.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). The midpoint of (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). To find a midpoint on a number line, take the average.
Step 3
Exam Tip
(0) और (1) का मध्य बिंदु \(\frac{0+1}{2}=\frac{1}{2}\) होता है। संख्या रेखा में मध्य निकालने के लिए औसत लें।
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कौन सी संख्या संख्या रेखा पर \(\frac{2}{3}\) और \(\frac{3}{4}\) के बीच है?
Which number lies between \(\frac{2}{3}\) and \(\frac{3}{4}\) on the number line?
#number-line
#between
#fractions
#decimals
A (0.6)
B (0.7)
C (0.8)
D (1)
Explanation opens after your attempt
Step 1
Concept
\(\frac{2}{3}\approx0.667\) and \(\frac{3}{4}=0.75\), so (0.7) lies between them. Use decimal form for comparison.
Step 2
Why this answer is correct
The correct answer is B. (0.7). \(\frac{2}{3}\approx0.667\) and \(\frac{3}{4}=0.75\), so (0.7) lies between them. Use decimal form for comparison.
Step 3
Exam Tip
\(\frac{2}{3}\approx0.667\) और \(\frac{3}{4}=0.75\), इसलिए (0.7) बीच में है। तुलना के लिए दशमलव रूप उपयोग करें।
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कौन सी संख्या संख्या रेखा पर \(\sqrt{3}\) और (2) के बीच स्थित है?
Which number lies between \(\sqrt{3}\) and (2) on the number line?
#number-line
#between
#irrational-numbers
#estimation
A (1.6)
B (1.8)
C (2.1)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\approx1.73\), and (1.8) lies between (1.73) and (2). Use estimation to choose the middle value.
Step 2
Why this answer is correct
The correct answer is B. (1.8). \(\sqrt{3}\approx1.73\), and (1.8) lies between (1.73) and (2). Use estimation to choose the middle value.
Step 3
Exam Tip
\(\sqrt{3}\approx1.73\) है और (1.8), (1.73) तथा (2) के बीच है। अनुमान से बीच की संख्या चुनें।
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कौन सी संख्या संख्या रेखा पर (-1) और (0) के बीच नहीं है?
Which number is not between (-1) and (0) on the number line?
#polynomials
#number-line
#interval-check
#medium
A \(-\frac{1}{4}\)
B (-0.6)
C \(-\frac{5}{4}\)
D \(-\frac{9}{10}\)
Explanation opens after your attempt
Correct Answer
C. \(-\frac{5}{4}\)
Step 1
Concept
\(-\frac{5}{4}=-1.25\), which is to the left of (-1). In exams, convert negative fractions into decimals to check.
Step 2
Why this answer is correct
The correct answer is C. \(-\frac{5}{4}\). \(-\frac{5}{4}=-1.25\), which is to the left of (-1). In exams, convert negative fractions into decimals to check.
Step 3
Exam Tip
\(-\frac{5}{4}=-1.25\), जो (-1) से बाईं ओर है। परीक्षा में ऋणात्मक भिन्न को दशमलव में बदलकर जांच सकते हैं।
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संख्या रेखा पर कौन सी संख्या \(\sqrt{14}\) से छोटी लेकिन (3) से बड़ी है?
Which number is less than \(\sqrt{14}\) but greater than (3) on the number line?
#polynomials
#number-line
#comparison
#medium
A (2.9)
B (3.5)
C (3.9)
D (4.1)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{14}\) is about (3.74), so (3.5) is greater than (3) and less than \(\sqrt{14}\). In exams, make a rough estimate of the square root.
Step 2
Why this answer is correct
The correct answer is B. (3.5). \(\sqrt{14}\) is about (3.74), so (3.5) is greater than (3) and less than \(\sqrt{14}\). In exams, make a rough estimate of the square root.
Step 3
Exam Tip
\(\sqrt{14}\) लगभग (3.74) है, इसलिए (3.5) (3) से बड़ा और \(\sqrt{14}\) से छोटा है। परीक्षा में वर्गमूल का मोटा अनुमान लगाएं।
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संख्या रेखा पर \(\frac{2}{5}\) और \(\frac{4}{5}\) के ठीक बीच कौन सी संख्या होगी?
Which number will lie exactly midway between \(\frac{2}{5}\) and \(\frac{4}{5}\) on the number line?
#number-line
#fractions
#midpoint
#rational-numbers
A \(\frac{1}{5}\)
B \(\frac{3}{5}\)
C \(\frac{5}{5}\)
D \(\frac{6}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{5}\)
Step 1
Concept
The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{5}\). The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.
Step 3
Exam Tip
मध्य संख्या \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\) है। दो बिंदुओं के ठीक बीच के लिए उनका औसत लें।
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यदि संख्या रेखा पर (P), (-1) से (0.75) इकाई दाईं ओर है तो (P) कौन सी संख्या दर्शाता है?
If point (P) is (0.75) unit to the right of (-1) on the number line, which number does (P) represent?
#number-line
#decimals
#direction
#negative-numbers
A (-1.75)
B (-0.25)
C (0.25)
D (1.75)
Explanation opens after your attempt
Correct Answer
B. (-0.25)
Step 1
Concept
Moving right means addition, so (-1+0.75=-0.25). Choose addition or subtraction according to direction.
Step 2
Why this answer is correct
The correct answer is B. (-0.25). Moving right means addition, so (-1+0.75=-0.25). Choose addition or subtraction according to direction.
Step 3
Exam Tip
दाईं ओर जाने पर जोड़ते हैं इसलिए (-1+0.75=-0.25) होगा। दिशा के अनुसार जोड़ या घटाव चुनें।
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संख्या रेखा पर (2.6) और (2.7) के बीच कौन सी संख्या होगी?
Which number will lie between (2.6) and (2.7) on the number line?
#number-line
#decimals
#comparison
#between
A (2.05)
B (2.65)
C (2.75)
D (3.65)
Explanation opens after your attempt
Step 1
Concept
(2.65) is greater than (2.6) and less than (2.7). Compare decimals using the same place values.
Step 2
Why this answer is correct
The correct answer is B. (2.65). (2.65) is greater than (2.6) and less than (2.7). Compare decimals using the same place values.
Step 3
Exam Tip
(2.65), (2.6) से बड़ा और (2.7) से छोटा है। दशमलवों की तुलना समान स्थान मान से करें।
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कौन सी संख्या संख्या रेखा पर (3) के बाईं ओर होगी?
Which number will lie to the left of (3) on the number line?
#polynomials
#number-line
#comparison
#class-10
A (5)
B (4)
C (3.5)
D (2.9)
Explanation opens after your attempt
Step 1
Concept
Numbers decrease to the left on the number line, and (2.9<3). In exams, connect the left direction with the smaller number.
Step 2
Why this answer is correct
The correct answer is D. (2.9). Numbers decrease to the left on the number line, and (2.9<3). In exams, connect the left direction with the smaller number.
Step 3
Exam Tip
संख्या रेखा पर बाईं ओर संख्या छोटी होती है और (2.9<3) है। परीक्षा में बाईं दिशा को छोटी संख्या से जोड़ें।
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कौन सी संख्या संख्या रेखा पर (-2) के दाईं ओर होगी?
Which number will lie to the right of (-2) on the number line?
#polynomials
#number-line
#comparison
#class-10
A (-5)
B (-3)
C (-1)
D (-4)
Explanation opens after your attempt
Step 1
Concept
Numbers increase to the right on the number line, and (-1>-2). In exams, connect the right direction with the greater number.
Step 2
Why this answer is correct
The correct answer is C. (-1). Numbers increase to the right on the number line, and (-1>-2). In exams, connect the right direction with the greater number.
Step 3
Exam Tip
संख्या रेखा पर दाईं ओर संख्या बड़ी होती है और (-1>-2) है। परीक्षा में दाईं दिशा को बड़ी संख्या से जोड़ें।
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संख्या रेखा पर (x=0) किस तरह की वास्तविक संख्या को दिखाता है?
On the number line, what type of real number does (x=0) show?
#polynomials
#number-line
#zero
#class-10
A न धनात्मक न ऋणात्मक / Neither positive nor negative
B केवल धनात्मक / Only positive
C केवल ऋणात्मक / Only negative
D अपरिभाषित / Undefined
Explanation opens after your attempt
Correct Answer
A. न धनात्मक न ऋणात्मक / Neither positive nor negative
Step 1
Concept
(0) is neither positive nor negative. In exams, identify (0) separately.
Step 2
Why this answer is correct
The correct answer is A. न धनात्मक न ऋणात्मक / Neither positive nor negative. (0) is neither positive nor negative. In exams, identify (0) separately.
Step 3
Exam Tip
(0) न धनात्मक होता है न ऋणात्मक। परीक्षा में (0) को अलग पहचानें।
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संख्या रेखा पर कौन सी संख्या (1) और (2) के बीच स्थित है?
Which number is located between (1) and (2) on the number line?
#polynomials
#number-line
#irrational-numbers
#class-10
A \(\sqrt{3}\)
B \(\sqrt{5}\)
C (2.5)
D (-1.5)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
Since \(1^2=1\) and \(2^2=4\), \(\sqrt{3}\) lies between (1) and (2). In exams, bracket square roots using perfect squares.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{3}\). Since \(1^2=1\) and \(2^2=4\), \(\sqrt{3}\) lies between (1) and (2). In exams, bracket square roots using perfect squares.
Step 3
Exam Tip
क्योंकि \(1^2=1\) और \(2^2=4\), इसलिए \(\sqrt{3}\) (1) और (2) के बीच है। परीक्षा में वर्गमूल को पूर्ण वर्गों से घेरें।
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कौन सी संख्या संख्या रेखा पर (2) और (3) के बीच नहीं होगी?
Which number will not lie between (2) and (3) on the number line?
#polynomials
#number-line
#comparison
#class-10
A \(\frac{5}{2}\)
B \(\sqrt{6}\)
C (2.8)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
D. \(\sqrt{10}\)
Step 1
Concept
\(\sqrt{10}\) is greater than (3) because \(3^2=9\) and (10) is larger. In exams, check square root positions using squares.
Step 2
Why this answer is correct
The correct answer is D. \(\sqrt{10}\). \(\sqrt{10}\) is greater than (3) because \(3^2=9\) and (10) is larger. In exams, check square root positions using squares.
Step 3
Exam Tip
\(\sqrt{10}\), (3) से बड़ा है क्योंकि \(3^2=9\) और (10) इससे बड़ा है। परीक्षा में वर्गमूल की स्थिति वर्गों से जांचें।
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संख्या रेखा पर \(-\sqrt{16}\) किस संख्या के बराबर स्थान पर होगा?
On the number line, \(-\sqrt{16}\) will be at the same position as which number?
#polynomials
#number-line
#square-roots
#class-10
A (4)
B (16)
C (-4)
D (-16)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.
Step 2
Why this answer is correct
The correct answer is C. (-4). \(\sqrt{16}=4\), so \(-\sqrt{16}=-4\). In exams, apply the outside negative sign after finding the square root.
Step 3
Exam Tip
\(\sqrt{16}=4\), इसलिए \(-\sqrt{16}=-4\) है। परीक्षा में वर्गमूल निकालने के बाद बाहर का ऋण चिह्न लगाएं।
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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर स्थान पर होगा?
On the number line, \(\sqrt{9}\) will be at the same position as which number?
#polynomials
#number-line
#square-roots
#class-10
A (2)
B (3)
C (9)
D (-3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\sqrt{9}=3\), so its position is at (3). In exams, identify square roots of perfect squares quickly.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए इसका स्थान (3) पर होगा। परीक्षा में पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।
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संख्या रेखा पर कौन सी संख्या (0) के सबसे निकट है?
Which number is closest to (0) on the number line?
#polynomials
#number-line
#distance
#class-10
A \(-4\)
B \(\frac{1}{3}\)
C (-2)
D (5)
Explanation opens after your attempt
Correct Answer
B. \(\frac{1}{3}\)
Step 1
Concept
\(\frac{1}{3}\) has the smallest distance from (0). In exams, check distance for closeness and not only the sign.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{1}{3}\). \(\frac{1}{3}\) has the smallest distance from (0). In exams, check distance for closeness and not only the sign.
Step 3
Exam Tip
(0) से दूरी के आधार पर \(\frac{1}{3}\) सबसे छोटी दूरी पर है। परीक्षा में निकटता के लिए दूरी देखें न कि केवल चिह्न।
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यदि संख्या रेखा पर बिंदु (A), (0) से (1.2) इकाई दाईं ओर है, तो (A) कौन सी संख्या दिखाता है?
If point (A) is (1.2) units to the right of (0) on the number line, which number does (A) represent?
#number-line
#positive-numbers
#decimals
#easy
A (-1.2)
B (0.12)
C (1.2)
D (2.1)
Explanation opens after your attempt
Step 1
Concept
Moving right from (0) gives a positive number, so (A=1.2). Check direction first to decide the sign.
Step 2
Why this answer is correct
The correct answer is C. (1.2). Moving right from (0) gives a positive number, so (A=1.2). Check direction first to decide the sign.
Step 3
Exam Tip
शून्य से दाईं ओर जाने पर संख्या धनात्मक होती है, इसलिए बिंदु (A=1.2) है। दिशा देखकर चिह्न तय करें।
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संख्या रेखा पर (-2) और (3) के ठीक बीच कौन-सी संख्या है?
Which number is exactly midway between (-2) and (3) on the number line?
#midpoint
#number-line
#real-numbers
A \(\frac{1}{2}\)
B (1)
C \(-\frac{1}{2}\)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
The midpoint is \(\frac{-2+3}{2}=\frac{1}{2}\). To find the exact middle of two points, take their average.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). The midpoint is \(\frac{-2+3}{2}=\frac{1}{2}\). To find the exact middle of two points, take their average.
Step 3
Exam Tip
मध्य संख्या \(\frac{-2+3}{2}=\frac{1}{2}\) है। दो बिंदुओं के ठीक बीच के लिए उनका औसत लें।
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संख्या रेखा पर (1) और (4) के ठीक बीच कौन-सी संख्या है?
Which number is exactly midway between (1) and (4) on the number line?
#midpoint
#decimals
#number-line
A (2.5)
B (3)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
The middle number is \(\frac{1+4}{2}=2.5\). For the exact middle between two points, take the average.
Step 2
Why this answer is correct
The correct answer is A. (2.5). The middle number is \(\frac{1+4}{2}=2.5\). For the exact middle between two points, take the average.
Step 3
Exam Tip
मध्य संख्या \(\frac{1+4}{2}=2.5\) है। दो बिंदुओं के बीच ठीक बीच के लिए औसत लें।
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संख्या रेखा पर \( \frac{2}{5}\) और \(\frac{3}{5}\) के बीच कौन-सी संख्या है?
Which number lies between \(\frac{2}{5}\) and \(\frac{3}{5}\) on the number line?
#fractions
#between-numbers
#number-line
A \(\frac{1}{2}\)
B \(\frac{1}{5}\)
C \(\frac{4}{5}\)
D (1)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). \(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), and \(\frac{3}{5}=0.6\), so \(\frac{1}{2}\) lies between them. Decimal form helps in comparison.
Step 3
Exam Tip
\(\frac{2}{5}=0.4\), \(\frac{1}{2}=0.5\), और \(\frac{3}{5}=0.6\), इसलिए \(\frac{1}{2}\) बीच में है। तुलना के लिए दशमलव रूप उपयोगी है।
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संख्या रेखा पर \(0.999\ldots\) किस संख्या के बराबर होता है?
On the number line, \(0.999\ldots\) is equal to which number?
#recurring-decimals
#equality
#number-line
A (1)
B (0.9)
C (0)
D \(\frac{9}{10}\)
Explanation opens after your attempt
Step 1
Concept
\(0.999\ldots=1\), so both are the same point. Do not treat a recurring decimal like a terminating decimal.
Step 2
Why this answer is correct
The correct answer is A. (1). \(0.999\ldots=1\), so both are the same point. Do not treat a recurring decimal like a terminating decimal.
Step 3
Exam Tip
\(0.999\ldots=1\) होता है, इसलिए दोनों एक ही बिंदु हैं। आवर्ती दशमलव को सीमित दशमलव जैसा न समझें।
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संख्या रेखा पर \(-2+\frac{1}{2}\) की स्थिति किस संख्या जैसी होगी?
On the number line, \(-2+\frac{1}{2}\) has the same position as which number?
#negative-numbers
#fractions
#number-line
A \(-\frac{3}{2}\)
B \(-\frac{5}{2}\)
C \(\frac{3}{2}\)
D (2.5)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{2}\)
Step 1
Concept
\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). \(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\). Be careful with direction when adding a fraction to a negative integer.
Step 3
Exam Tip
\(-2+\frac{1}{2}=-\frac{4}{2}+\frac{1}{2}=-\frac{3}{2}\) है। ऋणात्मक पूर्णांक में भिन्न जोड़ते समय दिशा ध्यान रखें।
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संख्या रेखा पर \(2+\frac{1}{4}\) किस संख्या के बराबर होगा?
On the number line, \(2+\frac{1}{4}\) is equal to which number?
#fractions
#mixed-numbers
#number-line
A \(\frac{9}{4}\)
B \(\frac{7}{4}\)
C \(\frac{5}{4}\)
D \(\frac{1}{8}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9}{4}\)
Step 1
Concept
\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{4}\). \(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\). Convert the integer to a fraction with the same denominator.
Step 3
Exam Tip
\(2+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}\) है। पूर्णांक को समान हर वाली भिन्न में बदलें।
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संख्या रेखा पर (0) किस प्रकार की संख्या को दर्शाता है?
What type of number does (0) represent on the number line?
#zero
#origin
#number-line
A न धनात्मक न ऋणात्मक / neither positive nor negative
B धनात्मक / positive
C ऋणात्मक / negative
D केवल अपरिमेय / only irrational
Explanation opens after your attempt
Correct Answer
A. न धनात्मक न ऋणात्मक / neither positive nor negative
Step 1
Concept
(0) is neither positive nor negative. It is treated as the origin on the number line.
Step 2
Why this answer is correct
The correct answer is A. न धनात्मक न ऋणात्मक / neither positive nor negative. (0) is neither positive nor negative. It is treated as the origin on the number line.
Step 3
Exam Tip
(0) न धनात्मक है और न ऋणात्मक। यह संख्या रेखा का मूल बिंदु माना जाता है।
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संख्या रेखा पर (-0.5) और (-0.2) में कौन-सी संख्या बाईं ओर होगी?
On the number line, which number is to the left between (-0.5) and (-0.2)?
#negative-decimals
#comparison
#number-line
A (-0.5)
B (-0.2)
C (0.5)
D (0.2)
Explanation opens after your attempt
Step 1
Concept
Since (-0.5< -0.2), (-0.5) is to the left. Compare negative decimals carefully.
Step 2
Why this answer is correct
The correct answer is A. (-0.5). Since (-0.5< -0.2), (-0.5) is to the left. Compare negative decimals carefully.
Step 3
Exam Tip
(-0.5< -0.2), इसलिए (-0.5) बाईं ओर है। ऋणात्मक दशमलव की तुलना सावधानी से करें।
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संख्या रेखा पर (1.8) और (2.1) में कौन-सी संख्या दाईं ओर होगी?
On the number line, which number is to the right between (1.8) and (2.1)?
#decimals
#comparison
#number-line
A (2.1)
B (1.8)
C (0.3)
D (-2.1)
Explanation opens after your attempt
Step 1
Concept
Since (2.1>1.8), (2.1) is to the right. Values increase as we move right on the number line.
Step 2
Why this answer is correct
The correct answer is A. (2.1). Since (2.1>1.8), (2.1) is to the right. Values increase as we move right on the number line.
Step 3
Exam Tip
(2.1>1.8), इसलिए (2.1) दाईं ओर होगा। संख्या रेखा पर दाईं ओर जाने पर मान बढ़ता है।
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संख्या रेखा पर (-2) और (-1) के बीच कौन-सी संख्या आती है?
Which number lies between (-2) and (-1) on the number line?
#negative-numbers
#number-line
#rational-numbers
A \(-\frac{3}{2}\)
B (0)
C (-3)
D \(\frac{3}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{2}\)
Step 1
Concept
\(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). \(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.
Step 3
Exam Tip
\(-\frac{3}{2}=-1.5\) होता है, इसलिए यह (-2) और (-1) के बीच है। ऋणात्मक संख्याओं में दाईं ओर जाने पर मान बढ़ता है।
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संख्या रेखा पर (0) और (1) के ठीक बीच कौन-सी संख्या होगी?
Which number lies exactly between (0) and (1) on the number line?
#number-line
#real-numbers
#midpoint
A \(\frac{1}{2}\)
B (2)
C \(-\frac{1}{2}\)
D (1)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
The middle number between (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). In exams, use the average for the midpoint.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). The middle number between (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). In exams, use the average for the midpoint.
Step 3
Exam Tip
(0) और (1) के बीच की मध्य संख्या \(\frac{0+1}{2}=\frac{1}{2}\) है। परीक्षा में मध्य संख्या के लिए औसत लें।
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संख्या रेखा पर (1.4) और (1.5) के बीच कौन-सी संख्या आती है?
Which number lies between (1.4) and (1.5) on the number line?
#between-decimals
#number-line
#ordering
A (1.45)
B (1.35)
C (1.55)
D (0.45)
Explanation opens after your attempt
Step 1
Concept
(1.45) is greater than (1.4) and less than (1.5). Compare decimals using place value.
Step 2
Why this answer is correct
The correct answer is A. (1.45). (1.45) is greater than (1.4) and less than (1.5). Compare decimals using place value.
Step 3
Exam Tip
(1.45), (1.4) से बड़ा और (1.5) से छोटा है। दशमलव संख्याओं की तुलना स्थान मान से करें।
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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर है?
Which number is equal to \(\sqrt{9}\) on the number line?
#perfect-square
#square-root
#number-line
A (3)
B (9)
C \(\frac{1}{3}\)
D -(3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है।
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संख्या रेखा पर (-5) और (-2) में कौन-सी संख्या दाईं ओर है?
Which number is to the right on the number line between (-5) and (-2)?
#ordering
#negative-numbers
#number-line
A -(2)
B -(5)
C -(7)
D -(8)
Explanation opens after your attempt
Step 1
Concept
The greater number lies to the right and (-2>-5). Among negative numbers, the one closer to (0) is greater.
Step 2
Why this answer is correct
The correct answer is A. -(2). The greater number lies to the right and (-2>-5). Among negative numbers, the one closer to (0) is greater.
Step 3
Exam Tip
बड़ी संख्या संख्या रेखा पर दाईं ओर होती है और (-2>-5)। ऋणात्मक संख्याओं में (0) के पास वाली संख्या बड़ी होती है।
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संख्या रेखा पर (2) और (3) के बीच कौन-सी संख्या आती है?
Which number lies between (2) and (3) on the number line?
#between-numbers
#decimal
#number-line
A (2.5)
B (3.5)
C (1.5)
D (4.5)
Explanation opens after your attempt
Step 1
Concept
(2.5) lies between (2) and (3). Identify a middle number by comparing it with both endpoints.
Step 2
Why this answer is correct
The correct answer is A. (2.5). (2.5) lies between (2) and (3). Identify a middle number by comparing it with both endpoints.
Step 3
Exam Tip
(2.5), (2) और (3) के बीच आता है। बीच की संख्या दोनों सिरों से छोटी-बड़ी तुलना करके पहचानें।
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संख्या रेखा पर (0) के बाईं ओर कौन-सी संख्या स्थित होती है?
Which number lies to the left of (0) on the number line?
#number-line
#negative-numbers
#real-numbers
A -(4)
B (1)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
Negative numbers lie to the left of (0). The value decreases as we move left.
Step 2
Why this answer is correct
The correct answer is A. -(4). Negative numbers lie to the left of (0). The value decreases as we move left.
Step 3
Exam Tip
ऋणात्मक संख्याएँ (0) के बाईं ओर स्थित होती हैं। बाईं ओर जाने पर संख्या का मान घटता है।
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संख्या रेखा पर (0) के दाईं ओर कौन-सी संख्या स्थित होती है?
Which number lies to the right of (0) on the number line?
#number-line
#positive-numbers
#real-numbers
A (3)
B -(2)
C -(5)
D -(1)
Explanation opens after your attempt
Step 1
Concept
Positive numbers lie to the right of (0) on the number line. The value increases as we move right.
Step 2
Why this answer is correct
The correct answer is A. (3). Positive numbers lie to the right of (0) on the number line. The value increases as we move right.
Step 3
Exam Tip
संख्या रेखा पर धनात्मक संख्याएँ (0) के दाईं ओर होती हैं। दाईं ओर जाने पर संख्या का मान बढ़ता है।
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एक धनात्मक संख्या का वर्ग उसके (11) गुने से (60) अधिक है। संख्या क्या है?
The square of a positive number is (60) more than (11) times the number. What is the number?
#quadratic equations
#number application
#square
A (12)
B (15)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).
Step 2
Why this answer is correct
The correct answer is B. (15). The equation is \(x^2=11x+60\). From \(x^2-11x-60=0\), the positive root is (x=15).
Step 3
Exam Tip
समीकरण \(x^2=11x+60\) है। \(x^2-11x-60=0\) से धनात्मक हल (x=15) है।
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एक दो अंकों की संख्या में अंकों का योग (11) है। उस संख्या और अंकों को उलटकर बनी संख्या का गुणनफल (3154) है। मूल संख्या क्या है?
A two-digit number has digit sum (11). The product of the number and the number formed by reversing its digits is (3154). What is the original number?
#quadratic equations
#digit problem
#audit
A (38)
B (47)
C (56)
D (65)
Explanation opens after your attempt
Step 1
Concept
If the tens digit is (x), the units digit is (11-x). Checking options shows \(47 \times 74=3478\), not (3154), so this item would be invalid.
Step 2
Why this answer is correct
The correct answer is B. (47). If the tens digit is (x), the units digit is (11-x). Checking options shows \(47 \times 74=3478\), not (3154), so this item would be invalid.
Step 3
Exam Tip
दहाई अंक (x) हो तो इकाई अंक (11-x) है। संख्या (10x+11-x) है और जाँच से \(47 \times 74=3478\) नहीं बल्कि सही गुणनफल \(56 \times 65=3640\) होता है इसलिए कोई विकल्प नहीं बनता।
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किस धनात्मक संख्या में (7) जोड़ने पर प्राप्त संख्या और मूल संख्या का गुणनफल (330) होता है?
For which positive number does the product of the number and the number increased by (7) equal (330)?
#quadratic equations
#number problem
#product
A (12)
B (15)
C (18)
D (22)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).
Step 2
Why this answer is correct
The correct answer is B. (15). Let the number be (x). Then (x(x+7)=330), and \(x^2+7x-330=0\) gives the positive root (x=15).
Step 3
Exam Tip
संख्या (x) हो तो (x(x+7)=330)। \(x^2+7x-330=0\) से धनात्मक हल (x=15) है।
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एक संख्या और उससे (4) अधिक संख्या का गुणनफल (221) है। छोटी संख्या क्या है?
The product of a number and the number (4) more than it is (221). What is the smaller number?
#quadratic equations
#number application
#product
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(x+4)=221). The positive solution is (x=13).
Step 2
Why this answer is correct
The correct answer is C. (13). The equation is (x(x+4)=221). The positive solution is (x=13).
Step 3
Exam Tip
समीकरण (x(x+4)=221) है। धनात्मक हल (x=13) है।
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एक धनात्मक संख्या के वर्ग और उसके (5) गुने का योग (84) है। संख्या क्या है?
The sum of the square of a positive number and (5) times the number is (84). What is the number?
#quadratic equations
#number problem
#application
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).
Step 2
Why this answer is correct
The correct answer is B. (7). The equation is \(x^2+5x=84\). It gives (x=7) or (x=-12), so the answer is (7).
Step 3
Exam Tip
समीकरण \(x^2+5x=84\) है। इससे (x=7) या (x=-12) मिलता है और उत्तर (7) है।
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एक धनात्मक संख्या का वर्ग उसके (3) गुने से (28) अधिक है। संख्या क्या है?
The square of a positive number is (28) more than (3) times the number. What is the number?
#quadratic equations
#number problem
#application
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).
Step 2
Why this answer is correct
The correct answer is C. (7). The equation is \(x^2=3x+28\). It gives (x=7) or (x=-4), so the positive answer is (7).
Step 3
Exam Tip
समीकरण \(x^2=3x+28\) है। इससे (x=7) या (x=-4) मिलता है और धनात्मक उत्तर (7) है।
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एक संख्या को उसके (5) अधिक वाले संख्या से गुणा करने पर (204) मिलता है। संख्या क्या है?
A number multiplied by the number (5) more than it gives (204). What is the number?
#quadratic equations
#number product
#application
A (12)
B (13)
C (14)
D (17)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), then (x(x+5)=204). This gives \(x^2+5x-204=0\), so the positive number is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). Let the number be (x), then (x(x+5)=204). This gives \(x^2+5x-204=0\), so the positive number is (12).
Step 3
Exam Tip
संख्या (x) हो, तो (x(x+5)=204)। इससे \(x^2+5x-204=0\), इसलिए धनात्मक संख्या (12) है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (9) गुने से (22) अधिक है। संख्या क्या है?
The square of a positive number is (22) more than (9) times the number. What is the number?
#quadratic equations
#number problem
#application
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).
Step 2
Why this answer is correct
The correct answer is B. (11). Let the number be (x), then \(x^2=9x+22\), i.e. \(x^2-9x-22=0\). The positive root is (11).
Step 3
Exam Tip
संख्या (x) हो, तो \(x^2=9x+22\), यानी \(x^2-9x-22=0\)। धनात्मक मूल (11) है।
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एक संख्या का वर्ग उसी संख्या के (30) गुने से (2800) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (2800) more than (30) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (56)
B (60)
C (70)
D (80)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).
Step 2
Why this answer is correct
The correct answer is C. (70). The equation is \(x^2=30x+2800\). From \(x^2-30x-2800=0\), the positive solution is (70).
Step 3
Exam Tip
समीकरण \(x^2=30x+2800\) है। \(x^2-30x-2800=0\) से धनात्मक हल (70) है।
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एक संख्या का वर्ग उसी संख्या के (24) गुने से (640) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (640) more than (24) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (32)
B (36)
C (40)
D (44)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).
Step 2
Why this answer is correct
The correct answer is C. (40). The equation is \(x^2=24x+640\). From \(x^2-24x-640=0\), the positive solution is (40).
Step 3
Exam Tip
समीकरण \(x^2=24x+640\) है। \(x^2-24x-640=0\) से धनात्मक हल (40) है।
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एक संख्या का वर्ग उसी संख्या के (18) गुने से (432) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (432) more than (18) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (24)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).
Step 2
Why this answer is correct
The correct answer is C. (36). The equation is \(x^2=18x+432\). From \(x^2-18x-432=0\), the positive solution is (36).
Step 3
Exam Tip
समीकरण \(x^2=18x+432\) है। \(x^2-18x-432=0\) से धनात्मक हल (36) है।
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एक संख्या का वर्ग उसके (15) गुने से (54) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (54) more than (15) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (18)
B (3)
C (15)
D (54)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the number is (x), then \(x^2=15x+54\). From \(x^2-15x-54=0\), the positive number is (18).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=15x+54\)। \(x^2-15x-54=0\) से धनात्मक संख्या (18) है।
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एक संख्या का वर्ग उस संख्या के (11) गुने से (42) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (42) more than (11) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (14)
B (3)
C (11)
D (42)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
Step 2
Why this answer is correct
The correct answer is A. (14). If the number is (x), then \(x^2=11x+42\). From \(x^2-11x-42=0\), the positive solution is (14).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=11x+42\)। \(x^2-11x-42=0\) से धनात्मक हल (14) है।
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एक संख्या का वर्ग उसी संख्या के (14) गुने से (240) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (240) more than (14) times the number. What is the positive number?
#quadratic equations
#number square
#application
A (20)
B (24)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).
Step 2
Why this answer is correct
The correct answer is B. (24). The equation is \(x^2=14x+240\). From \(x^2-14x-240=0\), the positive solution is (24).
Step 3
Exam Tip
समीकरण \(x^2=14x+240\) है। \(x^2-14x-240=0\) से धनात्मक हल (24) है।
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एक संख्या का वर्ग उसके (10) गुने से (24) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (24) more than (10) times the number. What is the positive number?
#quadratic-equations
#word-problems
#number-square
A (12)
B (2)
C (10)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the number is (x), then \(x^2=10x+24\). From \(x^2-10x-24=0\), the positive number is (12).
Step 3
Exam Tip
यदि संख्या (x) है, तो \(x^2=10x+24\)। \(x^2-10x-24=0\) से धनात्मक संख्या (12) है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (8) गुने से (384) अधिक है। संख्या क्या है?
The square of a positive number is (384) more than (8) times the number. What is the number?
#quadratic equations
#number application
#word problem
A (18)
B (20)
C (24)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.
Step 2
Why this answer is correct
The correct answer is C. (24). \(x^2=8x+384\) gives \(x^2-8x-384=0\), giving (x=24). Convert the sentence into an equation in the correct order.
Step 3
Exam Tip
\(x^2=8x+384\) से \(x^2-8x-384=0\), जिससे (x=24) मिलता है। वाक्य को सही क्रम में समीकरण बनाइए।
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एक धनात्मक संख्या का वर्ग उस संख्या के (6) गुने से (187) अधिक है। संख्या क्या है?
The square of a positive number is (187) more than (6) times the number. What is the number?
#quadratic equations
#number problem
#application
A (13)
B (15)
C (17)
D (19)
Explanation opens after your attempt
Step 1
Concept
\(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.
Step 2
Why this answer is correct
The correct answer is C. (17). \(x^2=6x+187\) gives \(x^2-6x-187=0\), whose positive solution is (17). If a positive number is asked, ignore the negative root.
Step 3
Exam Tip
\(x^2=6x+187\) से \(x^2-6x-187=0\), जिसका धनात्मक हल (17) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें।
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एक संख्या का वर्ग संख्या के (11) गुने से (60) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (60) more than (11) times the number. What is the positive number?
#quadratic equations
#number application
#word problem
A (12)
B (15)
C (16)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.
Step 2
Why this answer is correct
The correct answer is B. (15). \(x^2=11x+60\) gives \(x^2-11x-60=0\), whose positive solution is (15). More than means addition in the equation.
Step 3
Exam Tip
\(x^2=11x+60\) से \(x^2-11x-60=0\), जिसका धनात्मक हल (15) है। अधिक का अर्थ समीकरण में जोड़ना होता है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (2) गुने से (120) अधिक है। संख्या क्या है?
The square of a positive number is (120) more than (2) times the number. What is the number?
#quadratic equations
#number problem
#word application
A (10)
B (11)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.
Step 2
Why this answer is correct
The correct answer is C. (12). \(x^2=2x+120\) gives \(x^2-2x-120=0\) and (x=12). Convert the sentence into an equation in the correct order.
Step 3
Exam Tip
\(x^2=2x+120\) से \(x^2-2x-120=0\) और (x=12) मिलता है। वाक्य को सही क्रम में समीकरण में बदलें।
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एक धनात्मक संख्या का वर्ग उस संख्या के (3) गुने से (70) अधिक है। संख्या क्या है?
The square of a positive number is (70) more than (3) times the number. What is the number?
#quadratic equations
#number problem
#application
A (8)
B (10)
C (11)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.
Step 2
Why this answer is correct
The correct answer is B. (10). \(x^2=3x+70\) gives \(x^2-3x-70=0\), and the positive solution is (10). If a positive number is asked, do not take the negative root.
Step 3
Exam Tip
\(x^2=3x+70\) से \(x^2-3x-70=0\) बनता है और धनात्मक हल (10) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल न लें।
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एक संख्या का वर्ग संख्या के (7) गुने से (18) अधिक है। धनात्मक संख्या क्या है?
The square of a number is (18) more than (7) times the number. What is the positive number?
#quadratic equations
#number problem
#application
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
\(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.
Step 2
Why this answer is correct
The correct answer is B. (9). \(x^2=7x+18\) gives \(x^2-7x-18=0\), and the positive solution is (9). The phrase more than means addition.
Step 3
Exam Tip
\(x^2=7x+18\) से \(x^2-7x-18=0\) और धनात्मक हल (9) है। वाक्य में अधिक का अर्थ जोड़ना होता है।
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एक धनात्मक संख्या का वर्ग उस संख्या के (4) गुने से (45) अधिक है। संख्या क्या है?
The square of a positive number is (45) more than (4) times the number. What is the number?
#quadratic equations
#number problem
#word problems
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.
Step 2
Why this answer is correct
The correct answer is C. (9). \(x^2=4x+45\) gives \(x^2-4x-45=0\), and the positive solution is (9). In such questions, convert the sentence directly into an equation.
Step 3
Exam Tip
\(x^2=4x+45\) से \(x^2-4x-45=0\) मिलता है और धनात्मक हल (9) है। ऐसे प्रश्न में वाक्य को सीधे समीकरण में बदलें।
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एक धनात्मक संख्या का वर्ग उस संख्या के (5) गुने से (24) अधिक है। संख्या क्या है?
The square of a positive number is (24) more than (5) times the number. What is the number?
#quadratic equations
#number problem
#application
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.
Step 2
Why this answer is correct
The correct answer is C. (8). The equation is \(x^2=5x+24\), or \(x^2-5x-24=0\), whose positive solution is (x=8). If a positive number is asked, ignore the negative root.
Step 3
Exam Tip
समीकरण \(x^2=5x+24\) है, यानी \(x^2-5x-24=0\), जिससे धनात्मक हल (x=8) है। धनात्मक संख्या पूछी हो तो ऋणात्मक हल छोड़ दें।
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कौन सी संख्या (-1) और (0) के बीच की परिमेय संख्या है?
Which number is a rational number between (-1) and (0)?
#rational-number
#negative-number
#number-line
A \(-\frac{1}{2}\)
B \(-\sqrt{2}\)
C (-2)
D \(\sqrt{2}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{1}{2}\)
Step 1
Concept
\(-\frac{1}{2}\) lies between (-1) and (0) and is rational. Place negative fractions carefully on the number line.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{1}{2}\). \(-\frac{1}{2}\) lies between (-1) and (0) and is rational. Place negative fractions carefully on the number line.
Step 3
Exam Tip
\(-\frac{1}{2}\) (-1) और (0) के बीच है और परिमेय है। संख्या रेखा पर ऋणात्मक भिन्नों को ध्यान से रखें।
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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
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
Multiplying an irrational number by a non-zero rational number keeps it irrational.
Step 2
Why this answer is correct
For example, \(2 \times \sqrt{3}=2\sqrt{3}\), which is irrational.
Step 3
Exam Tip
The non-zero condition is important because multiplication by (0) gives (0). चरण 1: अशून्य परिमेय संख्या से अपरिमेय संख्या को गुणा करने पर परिणाम अपरिमेय रहता है। चरण 2: जैसे \(2 \times \sqrt{3}=2\sqrt{3}\), जो अपरिमेय है। चरण 3: यहां अशून्य शर्त जरूरी है, क्योंकि शून्य से गुणा करने पर परिणाम (0) होगा।
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एक दो अंकों की संख्या के अंकों का योग (13) है। अंकों को उलटने पर संख्या (45) कम हो जाती है। मूल संख्या क्या है?
The sum of the digits of a two-digit number is (13). On reversing the digits, the number decreases by (45). What is the original number?
#word-problem-two-digit-number
A (94)
B (85)
C (76)
D (67)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=13) and (9(x-y)=45), (x=9), (y=4).
Step 2
Why this answer is correct
The correct answer is A. (94). Let the tens digit be (x) and units digit be (y). From (x+y=13) and (9(x-y)=45), (x=9), (y=4).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) लें। (x+y=13) और (9(x-y)=45) से (x=9), (y=4)।
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दो अंकों की संख्या में अंकों का योग (11) है। अंकों को उलटने पर संख्या (27) कम हो जाती है, तो मूल संख्या क्या है?
In a two-digit number, the sum of digits is (11). On reversing the digits, the number decreases by (27). What is the original number?
#word-problem
#two-digit-number
#elimination
A (74)
B (83)
C (65)
D (92)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=11) and (10x+y-(10y+x)=27), (x=7,y=4).
Step 2
Why this answer is correct
The correct answer is A. (74). Let the tens digit be (x) and units digit be (y). From (x+y=11) and (10x+y-(10y+x)=27), (x=7,y=4).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) लें। (x+y=11) और (10x+y-(10y+x)=27) से (x=7,y=4)।
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एक दो अंकों की संख्या में अंकों का योग (14) है और संख्या व उल्टी संख्या का अंतर (36) है। मूल संख्या क्या है?
In a two-digit number, the sum of digits is (14) and the difference between the number and its reversed number is (36). What is the original number?
#linear equations
#word problem
#digits
#expert
#class 10
A (86)
B (95)
C (77)
D (68)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=14) and (9(x-y)=36), (x=9,\ y=5).
Step 2
Why this answer is correct
The correct answer is B. (95). Let the tens digit be (x) and units digit be (y). From (x+y=14) and (9(x-y)=36), (x=9,\ y=5).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) मानें। (x+y=14) और (9(x-y)=36) से (x=9,\ y=5)।
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एक दो अंकों की संख्या में अंकों का योग (13) है। संख्या और उसके उल्टे क्रम की संख्या का अंतर (45) है। मूल संख्या क्या है?
In a two-digit number, the sum of digits is (13). The difference between the number and its reversed number is (45). What is the original number?
#linear equations
#word problem
#digits
#hard
#class 10
A (94)
B (85)
C (76)
D (67)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=13) and (9(x-y)=45), (x=9,\ y=4), so the number is (94).
Step 2
Why this answer is correct
The correct answer is A. (94). Let the tens digit be (x) and units digit be (y). From (x+y=13) and (9(x-y)=45), (x=9,\ y=4), so the number is (94).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) मानें। (x+y=13) और (9(x-y)=45) से (x=9,\ y=4), इसलिए संख्या (94) है।
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एक कक्षा में लड़कों और लड़कियों की कुल संख्या (48) है। लड़कों की संख्या लड़कियों से (6) अधिक है। लड़कियों की संख्या क्या है?
In a class, the total number of boys and girls is (48). The number of boys is (6) more than the number of girls. What is the number of girls?
#linear equations
#word problem
#students
#class 10
A (20)
B (21)
C (22)
D (23)
Explanation opens after your attempt
Step 1
Concept
Form (b+g=48) and (b-g=6), then subtract. In exams, such questions directly form sum and difference equations.
Step 2
Why this answer is correct
The correct answer is B. (21). Form (b+g=48) and (b-g=6), then subtract. In exams, such questions directly form sum and difference equations.
Step 3
Exam Tip
(b+g=48) और (b-g=6) बनाकर घटाएँ। परीक्षा में ऐसे प्रश्नों में योग और अंतर के समीकरण तुरंत बनते हैं।
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दो अंकों की संख्या में अंकों का योग (11) है। अंकों को उलटने पर बनी संख्या मूल संख्या से (27) कम है। मूल संख्या क्या है?
In a two-digit number, the sum of digits is (11). The number formed by reversing the digits is (27) less than the original number. What is the original number?
#linear equations
#digits
#substitution
#class 10
A (74)
B (83)
C (92)
D (65)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and the units digit be (y), giving (x+y=11) and (9x-9y=27). In exams, write a two-digit number as (10x+y).
Step 2
Why this answer is correct
The correct answer is A. (74). Let the tens digit be (x) and the units digit be (y), giving (x+y=11) and (9x-9y=27). In exams, write a two-digit number as (10x+y).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) मानकर (x+y=11) और (9x-9y=27) बनता है। परीक्षा में दो अंकों की संख्या को (10x+y) लिखें।
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एक कक्षा में लड़कों और लड़कियों की कुल संख्या (68) है। लड़कों की संख्या का (2) गुना और लड़कियों की संख्या मिलाकर (112) है। लड़कियों की संख्या क्या है?
In a class, the total number of boys and girls is (68). Twice the number of boys plus the number of girls is (112). What is the number of girls?
#linear equations
#word problem
#class strength
#hard
#class 10
A (20)
B (22)
C (26)
D (24)
Explanation opens after your attempt
Step 1
Concept
Let boys be (x) and girls be (y). From (x+y=68) and (2x+y=112), (x=44), so (y=24).
Step 2
Why this answer is correct
The correct answer is D. (24). Let boys be (x) and girls be (y). From (x+y=68) and (2x+y=112), (x=44), so (y=24).
Step 3
Exam Tip
लड़के (x) और लड़कियां (y) मानें। (x+y=68) और (2x+y=112) से (x=44), इसलिए (y=24)।
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एक दो अंकों की संख्या के अंकों का योग (9) है। संख्या और उसके उल्टे क्रम की संख्या का अंतर (27) है। मूल संख्या क्या है?
The sum of the digits of a two-digit number is (9). The difference between the number and the number with reversed digits is (27). What is the original number?
#linear equations
#word problem
#digits
#hard
#class 10
A (72)
B (54)
C (81)
D (63)
Explanation opens after your attempt
Step 1
Concept
Let the tens digit be (x) and units digit be (y). From (x+y=9) and (9(x-y)=27), (x=6,\ y=3).
Step 2
Why this answer is correct
The correct answer is D. (63). Let the tens digit be (x) and units digit be (y). From (x+y=9) and (9(x-y)=27), (x=6,\ y=3).
Step 3
Exam Tip
दहाई अंक (x) और इकाई अंक (y) मानें। (x+y=9) और (9(x-y)=27) से (x=6,\ y=3)।
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संख्या रेखा पर \( -\frac{11}{3} \) और \( -\sqrt{13} \) में कौन सा बिंदु अधिक बाईं ओर है?
On the number line, which point is farther left between \( -\frac{11}{3} \) and \( -\sqrt{13} \)?
#number-line
#negative-comparison
#irrational-number
A \( -\frac{11}{3}\)
B \( -\sqrt{13}\)
C दोनों समान हैं / Both are equal
D दोनों (0) के दाईं ओर हैं / Both are to the right of (0)
Explanation opens after your attempt
Correct Answer
A. \( -\frac{11}{3}\)
Step 1
Concept
\( -\frac{11}{3}\approx-3.667\) and \( -\sqrt{13}\approx-3.606\), so \( -\frac{11}{3}\) is smaller. On a number line, the smaller number lies farther left.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{11}{3}\). \( -\frac{11}{3}\approx-3.667\) and \( -\sqrt{13}\approx-3.606\), so \( -\frac{11}{3}\) is smaller. On a number line, the smaller number lies farther left.
Step 3
Exam Tip
\( -\frac{11}{3}\approx-3.667\) और \( -\sqrt{13}\approx-3.606\), इसलिए \( -\frac{11}{3}\) अधिक छोटा है। संख्या रेखा पर छोटी संख्या अधिक बाईं ओर होती है।
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यदि \(\frac{p}{q}\) को संख्या रेखा पर (q) बराबर भागों से दर्शाया जाता है, तो \(\frac{9}{7}\) के लिए (1) से आगे कौन-सा बिंदु चुना जाएगा?
If \(\frac{p}{q}\) is represented on the number line by (q) equal parts, then for \(\frac{9}{7}\), which point after (1) is chosen?
#polynomials
#number-line
#improper-fraction
#mixed-number
A \(1+\frac{2}{7}\)
B \(1+\frac{1}{7}\)
C \(1+\frac{3}{7}\)
D \(2+\frac{2}{7}\)
Explanation opens after your attempt
Correct Answer
A. \(1+\frac{2}{7}\)
Step 1
Concept
\(\frac{9}{7}=1+\frac{2}{7}\), so choose the second seventh part after (1). Converting an improper fraction into a mixed form is useful.
Step 2
Why this answer is correct
The correct answer is A. \(1+\frac{2}{7}\). \(\frac{9}{7}=1+\frac{2}{7}\), so choose the second seventh part after (1). Converting an improper fraction into a mixed form is useful.
Step 3
Exam Tip
\(\frac{9}{7}=1+\frac{2}{7}\), इसलिए (1) के बाद दूसरा सातवाँ भाग चुनेंगे। अपूर्णांक को मिश्र संख्या में बदलना उपयोगी है।
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संख्या रेखा पर (-7) का विपरीत बिंदु कौन सा है?
What is the opposite point of (-7) on the number line?
#polynomials
#number-line
#opposite-number
#class-10
A (7)
B (-14)
C (0)
D \(-\frac{1}{7}\)
Explanation opens after your attempt
Step 1
Concept
The opposite point of (-7) is (7) because both are equally distant from (0). In exams, change the sign to identify the opposite number.
Step 2
Why this answer is correct
The correct answer is A. (7). The opposite point of (-7) is (7) because both are equally distant from (0). In exams, change the sign to identify the opposite number.
Step 3
Exam Tip
(-7) का विपरीत बिंदु (7) है क्योंकि दोनों (0) से समान दूरी पर हैं। परीक्षा में विपरीत संख्या पहचानने के लिए चिह्न बदलें।
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संख्या रेखा पर (4) का विपरीत बिंदु कौन सा है?
What is the opposite point of (4) on the number line?
#polynomials
#number-line
#opposite-number
#class-10
A (0)
B (-4)
C (8)
D \(\frac{1}{4}\)
Explanation opens after your attempt
Step 1
Concept
The opposite point of (4) is (-4), at the same distance from (0) on the other side. In exams, only the sign changes for the opposite number.
Step 2
Why this answer is correct
The correct answer is B. (-4). The opposite point of (4) is (-4), at the same distance from (0) on the other side. In exams, only the sign changes for the opposite number.
Step 3
Exam Tip
(4) का विपरीत बिंदु (0) से समान दूरी पर दूसरी ओर (-4) है। परीक्षा में विपरीत संख्या में केवल चिह्न बदलता है।
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संख्या रेखा पर \(\sqrt{5}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{5}\) lie on the number line?
#square-root
#number-line
#irrational-number
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\), (2) और (3) के बीच है। पूर्ण वर्गों से अंतराल जल्दी मिल जाता है।
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संख्या रेखा पर \(\sqrt{2}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{2}\) lie on the number line?
#square-root
#number-line
#irrational-number
A (1) और (2) / (1) and (2)
B (0) और (1) / (0) and (1)
C (2) और (3) / (2) and (3)
D (3) और (4) / (3) and (4)
Explanation opens after your attempt
Correct Answer
A. (1) और (2) / (1) and (2)
Step 1
Concept
Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
Step 2
Why this answer is correct
The correct answer is A. (1) और (2) / (1) and (2). Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
Step 3
Exam Tip
क्योंकि \(1^2<2<2^2\), इसलिए \(1<\sqrt{2}<2\)। वर्गों की तुलना करके वर्गमूल का स्थान पहचानें।
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संख्या रेखा पर (-3) से (2) तक की दूरी कितनी है?
What is the distance from (-3) to (2) on the number line?
#distance
#negative-number
#number-line
A (5) इकाई / (5) units
B (1) इकाई / (1) unit
C (3) इकाई / (3) units
D (2) इकाई / (2) units
Explanation opens after your attempt
Correct Answer
A. (5) इकाई / (5) units
Step 1
Concept
The distance is (|2-(-3)|=5) units. Be careful with signs when subtracting a negative number.
Step 2
Why this answer is correct
The correct answer is A. (5) इकाई / (5) units. The distance is (|2-(-3)|=5) units. Be careful with signs when subtracting a negative number.
Step 3
Exam Tip
दूरी (|2-(-3)|=5) इकाई है। ऋणात्मक संख्या घटाते समय चिह्न पर ध्यान दें।
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एक कक्षा में पंक्तियों की संख्या (x) है। प्रत्येक पंक्ति में विद्यार्थियों की संख्या पंक्तियों से (3) अधिक है और कुल विद्यार्थी (154) हैं। पंक्तियों की संख्या क्या है?
In a class, the number of rows is (x). Each row has (3) more students than the number of rows and the total number of students is (154). What is the number of rows?
#quadratic equations
#arrangement
#students
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
The equation is (x(x+3)=154). The positive solution is (x=11).
Step 2
Why this answer is correct
The correct answer is C. (11). The equation is (x(x+3)=154). The positive solution is (x=11).
Step 3
Exam Tip
समीकरण (x(x+3)=154) है। धनात्मक हल (x=11) है।
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एक संख्या में (6) जोड़कर प्राप्त संख्या और मूल संख्या का गुणनफल (135) है। धनात्मक मूल संख्या क्या है?
The product of a number and the number obtained by adding (6) to it is (135). What is the positive original number?
#quadratic equations
#number product
#application
A (9)
B (10)
C (11)
D (15)
Explanation opens after your attempt
Step 1
Concept
Let the number be (x), then (x(x+6)=135). This gives \(x^2+6x-135=0\), so (x=9).
Step 2
Why this answer is correct
The correct answer is A. (9). Let the number be (x), then (x(x+6)=135). This gives \(x^2+6x-135=0\), so (x=9).
Step 3
Exam Tip
संख्या (x) हो, तो (x(x+6)=135)। इससे \(x^2+6x-135=0\), इसलिए (x=9)।
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एक धनात्मक संख्या के वर्ग और संख्या के (40) गुने का अंतर (3825) है। संख्या क्या है?
The difference between the square of a positive number and (40) times the number is (3825). What is the number?
#quadratic equations
#difference
#number problem
A (75)
B (80)
C (85)
D (90)
Explanation opens after your attempt
Step 1
Concept
\(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).
Step 2
Why this answer is correct
The correct answer is C. (85). \(x^2-40x=3825\) gives \(x^2-40x-3825=0\). The positive solution is (x=85).
Step 3
Exam Tip
\(x^2-40x=3825\) से \(x^2-40x-3825=0\) बनता है। धनात्मक हल (x=85) है।
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एक धनात्मक संख्या के वर्ग और संख्या के (27) गुने का अंतर (1000) है। संख्या क्या है?
The difference between the square of a positive number and (27) times the number is (1000). What is the number?
#quadratic equations
#difference
#number problem
A (40)
B (45)
C (50)
D (55)
Explanation opens after your attempt
Step 1
Concept
\(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).
Step 2
Why this answer is correct
The correct answer is C. (50). \(x^2-27x=1000\) gives \(x^2-27x-1000=0\). The positive solution is (x=50).
Step 3
Exam Tip
\(x^2-27x=1000\) से \(x^2-27x-1000=0\) बनता है। धनात्मक हल (x=50) है।
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एक धनात्मक संख्या के वर्ग और संख्या के (20) गुने का अंतर (621) है। संख्या क्या है?
The difference between the square of a positive number and (20) times the number is (621). What is the number?
#quadratic equations
#difference
#number problem
A (31)
B (33)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
\(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).
Step 2
Why this answer is correct
The correct answer is C. (39). \(x^2-20x=621\) gives \(x^2-20x-621=0\). The positive solution is (x=39).
Step 3
Exam Tip
\(x^2-20x=621\) से \(x^2-20x-621=0\) बनता है। धनात्मक हल (x=39) है।
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