Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Which number is both rational and an integer?
C. -12
हर पूर्णांक परिमेय होता है। (-12) दोनों श्रेणियों में है। / Every integer is rational. (-12) belongs to both categories.
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If \(x=\sqrt{14}\) then what is \(x^2-10\)?
D. 4
\(x^2=14\) इसलिए (14-10=4)। पहले वर्ग निकालें। / \(x^2=14\), hence (14-10=4). Evaluate the square first.
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What is the simplified form of \(\sqrt{18}+\sqrt{8}\)?
A. \(5\sqrt{2}\)
\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\)। योग \(5\sqrt{2}\) है। / \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\). Sum is \(5\sqrt{2}\).
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Which decimal represents an irrational number?
D. \(0.123456789101112\ldots\)
यह अनंत और अनावर्ती है इसलिए अपरिमेय है। आवृत्ति जाँचें। / It is infinite and non repeating, so it is irrational. Check for repetition.
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What is the value of \(\frac{\sqrt{81}}{\sqrt{9}}\)?
B. 3
\(\frac{9}{3}=3\)। वर्गमूल का सही मान लें। / \(\frac{9}{3}=3\). Evaluate square roots correctly.
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If \(a=\sqrt{2}\) then \(a+\frac{1}{a}\) is what type of number?
C. अपरिमेयIrrational
\(\sqrt{2}+\frac{\sqrt{2}}{2}\) अपरिमेय रहता है। अपरिमेय के गुण पहचानें। / \(\sqrt{2}+\frac{\sqrt{2}}{2}\) remains irrational. Use properties of irrationals.
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Which is the correct classification of real numbers?
B. परिमेय और अपरिमेयRational and irrational
वास्तविक संख्याएँ परिमेय और अपरिमेय दोनों को शामिल करती हैं। यह मूल परिभाषा है। / Real numbers include both rational and irrational numbers. This is the basic definition.
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If \(x=\sqrt{20}\) and \(y=\sqrt{45}\) then what is the simplified form of (x+y)?
A. \(7\sqrt{5}\)
\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\) इसलिए योग \(5\sqrt{5}\) नहीं बल्कि \(5\sqrt{5}\)? ध्यान दें सही जोड़ \(2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\) है। परीक्षा में पहले सरल रूप निकालें। / \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so the sum is \(5\sqrt{5}\). Simplify surds before adding.
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Which of the following does not give a terminating decimal?
C. \(\frac{11}{24}\)
सरल रूप में हर में 2 और 5 के अलावा 3 भी है इसलिए दशमलव समाप्त नहीं होगा। हर के अभाज्य गुणनखंड जाँचें। / In simplest form the denominator contains 3 along with 2, so the decimal will not terminate. Check prime factors of the denominator.
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If \(x=\sqrt{27}-\sqrt{12}\) then what is the value of (x)?
A. \(\sqrt{3}\)
\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) इसलिए \(x=\sqrt{3}\)। पहले मूलों को सरल करें। / \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{12}=2\sqrt{3}\), so \(x=\sqrt{3}\). Simplify surds first.
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