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Mathematics Operations on real numbers and the laws of exponents MCQ Questions for Class 10

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Operations on real numbers and the laws of exponents Practice Questions

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Question 481/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(32^{\frac{2}{5}}\right\)\cdot\left\(4^{-\frac{3}{2}}\right\)) का मान क्या है?

What is the value of (\left\(32^{\frac{2}{5}}\right\)\cdot\left\(4^{-\frac{3}{2}}\right\))?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{2}\)

Explanation

Simple Explanation

(32^{\frac{2}{5}}=\(2^{5}\)^{\frac{2}{5}}=2^{2}=4), और (4^{-\frac{3}{2}}=\(2^{2}\)^{-\frac{3}{2}}=2^{-3}=\frac{1}{8})। गुणनफल \(\frac{1}{2}\) है। / Here (32^{\frac{2}{5}}=\(2^{5}\)^{\frac{2}{5}}=2^{2}=4), and (4^{-\frac{3}{2}}=\(2^{2}\)^{-\frac{3}{2}}=2^{-3}=\frac{1}{8}). The product is \(\frac{1}{2}\).

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Question 482/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (\left\(x^{2}y^{-1}\right\)^{k}=x^{10}y^{-5}), तो (k) का मान क्या है?

If (\left\(x^{2}y^{-1}\right\)^{k}=x^{10}y^{-5}), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

बाएँ पक्ष में घातें (2k) और (-k) हैं। (2k=10) और (-k=-5) दोनों से (k=5) मिलता है। / The left side has exponents (2k) and (-k). Both (2k=10) and (-k=-5) give (k=5).

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Question 483/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(\sqrt[3]{125a^{9}b^{6}}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt[3]{125a^{9}b^{6}}\)?

Explanation opens after your attempt
Correct Answer

A. \(5a^{3}b^{2}\)

Explanation

Simple Explanation

\(\sqrt[3]{125}=5\), \(\sqrt[3]{a^{9}}=a^{3}\), और \(\sqrt[3]{b^{6}}=b^{2}\)। परीक्षा में घनमूल में घातों को (3) से भाग दें। / We have \(\sqrt[3]{125}=5\), \(\sqrt[3]{a^{9}}=a^{3}\), and \(\sqrt[3]{b^{6}}=b^{2}\). In exams, divide exponents by (3) under a cube root.

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Question 484/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

कौन-सा विकल्प \(\frac{x^{6}-1}{x^{3}-1}\) का सरल रूप है, जहाँ \(x^{3}\neq1\)?

Which option is the simplified form of \(\frac{x^{6}-1}{x^{3}-1}\), where \(x^{3}\neq1\)?

Explanation opens after your attempt
Correct Answer

A. \(x^{3}+1\)

Explanation

Simple Explanation

(x^{6}-1=\(x^{3}-1\)\(x^{3}+1\)), इसलिए समान गुणनखंड कटने पर \(x^{3}+1\) मिलता है। परीक्षा में \(A^{2}-B^{2}\) रूप पहचानें। / Since (x^{6}-1=\(x^{3}-1\)\(x^{3}+1\)), cancelling the common factor gives \(x^{3}+1\). In exams, recognize the \(A^{2}-B^{2}\) form.

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Question 485/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(p=4-\sqrt{15}\), तो \(\frac{1}{p}-p\) का मान क्या है?

If \(p=4-\sqrt{15}\), what is the value of \(\frac{1}{p}-p\)?

Explanation opens after your attempt
Correct Answer

A. \(2\sqrt{15}\)

Explanation

Simple Explanation

\(\frac{1}{4-\sqrt{15}}=4+\sqrt{15}\), इसलिए (\frac{1}{p}-p=\(4+\sqrt{15}\)-\(4-\sqrt{15}\)=2\sqrt{15})। परीक्षा में हर (1) बनने पर संयुग्म सीधे उत्तर देता है। / Since \(\frac{1}{4-\sqrt{15}}=4+\sqrt{15}\), (\frac{1}{p}-p=\(4+\sqrt{15}\)-\(4-\sqrt{15}\)=2\sqrt{15}). In exams, the conjugate gives the reciprocal directly when the denominator product is (1).

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Question 486/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\frac{\(2^{-3}+2^{-4}\)}{2^{-5}}) का मान क्या है?

What is the value of (\frac{\(2^{-3}+2^{-4}\)}{2^{-5}})?

Explanation opens after your attempt
Correct Answer

A. (6)

Explanation

Simple Explanation

\(2^{-3}+2^{-4}=\frac{1}{8}+\frac{1}{16}=\frac{3}{16}\), और \(2^{-5}=\frac{1}{32}\)। इसलिए मान \(\frac{3}{16}\div\frac{1}{32}=6\) है। / Here \(2^{-3}+2^{-4}=\frac{1}{8}+\frac{1}{16}=\frac{3}{16}\), and \(2^{-5}=\frac{1}{32}\). Therefore, the value is \(\frac{3}{16}\div\frac{1}{32}=6\).

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Question 487/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(x=\sqrt{5}-\sqrt{2}\), तो \(x^{2}+2\sqrt{10}\) का मान क्या है?

If \(x=\sqrt{5}-\sqrt{2}\), what is the value of \(x^{2}+2\sqrt{10}\)?

Explanation opens after your attempt
Correct Answer

A. (7)

Explanation

Simple Explanation

\(x^{2}=5+2-2\sqrt{10}=7-2\sqrt{10}\), इसलिए \(x^{2}+2\sqrt{10}=7\)। परीक्षा में ((a-b)^{2}) का मध्य पद ध्यान से लिखें। / Since \(x^{2}=5+2-2\sqrt{10}=7-2\sqrt{10}\), \(x^{2}+2\sqrt{10}=7\). In exams, write the middle term of ((a-b)^{2}) carefully.

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Question 488/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}\right\)^{-1}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}\right\)^{-1})?

Explanation opens after your attempt
Correct Answer

A. \(5m^{6}n^{-4}\)

Explanation

Simple Explanation

अंदर \(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}\), इसलिए (-1) घात लेने पर \(5m^{6}n^{-4}\) है। परीक्षा में गुणांक भी उलटना न भूलें। / Inside, \(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}\), so raising to (-1) gives \(5m^{6}n^{-4}\). In exams, do not forget to invert the coefficient too.

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Question 489/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(6^{x}=216\) और \(36^{y}=216\), तो (x+y) का मान क्या है?

If \(6^{x}=216\) and \(36^{y}=216\), what is the value of (x+y)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9}{2}\)

Explanation

Simple Explanation

\(216=6^{3}\), इसलिए (x=3)। (36^{y}=\(6^{2}\)^{y}=6^{2y}=6^{3}), इसलिए \(y=\frac{3}{2}\) और योग \(\frac{9}{2}\) है। / Since \(216=6^{3}\), (x=3). Also (36^{y}=\(6^{2}\)^{y}=6^{2y}=6^{3}), so \(y=\frac{3}{2}\) and the sum is \(\frac{9}{2}\).

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Question 490/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\sqrt{13}+\sqrt{3}\right\)\left\(\sqrt{13}-\sqrt{3}\right\)-\sqrt{100}) का मान क्या है?

What is the value of (\left\(\sqrt{13}+\sqrt{3}\right\)\left\(\sqrt{13}-\sqrt{3}\right\)-\sqrt{100})?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

संयुग्म गुणनफल (13-3=10) है और \(\sqrt{100}=10\), इसलिए अंतर (0) है। परीक्षा में संयुग्म गुणनफल को तुरंत परिमेय करें। / The conjugate product is (13-3=10), and \(\sqrt{100}=10\), so the difference is (0). In exams, simplify conjugate products directly.

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