\(\sqrt{147}\) को सरल करने पर क्या मिलता है?
What is obtained after simplifying \(\sqrt{147}\)?
#number-systems
#surd-simplification
#square-roots
A \(7\sqrt{3}\)
B \(3\sqrt{7}\)
C \(21\sqrt{7}\)
D \(\sqrt{49}\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{3}\)
Step 1
Concept
\(147=49\times3\), so \(\sqrt{147}=7\sqrt{3}\). Take the perfect square outside.
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{3}\). \(147=49\times3\), so \(\sqrt{147}=7\sqrt{3}\). Take the perfect square outside.
Step 3
Exam Tip
\(147=49\times3\), इसलिए \(\sqrt{147}=7\sqrt{3}\)। पूर्ण वर्ग को बाहर निकालें।
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कौन-सा कथन \(\sqrt{2}+\sqrt{8}\) के बारे में सही है?
Which statement about \(\sqrt{2}+\sqrt{8}\) is correct?
#number-systems
#surds
#common-error
A यह \(3\sqrt{2}\) है / It is \(3\sqrt{2}\)
B यह \(\sqrt{10}\) है / It is \(\sqrt{10}\)
C यह (4) है / It is (4)
D यह \(\sqrt{16}\) है / It is \(\sqrt{16}\)
Explanation opens after your attempt
Correct Answer
A. यह \(3\sqrt{2}\) है / It is \(3\sqrt{2}\)
Step 1
Concept
\(\sqrt{8}=2\sqrt{2}\), so the sum is \(3\sqrt{2}\). Do not directly add numbers inside roots.
Step 2
Why this answer is correct
The correct answer is A. यह \(3\sqrt{2}\) है / It is \(3\sqrt{2}\). \(\sqrt{8}=2\sqrt{2}\), so the sum is \(3\sqrt{2}\). Do not directly add numbers inside roots.
Step 3
Exam Tip
\(\sqrt{8}=2\sqrt{2}\), इसलिए योग \(3\sqrt{2}\) है। वर्गमूलों को सीधे अंदर जोड़ना गलत है।
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\(\frac{5}{6}\) का दशमलव प्रसार सांत क्यों नहीं है?
Why is the decimal expansion of \(\frac{5}{6}\) not terminating?
#number-systems
#decimal-expansion
#non-terminating
A क्योंकि \(6=2\times3\) और हर में (3) है / Because \(6=2\times3\) and the denominator contains (3)
B क्योंकि अंश (5) है / Because the numerator is (5)
C क्योंकि (6) सम संख्या है / Because (6) is even
D क्योंकि यह पूर्णांक है / Because it is an integer
Explanation opens after your attempt
Correct Answer
A. क्योंकि \(6=2\times3\) और हर में (3) है / Because \(6=2\times3\) and the denominator contains (3)
Step 1
Concept
Since the denominator in simplest form contains (3), the decimal is non-terminating recurring. A terminating decimal needs only (2) and (5).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि \(6=2\times3\) और हर में (3) है / Because \(6=2\times3\) and the denominator contains (3). Since the denominator in simplest form contains (3), the decimal is non-terminating recurring. A terminating decimal needs only (2) and (5).
Step 3
Exam Tip
सरल रूप में हर में (3) होने से दशमलव असांत आवर्ती होगा। सांत दशमलव के लिए केवल (2) और (5) चाहिए।
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कौन-सी संख्या \(\sqrt{10}\) से बड़ी और \(\sqrt{17}\) से छोटी है?
Which number is greater than \(\sqrt{10}\) and less than \(\sqrt{17}\)?
#number-systems
#comparison
#square-roots
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{10}\) lies between (3) and (4), while \(\sqrt{17}\) lies between (4) and (5). Therefore (4) lies between them.
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{10}\) lies between (3) and (4), while \(\sqrt{17}\) lies between (4) and (5). Therefore (4) lies between them.
Step 3
Exam Tip
\(\sqrt{10}\) (3) और (4) के बीच है, जबकि \(\sqrt{17}\) (4) और (5) के बीच है। इसलिए (4) बीच में है।
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यदि \(\sqrt{a}=9\), तो (a) का मान क्या है?
If \(\sqrt{a}=9\), what is the value of (a)?
#number-systems
#square-root
#equation
A (18)
B (81)
C (9)
D \(\sqrt{9}\)
Explanation opens after your attempt
Step 1
Concept
Squaring both sides gives (a=81). Squaring is useful in square root equations.
Step 2
Why this answer is correct
The correct answer is B. (81). Squaring both sides gives (a=81). Squaring is useful in square root equations.
Step 3
Exam Tip
दोनों ओर वर्ग करने पर (a=81) मिलता है। वर्गमूल समीकरण में वर्ग करना उपयोगी है।
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\(\sqrt{75}\div\sqrt{3}\) का मान क्या है?
What is the value of \(\sqrt{75}\div\sqrt{3}\)?
#number-systems
#surds
#division
A (5)
B \(\sqrt{25}\)
C दोनों (A) और (B) / Both (A) and (B)
D \(\sqrt{72}\)
Explanation opens after your attempt
Correct Answer
C. दोनों (A) और (B) / Both (A) and (B)
Step 1
Concept
\(\sqrt{75}\div\sqrt{3}=\sqrt{25}=5\). Both forms are equal, so read options carefully.
Step 2
Why this answer is correct
The correct answer is C. दोनों (A) और (B) / Both (A) and (B). \(\sqrt{75}\div\sqrt{3}=\sqrt{25}=5\). Both forms are equal, so read options carefully.
Step 3
Exam Tip
\(\sqrt{75}\div\sqrt{3}=\sqrt{25}=5\)। दोनों रूप समान हैं, इसलिए सावधानी से विकल्प पढ़ें।
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कौन-सा विकल्प \(0.\overline{6}\) का भिन्न रूप है?
Which option is the fractional form of \(0.\overline{6}\)?
#number-systems
#recurring-decimal
#fraction
A \(\frac{1}{6}\)
B \(\frac{2}{3}\)
C \(\frac{3}{5}\)
D \(\frac{6}{10}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{2}{3}\)
Step 1
Concept
\(0.\overline{6}=\frac{6}{9}=\frac{2}{3}\). Write the repeating digit over (9).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{2}{3}\). \(0.\overline{6}=\frac{6}{9}=\frac{2}{3}\). Write the repeating digit over (9).
Step 3
Exam Tip
\(0.\overline{6}=\frac{6}{9}=\frac{2}{3}\)। आवर्ती अंक को (9) के हर में लिखें।
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\(\sqrt{200}\) का सरलतम रूप क्या है?
What is the simplest form of \(\sqrt{200}\)?
#number-systems
#surd-simplification
#square-roots
A \(10\sqrt{2}\)
B \(20\sqrt{2}\)
C \(100\sqrt{2}\)
D \(5\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. \(10\sqrt{2}\)
Step 1
Concept
\(200=100\times2\), so \(\sqrt{200}=10\sqrt{2}\). Take out the largest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(10\sqrt{2}\). \(200=100\times2\), so \(\sqrt{200}=10\sqrt{2}\). Take out the largest perfect square.
Step 3
Exam Tip
\(200=100\times2\), इसलिए \(\sqrt{200}=10\sqrt{2}\)। सबसे बड़ा पूर्ण वर्ग निकालें।
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यदि \(x=2+\sqrt{3}\), तो (x) किस प्रकार की संख्या है?
If \(x=2+\sqrt{3}\), what type of number is (x)?
#number-systems
#irrational-numbers
#operations
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्णांक / Integer
D प्राकृत / Natural
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
The sum of rational (2) and irrational \(\sqrt{3}\) is irrational. In such questions, identify the type of each number.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. The sum of rational (2) and irrational \(\sqrt{3}\) is irrational. In such questions, identify the type of each number.
Step 3
Exam Tip
परिमेय (2) और अपरिमेय \(\sqrt{3}\) का योग अपरिमेय होता है। ऐसे प्रश्न में संख्या का प्रकार पहचानें।
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कौन-सा विकल्प \(\frac{13}{2^2\times5\times7}\) के दशमलव प्रसार के बारे में सही है?
Which option is correct about the decimal expansion of \(\frac{13}{2^2\times5\times7}\)?
#number-systems
#decimal-expansion
#recurring
A सांत / Terminating
B असांत आवर्ती / Non-terminating recurring
C असांत अनावर्ती / Non-terminating non-recurring
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. असांत आवर्ती / Non-terminating recurring
Step 1
Concept
The denominator contains (7), so the decimal will not terminate. Since it is rational, it will be non-terminating recurring.
Step 2
Why this answer is correct
The correct answer is B. असांत आवर्ती / Non-terminating recurring. The denominator contains (7), so the decimal will not terminate. Since it is rational, it will be non-terminating recurring.
Step 3
Exam Tip
हर में (7) है, इसलिए दशमलव सांत नहीं होगा। परिमेय संख्या होने से यह असांत आवर्ती होगा।
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