A rational number is in the form \(\frac{m}{n}\), where (m) and (n) are integers. The denominator must not be zero.
Step 2
Why this answer is correct
The correct answer is B. पूर्णांक / Integers. A rational number is in the form \(\frac{m}{n}\), where (m) and (n) are integers. The denominator must not be zero.
Step 3
Exam Tip
परिमेय संख्या \(\frac{m}{n}\) रूप में होती है जहाँ (m) और (n) पूर्णांक होते हैं। हर शून्य नहीं होना चाहिए।
C. कोई पूर्ण संख्या नहीं है/There is no whole number
Step 1
Concept
\(\sqrt{11}\approx3.3\) and \(\sqrt{15}\approx3.9\), so there is no whole number between them. Use nearest squares while estimating.
Step 2
Why this answer is correct
The correct answer is C. कोई पूर्ण संख्या नहीं है / There is no whole number. \(\sqrt{11}\approx3.3\) and \(\sqrt{15}\approx3.9\), so there is no whole number between them. Use nearest squares while estimating.
Step 3
Exam Tip
\(\sqrt{11}\approx3.3\) और \(\sqrt{15}\approx3.9\), इसलिए इनके बीच कोई पूर्ण संख्या नहीं है। अनुमान लगाते समय निकटतम वर्ग देखें।
To rationalise the denominator, multiply by the conjugate \(\sqrt{7}-\sqrt{5}\). The denominator becomes (7-5=2).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{\sqrt{7}-\sqrt{5}}{2}\). To rationalise the denominator, multiply by the conjugate \(\sqrt{7}-\sqrt{5}\). The denominator becomes (7-5=2).
Step 3
Exam Tip
हर को परिमेय करने के लिए संयुग्मी \(\sqrt{7}-\sqrt{5}\) से गुणा करें। हर (7-5=2) बनता है।
C. कोई पूर्ण संख्या नहीं है/There is no whole number
Step 1
Concept
Both square roots lie between (4) and (5), but \(\sqrt{18}>4\) and \(\sqrt{19}<5\). Therefore there is no whole number between them.
Step 2
Why this answer is correct
The correct answer is C. कोई पूर्ण संख्या नहीं है / There is no whole number. Both square roots lie between (4) and (5), but \(\sqrt{18}>4\) and \(\sqrt{19}<5\). Therefore there is no whole number between them.
Step 3
Exam Tip
दोनों वर्गमूल (4) और (5) के बीच हैं, पर \(\sqrt{18}>4\) और \(\sqrt{19}<5\) है। इसलिए इनके बीच कोई पूर्ण संख्या नहीं है।
\(\sqrt{121}=11\) is rational and \(\sqrt{2}\) is irrational. The sum of a rational and an irrational number is irrational.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. \(\sqrt{121}=11\) is rational and \(\sqrt{2}\) is irrational. The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
\(\sqrt{121}=11\) परिमेय है और \(\sqrt{2}\) अपरिमेय है। परिमेय और अपरिमेय का योग अपरिमेय होता है।
C. अपरिमेय क्योंकि यह असांत अनावर्ती है/Irrational because it is non-terminating non-recurring
Step 1
Concept
The decimal continues forever and has no fixed repetition. Therefore it is an irrational number.
Step 2
Why this answer is correct
The correct answer is C. अपरिमेय क्योंकि यह असांत अनावर्ती है / Irrational because it is non-terminating non-recurring. The decimal continues forever and has no fixed repetition. Therefore it is an irrational number.
Step 3
Exam Tip
दशमलव अनंत तक चलता है और कोई निश्चित आवृत्ति नहीं है। इसलिए यह अपरिमेय संख्या है।
