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

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Question 541/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(s=3+\sqrt{10}\), तो \(s^{2}-\frac{1}{s^{2}}\) का मान क्या है?

If \(s=3+\sqrt{10}\), what is the value of \(s^{2}-\frac{1}{s^{2}}\)?

Explanation opens after your attempt
Correct Answer

A. \(12\sqrt{10}\)

Explanation

Simple Explanation

\(\frac{1}{s}=\sqrt{10}-3\), इसलिए \(s-\frac{1}{s}=6\) और \(s+\frac{1}{s}=2\sqrt{10}\)। अतः \(s^{2}-\frac{1}{s^{2}}=12\sqrt{10}\)। / Here \(\frac{1}{s}=\sqrt{10}-3\), so \(s-\frac{1}{s}=6\) and \(s+\frac{1}{s}=2\sqrt{10}\). Thus \(s^{2}-\frac{1}{s^{2}}=12\sqrt{10}\).

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Question 542/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{-\frac{1}{3}}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{-\frac{1}{3}})?

Explanation opens after your attempt
Correct Answer

A. \(\frac{3x^{2}y^{3}}{4}\)

Explanation

Simple Explanation

(\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}})। \(-\frac{1}{3}\) घात लेने पर व्युत्क्रम \(\frac{3x^{2}y^{3}}{4}\) मिलता है। / We get (\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}}). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{3x^{2}y^{3}}{4}\).

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Question 543/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(x^{2}-\frac{1}{x^{2}}=40\) और \(x-\frac{1}{x}=5\), तो \(x+\frac{1}{x}\) का मान क्या है?

If \(x^{2}-\frac{1}{x^{2}}=40\) and \(x-\frac{1}{x}=5\), what is the value of \(x+\frac{1}{x}\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(x^{2}-\frac{1}{x^{2}}=\left\(x-\frac{1}{x}\right\)\left\(x+\frac{1}{x}\right\)) है। इसलिए (40=5\left\(x+\frac{1}{x}\right\)), और मान (8) है। / We use (x^{2}-\frac{1}{x^{2}}=\left\(x-\frac{1}{x}\right\)\left\(x+\frac{1}{x}\right\)). Thus (40=5\left\(x+\frac{1}{x}\right\)), so the value is (8).

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Question 544/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\frac{4b^{-2}+6b^{-2}}{5b^{-3}}\) का सरल रूप क्या है, जहाँ \(b\neq0\)?

What is the simplified form of \(\frac{4b^{-2}+6b^{-2}}{5b^{-3}}\), where \(b\neq0\)?

Explanation opens after your attempt
Correct Answer

A. (2b)

Explanation

Simple Explanation

ऊपर \(4b^{-2}+6b^{-2}=10b^{-2}\) है। \(\frac{10b^{-2}}{5b^{-3}}=2b\) मिलता है। / The numerator is \(4b^{-2}+6b^{-2}=10b^{-2}\). Thus \(\frac{10b^{-2}}{5b^{-3}}=2b\).

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Question 545/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(\sqrt{x}=4\sqrt{3}\), तो \(x^{\frac{3}{2}}\) का मान क्या है?

If \(\sqrt{x}=4\sqrt{3}\), what is the value of \(x^{\frac{3}{2}}\)?

Explanation opens after your attempt
Correct Answer

A. \(192\sqrt{3}\)

Explanation

Simple Explanation

\(\sqrt{x}=4\sqrt{3}\) से (x=48), और \(x^{\frac{3}{2}}=x\sqrt{x}=48\cdot4\sqrt{3}=192\sqrt{3}\)। परीक्षा में \(x^{\frac{3}{2}}\) को \(x\sqrt{x}\) लिखें। / From \(\sqrt{x}=4\sqrt{3}\), (x=48), and \(x^{\frac{3}{2}}=x\sqrt{x}=48\cdot4\sqrt{3}=192\sqrt{3}\). In exams, write \(x^{\frac{3}{2}}\) as \(x\sqrt{x}\).

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Question 546/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{4}{7}\right\)^{-2}+\left\(\frac{7}{4}\right\)^{-2}) का मान क्या है?

What is the value of (\left\(\frac{4}{7}\right\)^{-2}+\left\(\frac{7}{4}\right\)^{-2})?

Explanation opens after your attempt
Correct Answer

A. \(\frac{2657}{784}\)

Explanation

Simple Explanation

(\left\(\frac{4}{7}\right\)^{-2}=\frac{49}{16}) और (\left\(\frac{7}{4}\right\)^{-2}=\frac{16}{49})। योग \(\frac{2401+256}{784}=\frac{2657}{784}\) है। / Here (\left\(\frac{4}{7}\right\)^{-2}=\frac{49}{16}) and (\left\(\frac{7}{4}\right\)^{-2}=\frac{16}{49}). The sum is \(\frac{2401+256}{784}=\frac{2657}{784}\).

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Question 547/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (\left\(5^{x}\right\)^{2}\cdot5^{x-2}=3125), तो (x) का मान क्या है?

If (\left\(5^{x}\right\)^{2}\cdot5^{x-2}=3125), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{7}{3}\)

Explanation

Simple Explanation

बाएँ पक्ष \(5^{2x}\cdot5^{x-2}=5^{3x-2}\) है और \(3125=5^{5}\)। इसलिए (3x-2=5) और \(x=\frac{7}{3}\)। / The left side is \(5^{2x}\cdot5^{x-2}=5^{3x-2}\), and \(3125=5^{5}\). Hence (3x-2=5), so \(x=\frac{7}{3}\).

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Question 548/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\frac{\sqrt{192}-2\sqrt{48}+3\sqrt{12}}{\sqrt{3}}\) का मान क्या है?

What is the value of \(\frac{\sqrt{192}-2\sqrt{48}+3\sqrt{12}}{\sqrt{3}}\)?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

\(\sqrt{192}=8\sqrt{3}\), \(2\sqrt{48}=8\sqrt{3}\), और \(3\sqrt{12}=6\sqrt{3}\)। अंश \(6\sqrt{3}\) है, इसलिए मान (6) है। / Here \(\sqrt{192}=8\sqrt{3}\), \(2\sqrt{48}=8\sqrt{3}\), and \(3\sqrt{12}=6\sqrt{3}\). The numerator is \(6\sqrt{3}\), so the value is (6).

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Question 549/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (\left\(2x^{-1}y^{2}\right\)^{3}\cdot\left\(4x^{2}y^{-1}\right\)^{-1}) को \(cx^{r}y^{s}\) लिखा जाए, तो (c+r+s) का मान क्या है?

If (\left\(2x^{-1}y^{2}\right\)^{3}\cdot\left\(4x^{2}y^{-1}\right\)^{-1}) is written as \(cx^{r}y^{s}\), what is the value of (c+r+s)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{17}{4}\)

Explanation

Simple Explanation

अभिव्यक्ति \(8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=;2x^{-5}y^{7}\) है। इसलिए (c+r+s=2-5+7=4) है। / The expression is \(8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=2x^{-5}y^{7}\). Hence (c+r+s=2-5+7=4).

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Question 550/600 Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(x=\sqrt{2}+\sqrt{5}\), तो \(x^{3}-7x\) का मान क्या है?

If \(x=\sqrt{2}+\sqrt{5}\), what is the value of \(x^{3}-7x\)?

Explanation opens after your attempt
Correct Answer

A. \(10\sqrt{2}+4\sqrt{5}\)

Explanation

Simple Explanation

\(x^{2}=7+2\sqrt{10}\), इसलिए \(x^{3}=17\sqrt{2}+11\sqrt{5}\) और \(x^{3}-7x=10\sqrt{2}+4\sqrt{5}\)। परीक्षा में पहले \(x^{2}\) निकालकर फिर (x) से गुणा करें। / Here \(x^{2}=7+2\sqrt{10}\), so \(x^{3}=17\sqrt{2}+11\sqrt{5}\) and \(x^{3}-7x=10\sqrt{2}+4\sqrt{5}\). In exams, first find \(x^{2}\) and then multiply by (x).

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