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Class 10 Mathematics - Polynomials - Operations on real numbers and the laws of exponents Medium Quiz

Mathematics Polynomials Operations on real numbers and the laws of exponents Medium Class 10 Topic Quiz

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Question 1/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(2^3\cdot2^{-5}\cdot2^4\) का सरल रूप क्या है?

What is the simplified form of \(2^3\cdot2^{-5}\cdot2^4\)?

Explanation opens after your attempt
Correct Answer

A. \(2^2\)

Explanation

Simple Explanation

समान आधार में घातें (3-5+4=2) जुड़ती हैं। इसलिए सरल रूप \(2^2\) है। / For the same base, exponents add as (3-5+4=2). Hence the simplified form is \(2^2\).

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Question 2/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(\frac{3^2\cdot3^{-4}}{3^{-3}}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{3^2\cdot3^{-4}}{3^{-3}}\)?

Explanation opens after your attempt
Correct Answer

B. \(3^1\)

Explanation

Simple Explanation

घातों को (2-4-(-3)=1) करें। ऋणात्मक घात घटाते समय चिह्न बदलता है। / Combine the exponents as (2-4-(-3)=1). The sign changes when subtracting a negative exponent.

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Question 3/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(x\neq0\) है तो (\frac{\(x^3\)2\cdot x^{-4}}{x}) का सरल रूप क्या है?

If \(x\neq0\), what is the simplified form of (\frac{\(x^3\)2\cdot x^{-4}}{x})?

Explanation opens after your attempt
Correct Answer

A. (x)

Explanation

Simple Explanation

पहले (\(x^3\)2=x-6), फिर घात (6-4-1=1) है। इसलिए उत्तर (x) है। / First (\(x^3\)2=x-6), then the exponent is (6-4-1=1). So the answer is (x).

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Question 4/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{2^3\cdot5^3}{10^2}\right\)) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{2^3\cdot5^3}{10^2}\right\))?

Explanation opens after your attempt
Correct Answer

A. (10)

Explanation

Simple Explanation

क्योंकि (23\cdot53=(10)3), इसलिए \(\frac{10^3}{10^2}=10\)। समान घात वाले गुणकों को पहले जोड़ें। / Since (23\cdot53=(10)3), \(\frac{10^3}{10^2}=10\). Combine equal powers first.

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Question 5/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(\frac{16^2}{2^5}\) का मान क्या है?

What is the value of \(\frac{16^2}{2^5}\)?

Explanation opens after your attempt
Correct Answer

A. \(2^3\)

Explanation

Simple Explanation

(162=\(2^4\)2=28) होता है। इसलिए \(\frac{2^8}{2^5}=2^3\) है। / (162=\(2^4\)2=28). Therefore \(\frac{2^8}{2^5}=2^3\).

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Question 6/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((0.2)^{-2}) का मान क्या है?

What is the value of ((0.2)^{-2})?

Explanation opens after your attempt
Correct Answer

C. (25)

Explanation

Simple Explanation

\(0.2=\frac{1}{5}\), इसलिए ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25)। दशमलव को भिन्न में बदलना आसान होता है। / \(0.2=\frac{1}{5}\), so ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25). Converting decimals to fractions helps.

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Question 7/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\)) का मान क्या है?

What is the value of (\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\))?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2=\frac{4}{9}) है। इसलिए \(\frac{4}{9}\cdot\frac{9}{4}=1\) है। / (\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2=\frac{4}{9}). Hence \(\frac{4}{9}\cdot\frac{9}{4}=1\).

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Question 8/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (a=2) है तो \(a^3+a^{-1}\) का मान क्या है?

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

Explanation opens after your attempt
Correct Answer

B. \(\frac{17}{2}\)

Explanation

Simple Explanation

\(2^3=8\) और \(2^{-1}=\frac{1}{2}\) है। इसलिए योग \(8+\frac{1}{2}=\frac{17}{2}\) है। / \(2^3=8\) and \(2^{-1}=\frac{1}{2}\). Thus the sum is \(8+\frac{1}{2}=\frac{17}{2}\).

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Question 9/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(x^2y^3\)2) का सही सरल रूप क्या है?

What is the correct simplified form of (\(x^2y^3\)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^4y^6\)

Explanation

Simple Explanation

बाहरी घात दोनों कारकों की घातों से गुणा होती है। इसलिए (\(x^2y^3\)2=x-4y-6) है। / The outside exponent multiplies the exponents of both factors. Hence (\(x^2y^3\)2=x-4y-6).

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Question 10/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\frac{\(2x^3\)2}{4x-2}) का सरल रूप क्या है यदि \(x\neq0\)?

What is the simplified form of (\frac{\(2x^3\)2}{4x-2}) if \(x\neq0\)?

Explanation opens after your attempt
Correct Answer

B. \(x^4\)

Explanation

Simple Explanation

(\(2x^3\)2=4x-6) होता है। फिर \(\frac{4x^6}{4x^2}=x^4\) है। / (\(2x^3\)2=4x-6). Then \(\frac{4x^6}{4x^2}=x^4\).

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Question 11/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (p(x)=2x-2-3x+1) है तो (p(2)) का मान क्या है?

If (p(x)=2x-2-3x+1), what is the value of (p(2))?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

(p(2)=2(2)2-3(2)+1=8-6+1=3)। प्रतिस्थापन में पहले घात निकालें। / (p(2)=2(2)2-3(2)+1=8-6+1=3). Evaluate powers first while substituting.

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Question 12/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (q(x)=x-3-2x-2+x) है तो (q(-1)) का मान क्या है?

If (q(x)=x-3-2x-2+x), what is the value of (q(-1))?

Explanation opens after your attempt
Correct Answer

A. (-4)

Explanation

Simple Explanation

(q(-1)=(-1)3-2(-1)2+(-1)=-1-2-1=-4)। ऋणात्मक संख्या पर कोष्ठक लगाना जरूरी है। / (q(-1)=(-1)3-2(-1)2+(-1)=-1-2-1=-4). Use parentheses with negative substitution.

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Question 13/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(3x^2+5x^2-2x^2\) का सरल रूप क्या है?

What is the simplified form of \(3x^2+5x^2-2x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(6x^2\)

Explanation

Simple Explanation

समान पदों के गुणांक (3+5-2=6) होते हैं। इसलिए सरल रूप \(6x^2\) है। / The coefficients of like terms are (3+5-2=6). Thus the simplified form is \(6x^2\).

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Question 14/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((x+2)+(3x-5)) का सरल रूप क्या है?

What is the simplified form of ((x+2)+(3x-5))?

Explanation opens after your attempt
Correct Answer

A. (4x-3)

Explanation

Simple Explanation

समान पद जोड़ने पर (x+3x=4x) और (2-5=-3) है। इसलिए उत्तर (4x-3) है। / Combining like terms gives (x+3x=4x) and (2-5=-3). So the answer is (4x-3).

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Question 15/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((5x+1)-(2x-4)) का सरल रूप क्या है?

What is the simplified form of ((5x+1)-(2x-4))?

Explanation opens after your attempt
Correct Answer

B. (3x+5)

Explanation

Simple Explanation

ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (5x+1-2x+4=3x+5) है। / The minus sign applies to both terms in the second bracket. (5x+1-2x+4=3x+5).

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Question 16/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(2x\(3x^2-4x+1\)) का विस्तार क्या है?

What is the expansion of (2x\(3x^2-4x+1\))?

Explanation opens after your attempt
Correct Answer

A. \(6x^3-8x^2+2x\)

Explanation

Simple Explanation

(2x) को हर पद से गुणा करें। इससे \(6x^3-8x^2+2x\) मिलता है। / Multiply (2x) by every term. This gives \(6x^3-8x^2+2x\).

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Question 17/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((x+3)(x+2)) का विस्तार क्या है?

What is the expansion of ((x+3)(x+2))?

Explanation opens after your attempt
Correct Answer

A. \(x^2+5x+6\)

Explanation

Simple Explanation

वितरण नियम से \(x^2+2x+3x+6=x^2+5x+6\)। मध्य पद समान पद जोड़कर बनता है। / By distribution, \(x^2+2x+3x+6=x^2+5x+6\). The middle term forms by combining like terms.

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Question 18/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((x-4)(x+1)) का विस्तार क्या है?

What is the expansion of ((x-4)(x+1))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x-4\)

Explanation

Simple Explanation

गुणा करने पर \(x^2+x-4x-4=x^2-3x-4\) मिलता है। चिह्नों पर विशेष ध्यान दें। / Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.

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Question 19/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((2x+3)(x-2)) का विस्तार क्या है?

What is the expansion of ((2x+3)(x-2))?

Explanation opens after your attempt
Correct Answer

A. \(2x^2-x-6\)

Explanation

Simple Explanation

वितरण से \(2x^2-4x+3x-6=2x^2-x-6\) है। समान पदों को अंत में जोड़ें। / By distribution, \(2x^2-4x+3x-6=2x^2-x-6\). Combine like terms at the end.

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Question 20/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((x+5)2) का सही विस्तार क्या है?

What is the correct expansion of ((x+5)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+10x+25\)

Explanation

Simple Explanation

((a+b)2=a-2+2ab+b-2) लगाएँ। यहाँ मध्य पद \(2\cdot x\cdot5=10x\) है। / Use ((a+b)2=a-2+2ab+b-2). Here the middle term is \(2\cdot x\cdot5=10x\).

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Question 21/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((x-6)2) का सही विस्तार क्या है?

What is the correct expansion of ((x-6)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-12x+36\)

Explanation

Simple Explanation

((a-b)2=a-2-2ab+b-2) होता है। इसलिए मध्य पद (-12x) है। / ((a-b)2=a-2-2ab+b-2). Therefore the middle term is (-12x).

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Question 22/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((x+7)(x-7)) का सरल रूप क्या है?

What is the simplified form of ((x+7)(x-7))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-49\)

Explanation

Simple Explanation

यह ((a+b)(a-b)=a-2-b-2) का रूप है। इसलिए ((x+7)(x-7)=x-2-49) है। / This is of the form ((a+b)(a-b)=a-2-b-2). Hence ((x+7)(x-7)=x-2-49).

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Question 23/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(49x^2-64\) का गुणनखंड रूप क्या है?

What is the factorized form of \(49x^2-64\)?

Explanation opens after your attempt
Correct Answer

A. ((7x-8)(7x+8))

Explanation

Simple Explanation

(49x-2-64=(7x)2-82) है। अंतर के वर्ग का नियम लगाएँ। / (49x-2-64=(7x)2-82). Apply the difference of squares identity.

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Question 24/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(x^2+14x+49\) किसके बराबर है?

What is \(x^2+14x+49\) equal to?

Explanation opens after your attempt
Correct Answer

A. ((x+7)2)

Explanation

Simple Explanation

यह \(x^2+2\cdot x\cdot7+7^2\) है। इसलिए यह ((x+7)2) है। / This is \(x^2+2\cdot x\cdot7+7^2\). Therefore it is ((x+7)2).

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Question 25/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(x^2-16x+64\) किसके बराबर है?

What is \(x^2-16x+64\) equal to?

Explanation opens after your attempt
Correct Answer

A. ((x-8)2)

Explanation

Simple Explanation

यह \(x^2-2\cdot x\cdot8+8^2\) का रूप है। इसलिए ((x-8)2) सही है। / This is of the form \(x^2-2\cdot x\cdot8+8^2\). Hence ((x-8)2) is correct.

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Question 26/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (m+n=9) और (mn=18) है तो \(m^2+n^2\) का मान क्या है?

If (m+n=9) and (mn=18), what is the value of \(m^2+n^2\)?

Explanation opens after your attempt
Correct Answer

A. (45)

Explanation

Simple Explanation

(m-2+n-2=(m+n)2-2mn=81-36=45)। पहचान का उपयोग गणना को छोटा करता है। / (m-2+n-2=(m+n)2-2mn=81-36=45). Using identities makes calculation shorter.

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Question 27/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (a-b=5) और (ab=6) है तो \(a^2+b^2\) का मान क्या है?

If (a-b=5) and (ab=6), what is the value of \(a^2+b^2\)?

Explanation opens after your attempt
Correct Answer

C. (37)

Explanation

Simple Explanation

(a-2+b-2=(a-b)2+2ab=25+12=37)। सही पहचान चुनना जरूरी है। / (a-2+b-2=(a-b)2+2ab=25+12=37). Choosing the correct identity is important.

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Question 28/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(99^2\) को पहचान से निकालने पर सही मान क्या है?

Using an identity, what is the correct value of \(99^2\)?

Explanation opens after your attempt
Correct Answer

A. (9801)

Explanation

Simple Explanation

(992=(100-1)2=10000-200+1=9801)। निकट संख्या की पहचान तेज गणना देती है। / (992=(100-1)2=10000-200+1=9801). Using a nearby number identity gives quick calculation.

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Question 29/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(102^2\) का मान क्या है?

What is the value of \(102^2\)?

Explanation opens after your attempt
Correct Answer

A. (10404)

Explanation

Simple Explanation

(1022=(100+2)2=10000+400+4=10404)। ((a+b)2) में मध्य पद न भूलें। / (1022=(100+2)2=10000+400+4=10404). Do not forget the middle term in ((a+b)2).

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Question 30/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(53\cdot47\) का मान पहचान से क्या है?

Using an identity, what is the value of \(53\cdot47\)?

Explanation opens after your attempt
Correct Answer

A. (2491)

Explanation

Simple Explanation

(53\cdot47=(50+3)(50-3)=502-32=2491)। यह अंतर के वर्ग का उपयोग है। / (53\cdot47=(50+3)(50-3)=502-32=2491). This uses the difference of squares identity.

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Question 31/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(1.5^2-0.5^2\) का मान क्या है?

What is the value of \(1.5^2-0.5^2\)?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

(a-2-b-2=(a-b)(a+b)) से ((1.5-0.5)(1.5+0.5)=1\cdot2=2)। पहचान दशमलव में भी लागू होती है। / Using (a-2-b-2=(a-b)(a+b)), ((1.5-0.5)(1.5+0.5)=1\cdot2=2). Identities also work with decimals.

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Question 32/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{1}{3}\right\)^{-2}+\left\(\frac{1}{2}\right\)^{-2}) का मान क्या है?

What is the value of (\left\(\frac{1}{3}\right\)^{-2}+\left\(\frac{1}{2}\right\)^{-2})?

Explanation opens after your attempt
Correct Answer

B. (13)

Explanation

Simple Explanation

(\left\(\frac{1}{3}\right\)^{-2}=9) और (\left\(\frac{1}{2}\right\)^{-2}=4) है। योग (13) है। / (\left\(\frac{1}{3}\right\)^{-2}=9) and (\left\(\frac{1}{2}\right\)^{-2}=4). The sum is (13).

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Question 33/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (a=3) और (b=2) है तो \(a^2b+ab^2\) का मान क्या है?

If (a=3) and (b=2), what is the value of \(a^2b+ab^2\)?

Explanation opens after your attempt
Correct Answer

B. (30)

Explanation

Simple Explanation

(a-2b+ab-2=ab(a+b)) है। इसलिए \(3\cdot2\cdot5=30\) है। / (a-2b+ab-2=ab(a+b)). Thus \(3\cdot2\cdot5=30\).

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Question 34/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(2x^3+6x^2\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?

What is obtained by taking the common factor from \(2x^3+6x^2\)?

Explanation opens after your attempt
Correct Answer

A. (2x-2(x+3))

Explanation

Simple Explanation

दोनों पदों में सामान्य गुणनखंड \(2x^2\) है। इसलिए रूप (2x-2(x+3)) है। / The common factor in both terms is \(2x^2\). Hence the form is (2x-2(x+3)).

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Question 35/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(15a^4b^2\div5a^2b\) का सरल रूप क्या है यदि \(a\neq0\) और \(b\neq0\)?

What is the simplified form of \(15a^4b^2\div5a^2b\) if \(a\neq0\) and \(b\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(3a^2b\)

Explanation

Simple Explanation

गुणांक \(\frac{15}{5}=3\), \(a^{4-2}=a^2\) और \(b^{2-1}=b\) है। इसलिए उत्तर \(3a^2b\) है। / The coefficient is \(\frac{15}{5}=3\), \(a^{4-2}=a^2\), and \(b^{2-1}=b\). So the answer is \(3a^2b\).

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Question 36/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(3x^2y\)\(4xy^3\)) का गुणनफल क्या है?

What is the product of (\(3x^2y\)\(4xy^3\))?

Explanation opens after your attempt
Correct Answer

A. \(12x^3y^4\)

Explanation

Simple Explanation

गुणांक (12), \(x^{2+1}=x^3\) और \(y^{1+3}=y^4\) है। समान आधार की घातें जोड़ें। / The coefficient is (12), \(x^{2+1}=x^3\), and \(y^{1+3}=y^4\). Add exponents of like bases.

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Question 37/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (x=2) है तो \(3x^3-4x^2+5\) का मान क्या है?

If (x=2), what is the value of \(3x^3-4x^2+5\)?

Explanation opens after your attempt
Correct Answer

B. (13)

Explanation

Simple Explanation

मान रखने पर (3(8)-4(4)+5=24-16+5=13)। घात पहले निकालना सही क्रम है। / Substituting gives (3(8)-4(4)+5=24-16+5=13). Calculating powers first is the correct order.

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Question 38/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (x=-2) है तो \(x^4-2x^3\) का मान क्या है?

If (x=-2), what is the value of \(x^4-2x^3\)?

Explanation opens after your attempt
Correct Answer

C. (32)

Explanation

Simple Explanation

((-2)4=16) और ((-2)3=-8) है। इसलिए (16-2(-8)=32) है। / ((-2)4=16) and ((-2)3=-8). Hence (16-2(-8)=32).

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Question 39/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(\frac{x^5y^{-2}}{x^2y^{-4}}\) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of \(\frac{x^5y^{-2}}{x^2y^{-4}}\) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(x^3y^2\)

Explanation

Simple Explanation

(x) की घात (5-2=3) और (y) की घात (-2-(-4)=2) है। इसलिए \(x^3y^2\) है। / The exponent of (x) is (5-2=3), and that of (y) is (-2-(-4)=2). Hence it is \(x^3y^2\).

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Question 40/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{x^{-2}}{y^{-3}}\right\)^{-1}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of (\left\(\frac{x^{-2}}{y^{-3}}\right\)^{-1}) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

अंदर \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\) है। बाहरी (-1) घात से \(\frac{x^2}{y^3}\) मिलता है। / Inside, \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\). The outside power (-1) gives \(\frac{x^2}{y^3}\).

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Question 41/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(2^3\right\)0+5^{-1}) का मान क्या है?

What is the value of (\left\(2^3\right\)0+5^{-1})?

Explanation opens after your attempt
Correct Answer

B. \(\frac{6}{5}\)

Explanation

Simple Explanation

(\left\(2^3\right\)0=1) और \(5^{-1}=\frac{1}{5}\) है। इसलिए योग \(\frac{6}{5}\) है। / (\left\(2^3\right\)0=1) and \(5^{-1}=\frac{1}{5}\). Therefore the sum is \(\frac{6}{5}\).

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Question 42/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(4^{-1}+2^{-2}\) का मान क्या है?

What is the value of \(4^{-1}+2^{-2}\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(4^{-1}=\frac{1}{4}\) और \(2^{-2}=\frac{1}{4}\) है। इसलिए योग \(\frac{1}{2}\) है। / \(4^{-1}=\frac{1}{4}\) and \(2^{-2}=\frac{1}{4}\). So the sum is \(\frac{1}{2}\).

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Question 43/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(2^5\cdot4^{-1}\) का मान क्या है?

What is the value of \(2^5\cdot4^{-1}\)?

Explanation opens after your attempt
Correct Answer

B. (8)

Explanation

Simple Explanation

(4^{-1}=\(2^2\)^{-1}=2^{-2}) है। इसलिए \(2^5\cdot2^{-2}=2^3=8\) है। / (4^{-1}=\(2^2\)^{-1}=2^{-2}). Hence \(2^5\cdot2^{-2}=2^3=8\).

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Question 44/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((2x-3)2) का विस्तार क्या है?

What is the expansion of ((2x-3)2)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2-12x+9\)

Explanation

Simple Explanation

((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=2x) और (b=3) हैं। / Use ((a-b)2=a-2-2ab+b-2). Here (a=2x) and (b=3).

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Question 45/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((3x+2)2) का विस्तार क्या है?

What is the expansion of ((3x+2)2)?

Explanation opens after your attempt
Correct Answer

A. \(9x^2+12x+4\)

Explanation

Simple Explanation

((a+b)2) में (a=3x) और (b=2) लें। मध्य पद \(2\cdot3x\cdot2=12x\) है। / Take (a=3x) and (b=2) in ((a+b)2). The middle term is \(2\cdot3x\cdot2=12x\).

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Question 46/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

((5x+4)(5x-4)) का सरल रूप क्या है?

What is the simplified form of ((5x+4)(5x-4))?

Explanation opens after your attempt
Correct Answer

A. \(25x^2-16\)

Explanation

Simple Explanation

((a+b)(a-b)=a-2-b-2) है। यहाँ (a=5x) और (b=4) हैं। / ((a+b)(a-b)=a-2-b-2). Here (a=5x) and (b=4).

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Question 47/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(2^x=32\) है तो (x) का मान क्या है?

If \(2^x=32\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

क्योंकि \(32=2^5\), इसलिए \(2^x=2^5\) से (x=5)। समान आधार होने पर घातें बराबर होती हैं। / Since \(32=2^5\), \(2^x=2^5\) gives (x=5). Equal bases have equal exponents.

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Question 48/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(3^{x+1}=81\) है तो (x) का मान क्या है?

If \(3^{x+1}=81\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (3)

Explanation

Simple Explanation

\(81=3^4\), इसलिए (x+1=4) है। इससे (x=3) मिलता है। / \(81=3^4\), so (x+1=4). This gives (x=3).

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Question 49/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\frac{\(5^2\)3}{54\cdot5^{-1}}) का सरल रूप क्या है?

What is the simplified form of (\frac{\(5^2\)3}{54\cdot5^{-1}})?

Explanation opens after your attempt
Correct Answer

A. \(5^3\)

Explanation

Simple Explanation

पहले (\(5^2\)3=56) होता है। कुल घात (6-4-(-1)=3) है इसलिए उत्तर \(5^3\) है। / First (\(5^2\)3=56). The total exponent is (6-4-(-1)=3), so the answer is \(5^3\).

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Question 50/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\frac{\(3x^2y^{-1}\)2}{9xy^{-3}}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of (\frac{\(3x^2y^{-1}\)2}{9xy^{-3}}) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(x^3y\)

Explanation

Simple Explanation

ऊपर (\(3x^2y^{-1}\)2=9x-4y^{-2}) है। भाग देने पर \(x^{4-1}y^{-2-(-3)}=x^3y\) मिलता है। / The numerator is (\(3x^2y^{-1}\)2=9x-4y^{-2}). Dividing gives \(x^{4-1}y^{-2-(-3)}=x^3y\).

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Question 51/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(5^4\cdot5^{-2}\cdot5^3\) का सरल रूप क्या है?

What is the simplified form of \(5^4\cdot5^{-2}\cdot5^3\)?

Explanation opens after your attempt
Correct Answer

A. \(5^5\)

Explanation

Simple Explanation

समान आधार में घातें (4-2+3=5) जुड़ती हैं। इसलिए सरल रूप \(5^5\) है। / For the same base, exponents add as (4-2+3=5). Hence the simplified form is \(5^5\).

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Question 52/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\frac{7^3}{7^{-1}\cdot7^2}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{7^3}{7^{-1}\cdot7^2}\)?

Explanation opens after your attempt
Correct Answer

A. \(7^2\)

Explanation

Simple Explanation

हर में घात (-1+2=1) है। इसलिए कुल घात (3-1=2) होती है। / The denominator exponent is (-1+2=1). Therefore the total exponent is (3-1=2).

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Question 53/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(x\neq0\) है तो (\frac{\(x^2\)3\cdot x^{-1}}{x-2}) का सरल रूप क्या है?

If \(x\neq0\), what is the simplified form of (\frac{\(x^2\)3\cdot x^{-1}}{x-2})?

Explanation opens after your attempt
Correct Answer

B. \(x^3\)

Explanation

Simple Explanation

पहले (\(x^2\)3=x-6) है। कुल घात (6-1-2=3) मिलती है। / First (\(x^2\)3=x-6). The total exponent is (6-1-2=3).

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Question 54/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\frac{3^4\cdot2^4}{6^3}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{3^4\cdot2^4}{6^3}\)?

Explanation opens after your attempt
Correct Answer

A. (6)

Explanation

Simple Explanation

(34\cdot24=\(3\cdot2\)4=64) है। इसलिए \(\frac{6^4}{6^3}=6\) है। / (34\cdot24=\(3\cdot2\)4=64). Therefore \(\frac{6^4}{6^3}=6\).

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Question 55/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\frac{27^2}{3^4}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{27^2}{3^4}\)?

Explanation opens after your attempt
Correct Answer

A. \(3^2\)

Explanation

Simple Explanation

(272=\(3^3\)2=36) होता है। इसलिए \(\frac{3^6}{3^4}=3^2\) है। / (272=\(3^3\)2=36). Therefore \(\frac{3^6}{3^4}=3^2\).

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Question 56/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((0.25)^{-2}) का मान क्या है?

What is the value of ((0.25)^{-2})?

Explanation opens after your attempt
Correct Answer

C. (16)

Explanation

Simple Explanation

\(0.25=\frac{1}{4}\) है। इसलिए ((0.25)^{-2}=\left\(\frac{1}{4}\right\)^{-2}=16) होता है। / \(0.25=\frac{1}{4}\). Therefore ((0.25)^{-2}=\left\(\frac{1}{4}\right\)^{-2}=16).

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Question 57/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{4}{3}\right\)^{-2}\cdot\left\(\frac{16}{9}\right\)) का मान क्या है?

What is the value of (\left\(\frac{4}{3}\right\)^{-2}\cdot\left\(\frac{16}{9}\right\))?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(\left\(\frac{4}{3}\right\)^{-2}=\left\(\frac{3}{4}\right\)2=\frac{9}{16}) है। इसलिए \(\frac{9}{16}\cdot\frac{16}{9}=1\) है। / (\left\(\frac{4}{3}\right\)^{-2}=\left\(\frac{3}{4}\right\)2=\frac{9}{16}). Hence \(\frac{9}{16}\cdot\frac{16}{9}=1\).

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Question 58/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (a=3) है तो \(a^2+a^{-1}\) का मान क्या है?

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

Explanation opens after your attempt
Correct Answer

B. \(\frac{28}{3}\)

Explanation

Simple Explanation

\(3^2=9\) और \(3^{-1}=\frac{1}{3}\) है। इसलिए योग \(9+\frac{1}{3}=\frac{28}{3}\) है। / \(3^2=9\) and \(3^{-1}=\frac{1}{3}\). Thus the sum is \(9+\frac{1}{3}=\frac{28}{3}\).

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Question 59/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(a^3b^2\)3) का सही सरल रूप क्या है?

What is the correct simplified form of (\(a^3b^2\)3)?

Explanation opens after your attempt
Correct Answer

A. \(a^9b^6\)

Explanation

Simple Explanation

बाहरी घात प्रत्येक कारक की घात से गुणा होती है। इसलिए (\(a^3b^2\)3=a-9b-6) है। / The outside exponent multiplies the exponent of each factor. Hence (\(a^3b^2\)3=a-9b-6).

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Question 60/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\frac{\(3x^2\)2}{9x}) का सरल रूप क्या है यदि \(x\neq0\)?

What is the simplified form of (\frac{\(3x^2\)2}{9x}) if \(x\neq0\)?

Explanation opens after your attempt
Correct Answer

B. \(x^3\)

Explanation

Simple Explanation

(\(3x^2\)2=9x-4) होता है। फिर \(\frac{9x^4}{9x}=x^3\) है। / (\(3x^2\)2=9x-4). Then \(\frac{9x^4}{9x}=x^3\).

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Question 61/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (p(x)=3x-2-2x+4) है तो (p(2)) का मान क्या है?

If (p(x)=3x-2-2x+4), what is the value of (p(2))?

Explanation opens after your attempt
Correct Answer

C. (12)

Explanation

Simple Explanation

(p(2)=3(2)2-2(2)+4=12-4+4=12)। प्रतिस्थापन में पहले घात निकालें। / (p(2)=3(2)2-2(2)+4=12-4+4=12). Evaluate powers first while substituting.

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Question 62/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (q(x)=2x-3+x-2-3x) है तो (q(-1)) का मान क्या है?

If (q(x)=2x-3+x-2-3x), what is the value of (q(-1))?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

(q(-1)=2(-1)3+(-1)2-3(-1)=-2+1+3=2)। ऋणात्मक मान रखते समय कोष्ठक लगाएँ। / (q(-1)=2(-1)3+(-1)2-3(-1)=-2+1+3=2). Use parentheses for negative substitution.

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Question 63/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(4x^3+7x^3-5x^3\) का सरल रूप क्या है?

What is the simplified form of \(4x^3+7x^3-5x^3\)?

Explanation opens after your attempt
Correct Answer

A. \(6x^3\)

Explanation

Simple Explanation

समान पदों के गुणांक (4+7-5=6) हैं। इसलिए सरल रूप \(6x^3\) है। / The coefficients of like terms are (4+7-5=6). Thus the simplified form is \(6x^3\).

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Question 64/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((2x+3)+(4x-7)) का सरल रूप क्या है?

What is the simplified form of ((2x+3)+(4x-7))?

Explanation opens after your attempt
Correct Answer

A. (6x-4)

Explanation

Simple Explanation

समान पद जोड़ने पर (2x+4x=6x) और (3-7=-4) है। इसलिए उत्तर (6x-4) है। / Combining like terms gives (2x+4x=6x) and (3-7=-4). So the answer is (6x-4).

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Question 65/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((7x-2)-(3x+5)) का सरल रूप क्या है?

What is the simplified form of ((7x-2)-(3x+5))?

Explanation opens after your attempt
Correct Answer

A. (4x-7)

Explanation

Simple Explanation

ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (7x-2-3x-5=4x-7) है। / The minus sign applies to both terms in the second bracket. (7x-2-3x-5=4x-7).

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Question 66/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(3x\(2x^2-5x+4\)) का विस्तार क्या है?

What is the expansion of (3x\(2x^2-5x+4\))?

Explanation opens after your attempt
Correct Answer

A. \(6x^3-15x^2+12x\)

Explanation

Simple Explanation

(3x) को हर पद से गुणा करें। इससे \(6x^3-15x^2+12x\) मिलता है। / Multiply (3x) by every term. This gives \(6x^3-15x^2+12x\).

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Question 67/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+4)(x+3)) का विस्तार क्या है?

What is the expansion of ((x+4)(x+3))?

Explanation opens after your attempt
Correct Answer

A. \(x^2+7x+12\)

Explanation

Simple Explanation

वितरण नियम से \(x^2+3x+4x+12=x^2+7x+12\) मिलता है। समान पदों को जोड़ें। / By distribution, \(x^2+3x+4x+12=x^2+7x+12\). Combine like terms.

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Question 68/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x-5)(x+2)) का विस्तार क्या है?

What is the expansion of ((x-5)(x+2))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x-10\)

Explanation

Simple Explanation

गुणा करने पर \(x^2+2x-5x-10=x^2-3x-10\) है। चिह्नों पर ध्यान दें। / Multiplying gives \(x^2+2x-5x-10=x^2-3x-10\). Pay attention to signs.

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Question 69/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((3x+1)(x-4)) का विस्तार क्या है?

What is the expansion of ((3x+1)(x-4))?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-11x-4\)

Explanation

Simple Explanation

वितरण से \(3x^2-12x+x-4=3x^2-11x-4\) है। बीच के समान पद जोड़ें। / By distribution, \(3x^2-12x+x-4=3x^2-11x-4\). Combine the middle like terms.

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Question 70/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+8)2) का सही विस्तार क्या है?

What is the correct expansion of ((x+8)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+16x+64\)

Explanation

Simple Explanation

((a+b)2=a-2+2ab+b-2) लगाएँ। यहाँ मध्य पद \(2\cdot x\cdot8=16x\) है। / Use ((a+b)2=a-2+2ab+b-2). Here the middle term is \(2\cdot x\cdot8=16x\).

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Question 71/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x-9)2) का सही विस्तार क्या है?

What is the correct expansion of ((x-9)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-18x+81\)

Explanation

Simple Explanation

((a-b)2=a-2-2ab+b-2) होता है। इसलिए मध्य पद (-18x) है। / ((a-b)2=a-2-2ab+b-2). Therefore the middle term is (-18x).

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Question 72/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+9)(x-9)) का सरल रूप क्या है?

What is the simplified form of ((x+9)(x-9))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-81\)

Explanation

Simple Explanation

यह ((a+b)(a-b)=a-2-b-2) का रूप है। इसलिए उत्तर \(x^2-81\) है। / This is of the form ((a+b)(a-b)=a-2-b-2). Therefore the answer is \(x^2-81\).

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Question 73/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(64x^2-81\) का गुणनखंड रूप क्या है?

What is the factorized form of \(64x^2-81\)?

Explanation opens after your attempt
Correct Answer

A. ((8x-9)(8x+9))

Explanation

Simple Explanation

(64x-2-81=(8x)2-92) है। अंतर के वर्ग का नियम लगाएँ। / (64x-2-81=(8x)2-92). Apply the difference of squares identity.

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Question 74/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(x^2+18x+81\) किसके बराबर है?

What is \(x^2+18x+81\) equal to?

Explanation opens after your attempt
Correct Answer

A. ((x+9)2)

Explanation

Simple Explanation

यह \(x^2+2\cdot x\cdot9+9^2\) है। इसलिए यह ((x+9)2) है। / This is \(x^2+2\cdot x\cdot9+9^2\). Therefore it is ((x+9)2).

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Question 75/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(x^2-20x+100\) किसके बराबर है?

What is \(x^2-20x+100\) equal to?

Explanation opens after your attempt
Correct Answer

A. ((x-10)2)

Explanation

Simple Explanation

यह \(x^2-2\cdot x\cdot10+10^2\) है। इसलिए ((x-10)2) सही है। / This is \(x^2-2\cdot x\cdot10+10^2\). Hence ((x-10)2) is correct.

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Question 76/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (m+n=11) और (mn=24) है तो \(m^2+n^2\) का मान क्या है?

If (m+n=11) and (mn=24), what is the value of \(m^2+n^2\)?

Explanation opens after your attempt
Correct Answer

A. (73)

Explanation

Simple Explanation

(m-2+n-2=(m+n)2-2mn=121-48=73)। पहचान से गणना छोटी होती है। / (m-2+n-2=(m+n)2-2mn=121-48=73). Using an identity shortens the calculation.

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Question 77/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (a-b=7) और (ab=10) है तो \(a^2+b^2\) का मान क्या है?

If (a-b=7) and (ab=10), what is the value of \(a^2+b^2\)?

Explanation opens after your attempt
Correct Answer

C. (69)

Explanation

Simple Explanation

(a-2+b-2=(a-b)2+2ab=49+20=69)। सही पहचान चुनें। / (a-2+b-2=(a-b)2+2ab=49+20=69). Choose the correct identity.

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Question 78/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(98^2\) को पहचान से निकालने पर सही मान क्या है?

Using an identity, what is the correct value of \(98^2\)?

Explanation opens after your attempt
Correct Answer

A. (9604)

Explanation

Simple Explanation

(982=(100-2)2=10000-400+4=9604)। निकट संख्या की पहचान तेज गणना देती है। / (982=(100-2)2=10000-400+4=9604). Using a nearby number identity gives quick calculation.

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Question 79/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(103^2\) का मान क्या है?

What is the value of \(103^2\)?

Explanation opens after your attempt
Correct Answer

A. (10609)

Explanation

Simple Explanation

(1032=(100+3)2=10000+600+9=10609)। ((a+b)2) में मध्य पद न भूलें। / (1032=(100+3)2=10000+600+9=10609). Do not forget the middle term in ((a+b)2).

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Question 80/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(64\cdot56\) का मान पहचान से क्या है?

Using an identity, what is the value of \(64\cdot56\)?

Explanation opens after your attempt
Correct Answer

A. (3584)

Explanation

Simple Explanation

(64\cdot56=(60+4)(60-4)=602-42=3584)। यह अंतर के वर्ग का उपयोग है। / (64\cdot56=(60+4)(60-4)=602-42=3584). This uses the difference of squares identity.

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Question 81/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(2.5^2-1.5^2\) का मान क्या है?

What is the value of \(2.5^2-1.5^2\)?

Explanation opens after your attempt
Correct Answer

C. (4)

Explanation

Simple Explanation

(a-2-b-2=(a-b)(a+b)) से ((2.5-1.5)(2.5+1.5)=1\cdot4=4)। पहचान दशमलव में भी लागू होती है। / Using (a-2-b-2=(a-b)(a+b)), ((2.5-1.5)(2.5+1.5)=1\cdot4=4). Identities also work with decimals.

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Question 82/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{1}{4}\right\)^{-2}+\left\(\frac{1}{5}\right\)^{-2}) का मान क्या है?

What is the value of (\left\(\frac{1}{4}\right\)^{-2}+\left\(\frac{1}{5}\right\)^{-2})?

Explanation opens after your attempt
Correct Answer

B. (41)

Explanation

Simple Explanation

(\left\(\frac{1}{4}\right\)^{-2}=16) और (\left\(\frac{1}{5}\right\)^{-2}=25) है। योग (41) है। / (\left\(\frac{1}{4}\right\)^{-2}=16) and (\left\(\frac{1}{5}\right\)^{-2}=25). The sum is (41).

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Question 83/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (a=4) और (b=1) है तो \(a^2b+ab^2\) का मान क्या है?

If (a=4) and (b=1), what is the value of \(a^2b+ab^2\)?

Explanation opens after your attempt
Correct Answer

C. (20)

Explanation

Simple Explanation

(a-2b+ab-2=ab(a+b)) है। इसलिए \(4\cdot1\cdot5=20\) है। / (a-2b+ab-2=ab(a+b)). Thus \(4\cdot1\cdot5=20\).

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Question 84/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(3x^4+9x^3\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?

What is obtained by taking the common factor from \(3x^4+9x^3\)?

Explanation opens after your attempt
Correct Answer

A. (3x-3(x+3))

Explanation

Simple Explanation

दोनों पदों में सामान्य गुणनखंड \(3x^3\) है। इसलिए रूप (3x-3(x+3)) है। / The common factor in both terms is \(3x^3\). Hence the form is (3x-3(x+3)).

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Question 85/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(24a^5b^3\div6a^2b^2\) का सरल रूप क्या है यदि \(a\neq0\) और \(b\neq0\)?

What is the simplified form of \(24a^5b^3\div6a^2b^2\) if \(a\neq0\) and \(b\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(4a^3b\)

Explanation

Simple Explanation

गुणांक \(\frac{24}{6}=4\), \(a^{5-2}=a^3\) और \(b^{3-2}=b\) है। इसलिए उत्तर \(4a^3b\) है। / The coefficient is \(\frac{24}{6}=4\), \(a^{5-2}=a^3\), and \(b^{3-2}=b\). So the answer is \(4a^3b\).

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Question 86/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(5x^3y\)\(2xy^2\)) का गुणनफल क्या है?

What is the product of (\(5x^3y\)\(2xy^2\))?

Explanation opens after your attempt
Correct Answer

A. \(10x^4y^3\)

Explanation

Simple Explanation

गुणांक (10), \(x^{3+1}=x^4\) और \(y^{1+2}=y^3\) है। समान आधार की घातें जोड़ें। / The coefficient is (10), \(x^{3+1}=x^4\), and \(y^{1+2}=y^3\). Add exponents of like bases.

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Question 87/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (x=3) है तो \(2x^3-5x^2+4\) का मान क्या है?

If (x=3), what is the value of \(2x^3-5x^2+4\)?

Explanation opens after your attempt
Correct Answer

C. (13)

Explanation

Simple Explanation

मान रखने पर (2(27)-5(9)+4=54-45+4=13)। घात पहले निकालना सही क्रम है। / Substituting gives (2(27)-5(9)+4=54-45+4=13). Calculating powers first is the correct order.

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Question 88/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (x=-3) है तो \(x^4+x^3\) का मान क्या है?

If (x=-3), what is the value of \(x^4+x^3\)?

Explanation opens after your attempt
Correct Answer

B. (54)

Explanation

Simple Explanation

((-3)4=81) और ((-3)3=-27) है। इसलिए (81-27=54) है। / ((-3)4=81) and ((-3)3=-27). Hence (81-27=54).

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Question 89/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\frac{x^6y^{-3}}{x^3y^{-5}}\) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of \(\frac{x^6y^{-3}}{x^3y^{-5}}\) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(x^3y^2\)

Explanation

Simple Explanation

(x) की घात (6-3=3) और (y) की घात (-3-(-5)=2) है। इसलिए \(x^3y^2\) है। / The exponent of (x) is (6-3=3), and that of (y) is (-3-(-5)=2). Hence it is \(x^3y^2\).

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Question 90/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{x^{-3}}{y^{-2}}\right\)^{-1}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of (\left\(\frac{x^{-3}}{y^{-2}}\right\)^{-1}) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

अंदर \(\frac{x^{-3}}{y^{-2}}=x^{-3}y^2\) है। बाहरी (-1) घात से \(\frac{x^3}{y^2}\) मिलता है। / Inside, \(\frac{x^{-3}}{y^{-2}}=x^{-3}y^2\). The outside power (-1) gives \(\frac{x^3}{y^2}\).

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Question 91/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(3^2\right\)0+4^{-1}) का मान क्या है?

What is the value of (\left\(3^2\right\)0+4^{-1})?

Explanation opens after your attempt
Correct Answer

B. \(\frac{5}{4}\)

Explanation

Simple Explanation

(\left\(3^2\right\)0=1) और \(4^{-1}=\frac{1}{4}\) है। इसलिए योग \(\frac{5}{4}\) है। / (\left\(3^2\right\)0=1) and \(4^{-1}=\frac{1}{4}\). Therefore the sum is \(\frac{5}{4}\).

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Question 92/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(9^{-1}+3^{-2}\) का मान क्या है?

What is the value of \(9^{-1}+3^{-2}\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

\(9^{-1}=\frac{1}{9}\) और \(3^{-2}=\frac{1}{9}\) है। इसलिए योग \(\frac{2}{9}\) है। / \(9^{-1}=\frac{1}{9}\) and \(3^{-2}=\frac{1}{9}\). So the sum is \(\frac{2}{9}\).

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Question 93/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(3^5\cdot9^{-1}\) का मान क्या है?

What is the value of \(3^5\cdot9^{-1}\)?

Explanation opens after your attempt
Correct Answer

B. (27)

Explanation

Simple Explanation

(9^{-1}=\(3^2\)^{-1}=3^{-2}) है। इसलिए \(3^5\cdot3^{-2}=3^3=27\) है। / (9^{-1}=\(3^2\)^{-1}=3^{-2}). Hence \(3^5\cdot3^{-2}=3^3=27\).

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Question 94/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((3x-4)2) का विस्तार क्या है?

What is the expansion of ((3x-4)2)?

Explanation opens after your attempt
Correct Answer

A. \(9x^2-24x+16\)

Explanation

Simple Explanation

((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=3x) और (b=4) हैं। / Use ((a-b)2=a-2-2ab+b-2). Here (a=3x) and (b=4).

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Question 95/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((4x+3)2) का विस्तार क्या है?

What is the expansion of ((4x+3)2)?

Explanation opens after your attempt
Correct Answer

A. \(16x^2+24x+9\)

Explanation

Simple Explanation

((a+b)2) में (a=4x) और (b=3) लें। मध्य पद \(2\cdot4x\cdot3=24x\) है। / Take (a=4x) and (b=3) in ((a+b)2). The middle term is \(2\cdot4x\cdot3=24x\).

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Question 96/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((6x+5)(6x-5)) का सरल रूप क्या है?

What is the simplified form of ((6x+5)(6x-5))?

Explanation opens after your attempt
Correct Answer

A. \(36x^2-25\)

Explanation

Simple Explanation

((a+b)(a-b)=a-2-b-2) है। यहाँ (a=6x) और (b=5) हैं। / ((a+b)(a-b)=a-2-b-2). Here (a=6x) and (b=5).

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Question 97/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(2^{x+1}=64\) है तो (x) का मान क्या है?

If \(2^{x+1}=64\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

क्योंकि \(64=2^6\), इसलिए (x+1=6) है। इससे (x=5) मिलता है। / Since \(64=2^6\), (x+1=6). This gives (x=5).

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Question 98/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(5^{x-2}=125\) है तो (x) का मान क्या है?

If \(5^{x-2}=125\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

\(125=5^3\), इसलिए (x-2=3) है। इससे (x=5) मिलता है। / \(125=5^3\), so (x-2=3). This gives (x=5).

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Question 99/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\frac{\(2^3\)2\cdot4^{-1}}{8}) का सरल रूप क्या है?

What is the simplified form of (\frac{\(2^3\)2\cdot4^{-1}}{8})?

Explanation opens after your attempt
Correct Answer

A. (2)

Explanation

Simple Explanation

(\(2^3\)2=26), \(4^{-1}=2^{-2}\) और \(8=2^3\) है। कुल घात (6-2-3=1) है इसलिए उत्तर (2) है। / (\(2^3\)2=26), \(4^{-1}=2^{-2}\), and \(8=2^3\). The total exponent is (6-2-3=1), so the answer is (2).

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Question 100/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(81x^2-100y^2\) का गुणनखंड रूप क्या है?

What is the factorized form of \(81x^2-100y^2\)?

Explanation opens after your attempt
Correct Answer

A. ((9x-10y)(9x+10y))

Explanation

Simple Explanation

(81x-2-100y-2=(9x)2-(10y)2) है। अंतर के वर्ग का नियम (\(a^2-b^2\)=(a-b)(a+b)) लगाएँ। / (81x-2-100y-2=(9x)2-(10y)2). Apply the difference of squares rule (\(a^2-b^2\)=(a-b)(a+b)).

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Question 101/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\frac{\(3^2\)4}{35\cdot3^{-2}}) का सरल रूप क्या है?

What is the simplified form of (\frac{\(3^2\)4}{35\cdot3^{-2}})?

Explanation opens after your attempt
Correct Answer

A. \(3^5\)

Explanation

Simple Explanation

पहले (\(3^2\)4=38) और हर की घात (5-2=3) है। इसलिए कुल घात (8-3=5) होती है। / First (\(3^2\)4=38) and the denominator exponent is (5-2=3). Therefore the total exponent is (8-3=5).

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Question 102/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

सरलीकृत कीजिए: (\(3^2\)3 \div 34) का मान किसके बराबर है?

Simplify: (\(3^2\)3 \div 34) is equal to which value?

Explanation opens after your attempt
Correct Answer

A. \(,3^2,\)

Explanation

Simple Explanation

घात के नियम से (\(3^2\)3=36) और \(3^6 \div 3^4=3^2\) होता है। परीक्षा में पहले power of power का नियम लगाएं फिर division का। / By exponent laws, (\(3^2\)3=36) and \(3^6 \div 3^4=3^2\). In exams, apply power of a power first and then the division law.

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Question 103/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(\frac{4^3\cdot2^{-1}}{8}\) का मान क्या है?

What is the value of \(\frac{4^3\cdot2^{-1}}{8}\)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

(43=\(2^2\)3=26), \(2^{-1}\) और \(8=2^3\) है। कुल घात (6-1-3=2) है इसलिए मान \(2^2=4\) है। / (43=\(2^2\)3=26), \(2^{-1}\), and \(8=2^3\). The total exponent is (6-1-3=2), so the value is \(2^2=4\).

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Question 104/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(\dfrac{2^5 \times 8}{4^2}\) को घात के रूप में सरल किया जाए, तो इसका मान क्या होगा?

If \(\dfrac{2^5 \times 8}{4^2}\) is simplified using exponents, what is its value?

Explanation opens after your attempt
Correct Answer

A. (,16,)

Explanation

Simple Explanation

यहां \(8=2^3\) और (42=\(2^2\)2=24), इसलिए \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\)। परीक्षा में सभी संख्याओं को समान आधार में बदलना उपयोगी होता है। / Here \(8=2^3\) and (42=\(2^2\)2=24), so \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\). In exams, converting numbers to the same base is useful.

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Question 105/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(x\neq0\) है तो \(\frac{x^7\cdot x^{-3}}{x^2}\) का सरल रूप क्या है?

If \(x\neq0\), what is the simplified form of \(\frac{x^7\cdot x^{-3}}{x^2}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2\)

Explanation

Simple Explanation

समान आधार (x) की कुल घात (7-3-2=2) है। इसलिए सरल रूप \(x^2\) है। / The total exponent of the same base (x) is (7-3-2=2). Hence the simplified form is \(x^2\).

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Question 106/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\(2a^2b^3\)2) का सही विस्तार क्या है?

What is the correct expansion of (\(2a^2b^3\)2)?

Explanation opens after your attempt
Correct Answer

A. \(4a^4b^6\)

Explanation

Simple Explanation

बाहरी घात गुणांक और सभी घातों पर लगती है। इसलिए (\(2a^2b^3\)2=4a-4b-6) है। / The outside exponent applies to the coefficient and all powers. Thus (\(2a^2b^3\)2=4a-4b-6).

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Question 107/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(\frac{18x^5y^3}{6x^2y}\) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of \(\frac{18x^5y^3}{6x^2y}\) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(3x^3y^2\)

Explanation

Simple Explanation

गुणांक \(\frac{18}{6}=3\), \(x^{5-2}=x^3\) और \(y^{3-1}=y^2\) है। इसलिए उत्तर \(3x^3y^2\) है। / The coefficient is \(\frac{18}{6}=3\), \(x^{5-2}=x^3\), and \(y^{3-1}=y^2\). So the answer is \(3x^3y^2\).

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Question 108/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{1}{5}\right\)^{-2}+\left\(\frac{1}{3}\right\)^{-2}) का मान क्या है?

What is the value of (\left\(\frac{1}{5}\right\)^{-2}+\left\(\frac{1}{3}\right\)^{-2})?

Explanation opens after your attempt
Correct Answer

B. (34)

Explanation

Simple Explanation

(\left\(\frac{1}{5}\right\)^{-2}=25) और (\left\(\frac{1}{3}\right\)^{-2}=9) है। इसलिए योग (34) है। / (\left\(\frac{1}{5}\right\)^{-2}=25) and (\left\(\frac{1}{3}\right\)^{-2}=9). Therefore the sum is (34).

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Question 109/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((0.04)^{-1}) का मान क्या है?

What is the value of ((0.04)^{-1})?

Explanation opens after your attempt
Correct Answer

B. (25)

Explanation

Simple Explanation

\(0.04=\frac{4}{100}=\frac{1}{25}\) है। इसलिए ((0.04)^{-1}=25) होता है। / \(0.04=\frac{4}{100}=\frac{1}{25}\). Therefore ((0.04)^{-1}=25).

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Question 110/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (a=5) है तो \(a^2-a^{-1}\) का मान क्या है?

If (a=5), what is the value of \(a^2-a^{-1}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{124}{5}\)

Explanation

Simple Explanation

\(5^2=25\) और \(5^{-1}=\frac{1}{5}\) है। इसलिए \(25-\frac{1}{5}=\frac{124}{5}\) है। / \(5^2=25\) and \(5^{-1}=\frac{1}{5}\). Thus \(25-\frac{1}{5}=\frac{124}{5}\).

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Question 111/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (p(x)=4x-2-5x+2) है तो (p(3)) का मान क्या है?

If (p(x)=4x-2-5x+2), what is the value of (p(3))?

Explanation opens after your attempt
Correct Answer

B. (23)

Explanation

Simple Explanation

(p(3)=4(3)2-5(3)+2=36-15+2=23)। प्रतिस्थापन में पहले घात निकालें। / (p(3)=4(3)2-5(3)+2=36-15+2=23). Evaluate powers first while substituting.

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Question 112/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (q(x)=x-3+2x-2-4x) है तो (q(-2)) का मान क्या है?

If (q(x)=x-3+2x-2-4x), what is the value of (q(-2))?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(q(-2)=(-2)3+2(-2)2-4(-2)=-8+8+8=8)। ऋणात्मक मान रखते समय कोष्ठक लगाएँ। / (q(-2)=(-2)3+2(-2)2-4(-2)=-8+8+8=8). Use parentheses for negative substitution.

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Question 113/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(5x^2-3x^2+7x^2\) का सरल रूप क्या है?

What is the simplified form of \(5x^2-3x^2+7x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(9x^2\)

Explanation

Simple Explanation

समान पदों के गुणांक (5-3+7=9) हैं। इसलिए सरल रूप \(9x^2\) है। / The coefficients of like terms are (5-3+7=9). Thus the simplified form is \(9x^2\).

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Question 114/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((3x+4)+(5x-9)) का सरल रूप क्या है?

What is the simplified form of ((3x+4)+(5x-9))?

Explanation opens after your attempt
Correct Answer

A. (8x-5)

Explanation

Simple Explanation

समान पद जोड़ने पर (3x+5x=8x) और (4-9=-5) है। इसलिए उत्तर (8x-5) है। / Combining like terms gives (3x+5x=8x) and (4-9=-5). So the answer is (8x-5).

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Question 115/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((9x+2)-(4x-6)) का सरल रूप क्या है?

What is the simplified form of ((9x+2)-(4x-6))?

Explanation opens after your attempt
Correct Answer

B. (5x+8)

Explanation

Simple Explanation

ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (9x+2-4x+6=5x+8) है। / The minus sign applies to both terms in the second bracket. (9x+2-4x+6=5x+8).

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Question 116/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(4x\(3x^2-2x+5\)) का विस्तार क्या है?

What is the expansion of (4x\(3x^2-2x+5\))?

Explanation opens after your attempt
Correct Answer

A. \(12x^3-8x^2+20x\)

Explanation

Simple Explanation

(4x) को हर पद से गुणा करें। इससे \(12x^3-8x^2+20x\) मिलता है। / Multiply (4x) by every term. This gives \(12x^3-8x^2+20x\).

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Question 117/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((x+6)(x+4)) का विस्तार क्या है?

What is the expansion of ((x+6)(x+4))?

Explanation opens after your attempt
Correct Answer

A. \(x^2+10x+24\)

Explanation

Simple Explanation

वितरण नियम से \(x^2+4x+6x+24=x^2+10x+24\) मिलता है। मध्य पद समान पद जोड़कर बनता है। / By distribution, \(x^2+4x+6x+24=x^2+10x+24\). The middle term forms by combining like terms.

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Question 118/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((x-7)(x+3)) का विस्तार क्या है?

What is the expansion of ((x-7)(x+3))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-21\)

Explanation

Simple Explanation

गुणा करने पर \(x^2+3x-7x-21=x^2-4x-21\) है। चिह्नों पर ध्यान दें। / Multiplying gives \(x^2+3x-7x-21=x^2-4x-21\). Pay attention to signs.

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Question 119/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((4x+5)(x-3)) का विस्तार क्या है?

What is the expansion of ((4x+5)(x-3))?

Explanation opens after your attempt
Correct Answer

A. \(4x^2-7x-15\)

Explanation

Simple Explanation

वितरण से \(4x^2-12x+5x-15=4x^2-7x-15\) है। समान पदों को अंत में जोड़ें। / By distribution, \(4x^2-12x+5x-15=4x^2-7x-15\). Combine like terms at the end.

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Question 120/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((x+10)2) का सही विस्तार क्या है?

What is the correct expansion of ((x+10)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+20x+100\)

Explanation

Simple Explanation

((a+b)2=a-2+2ab+b-2) लगाएँ। यहाँ मध्य पद \(2\cdot x\cdot10=20x\) है। / Use ((a+b)2=a-2+2ab+b-2). Here the middle term is \(2\cdot x\cdot10=20x\).

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Question 121/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((x-11)2) का सही विस्तार क्या है?

What is the correct expansion of ((x-11)2)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-22x+121\)

Explanation

Simple Explanation

((a-b)2=a-2-2ab+b-2) होता है। इसलिए मध्य पद (-22x) है। / ((a-b)2=a-2-2ab+b-2). Therefore the middle term is (-22x).

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Question 122/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((x+12)(x-12)) का सरल रूप क्या है?

What is the simplified form of ((x+12)(x-12))?

Explanation opens after your attempt
Correct Answer

A. \(x^2-144\)

Explanation

Simple Explanation

यह ((a+b)(a-b)=a-2-b-2) का रूप है। इसलिए ((x+12)(x-12)=x-2-144) है। / This is of the form ((a+b)(a-b)=a-2-b-2). Hence ((x+12)(x-12)=x-2-144).

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Question 123/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(121x^2-144\) का गुणनखंड रूप क्या है?

What is the factorized form of \(121x^2-144\)?

Explanation opens after your attempt
Correct Answer

A. ((11x-12)(11x+12))

Explanation

Simple Explanation

(121x-2-144=(11x)2-122) है। अंतर के वर्ग का नियम लगाएँ। / (121x-2-144=(11x)2-122). Apply the difference of squares identity.

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Question 124/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(x^2+22x+121\) किसके बराबर है?

What is \(x^2+22x+121\) equal to?

Explanation opens after your attempt
Correct Answer

A. ((x+11)2)

Explanation

Simple Explanation

यह \(x^2+2\cdot x\cdot11+11^2\) है। इसलिए यह ((x+11)2) है। / This is \(x^2+2\cdot x\cdot11+11^2\). Therefore it is ((x+11)2).

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Question 125/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(x^2-24x+144\) किसके बराबर है?

What is \(x^2-24x+144\) equal to?

Explanation opens after your attempt
Correct Answer

A. ((x-12)2)

Explanation

Simple Explanation

यह \(x^2-2\cdot x\cdot12+12^2\) का रूप है। इसलिए ((x-12)2) सही है। / This is of the form \(x^2-2\cdot x\cdot12+12^2\). Hence ((x-12)2) is correct.

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Question 126/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (m+n=13) और (mn=36) है तो \(m^2+n^2\) का मान क्या है?

If (m+n=13) and (mn=36), what is the value of \(m^2+n^2\)?

Explanation opens after your attempt
Correct Answer

A. (97)

Explanation

Simple Explanation

(m-2+n-2=(m+n)2-2mn=169-72=97)। पहचान से गणना छोटी होती है। / (m-2+n-2=(m+n)2-2mn=169-72=97). Using an identity shortens the calculation.

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Question 127/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (a-b=8) और (ab=12) है तो \(a^2+b^2\) का मान क्या है?

If (a-b=8) and (ab=12), what is the value of \(a^2+b^2\)?

Explanation opens after your attempt
Correct Answer

C. (88)

Explanation

Simple Explanation

(a-2+b-2=(a-b)2+2ab=64+24=88)। सही पहचान चुनना जरूरी है। / (a-2+b-2=(a-b)2+2ab=64+24=88). Choosing the correct identity is important.

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Question 128/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(97^2\) को पहचान से निकालने पर सही मान क्या है?

Using an identity, what is the correct value of \(97^2\)?

Explanation opens after your attempt
Correct Answer

A. (9409)

Explanation

Simple Explanation

(972=(100-3)2=10000-600+9=9409)। निकट संख्या की पहचान तेज गणना देती है। / (972=(100-3)2=10000-600+9=9409). Using a nearby number identity gives quick calculation.

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Question 129/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(104^2\) का मान क्या है?

What is the value of \(104^2\)?

Explanation opens after your attempt
Correct Answer

A. (10816)

Explanation

Simple Explanation

(1042=(100+4)2=10000+800+16=10816)। ((a+b)2) में मध्य पद न भूलें। / (1042=(100+4)2=10000+800+16=10816). Do not forget the middle term in ((a+b)2).

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Question 130/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(72\cdot68\) का मान पहचान से क्या है?

Using an identity, what is the value of \(72\cdot68\)?

Explanation opens after your attempt
Correct Answer

A. (4896)

Explanation

Simple Explanation

(72\cdot68=(70+2)(70-2)=702-22=4896)। यह अंतर के वर्ग का उपयोग है। / (72\cdot68=(70+2)(70-2)=702-22=4896). This uses the difference of squares identity.

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Question 131/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(3.5^2-2.5^2\) का मान क्या है?

What is the value of \(3.5^2-2.5^2\)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

(a-2-b-2=(a-b)(a+b)) से ((3.5-2.5)(3.5+2.5)=1\cdot6=6)। पहचान दशमलव में भी लागू होती है। / Using (a-2-b-2=(a-b)(a+b)), ((3.5-2.5)(3.5+2.5)=1\cdot6=6). Identities also work with decimals.

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Question 132/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (a=2) और (b=5) है तो \(a^2b+ab^2\) का मान क्या है?

If (a=2) and (b=5), what is the value of \(a^2b+ab^2\)?

Explanation opens after your attempt
Correct Answer

B. (70)

Explanation

Simple Explanation

(a-2b+ab-2=ab(a+b)) है। इसलिए \(2\cdot5\cdot7=70\) है। / (a-2b+ab-2=ab(a+b)). Thus \(2\cdot5\cdot7=70\).

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Question 133/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(4x^5+12x^4\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?

What is obtained by taking the common factor from \(4x^5+12x^4\)?

Explanation opens after your attempt
Correct Answer

A. (4x-4(x+3))

Explanation

Simple Explanation

दोनों पदों में सामान्य गुणनखंड \(4x^4\) है। इसलिए रूप (4x-4(x+3)) है। / The common factor in both terms is \(4x^4\). Hence the form is (4x-4(x+3)).

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Question 134/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\(6x^2y\)\(3xy^4\)) का गुणनफल क्या है?

What is the product of (\(6x^2y\)\(3xy^4\))?

Explanation opens after your attempt
Correct Answer

A. \(18x^3y^5\)

Explanation

Simple Explanation

गुणांक (18), \(x^{2+1}=x^3\) और \(y^{1+4}=y^5\) है। समान आधार की घातें जोड़ें। / The coefficient is (18), \(x^{2+1}=x^3\), and \(y^{1+4}=y^5\). Add exponents of like bases.

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Question 135/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (x=4) है तो \(x^3-3x^2+2x\) का मान क्या है?

If (x=4), what is the value of \(x^3-3x^2+2x\)?

Explanation opens after your attempt
Correct Answer

C. (24)

Explanation

Simple Explanation

मान रखने पर (64-3(16)+8=64-48+8=24)। पहले घात निकालना सही क्रम है। / Substituting gives (64-3(16)+8=64-48+8=24). Calculating powers first is the correct order.

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Question 136/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (x=-4) है तो \(x^4+x^3\) का मान क्या है?

If (x=-4), what is the value of \(x^4+x^3\)?

Explanation opens after your attempt
Correct Answer

B. (192)

Explanation

Simple Explanation

((-4)4=256) और ((-4)3=-64) है। इसलिए (256-64=192) है। / ((-4)4=256) and ((-4)3=-64). Hence (256-64=192).

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Question 137/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(\frac{x^8y^{-4}}{x^5y^{-6}}\) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of \(\frac{x^8y^{-4}}{x^5y^{-6}}\) if \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(x^3y^2\)

Explanation

Simple Explanation

(x) की घात (8-5=3) और (y) की घात (-4-(-6)=2) है। इसलिए \(x^3y^2\) है। / The exponent of (x) is (8-5=3), and that of (y) is (-4-(-6)=2). Hence it is \(x^3y^2\).

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Question 138/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{a^{-2}}{b^{-4}}\right\)^{-1}) का सरल रूप क्या है यदि \(a\neq0\) और \(b\neq0\)?

What is the simplified form of (\left\(\frac{a^{-2}}{b^{-4}}\right\)^{-1}) if \(a\neq0\) and \(b\neq0\)?

Explanation opens after your attempt
Correct Answer

D. \(\frac{a^2}{b^4}\)

Explanation

Simple Explanation

अंदर \(\frac{a^{-2}}{b^{-4}}=a^{-2}b^4\) है। बाहरी (-1) घात से \(\frac{a^2}{b^4}\) मिलता है। / Inside, \(\frac{a^{-2}}{b^{-4}}=a^{-2}b^4\). The outside power (-1) gives \(\frac{a^2}{b^4}\).

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Question 139/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(5^2\right\)0+2^{-3}) का मान क्या है?

What is the value of (\left\(5^2\right\)0+2^{-3})?

Explanation opens after your attempt
Correct Answer

B. \(\frac{9}{8}\)

Explanation

Simple Explanation

(\left\(5^2\right\)0=1) और \(2^{-3}=\frac{1}{8}\) है। इसलिए योग \(\frac{9}{8}\) है। / (\left\(5^2\right\)0=1) and \(2^{-3}=\frac{1}{8}\). Therefore the sum is \(\frac{9}{8}\).

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Question 140/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(16^{-1}+4^{-2}\) का मान क्या है?

What is the value of \(16^{-1}+4^{-2}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{8}\)

Explanation

Simple Explanation

\(16^{-1}=\frac{1}{16}\) और \(4^{-2}=\frac{1}{16}\) है। इसलिए योग \(\frac{1}{8}\) है। / \(16^{-1}=\frac{1}{16}\) and \(4^{-2}=\frac{1}{16}\). So the sum is \(\frac{1}{8}\).

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Question 141/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(2^7\cdot16^{-1}\) का मान क्या है?

What is the value of \(2^7\cdot16^{-1}\)?

Explanation opens after your attempt
Correct Answer

B. (8)

Explanation

Simple Explanation

(16^{-1}=\(2^4\)^{-1}=2^{-4}) है। इसलिए \(2^7\cdot2^{-4}=2^3=8\) है। / (16^{-1}=\(2^4\)^{-1}=2^{-4}). Hence \(2^7\cdot2^{-4}=2^3=8\).

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Question 142/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((4x-5)2) का विस्तार क्या है?

What is the expansion of ((4x-5)2)?

Explanation opens after your attempt
Correct Answer

A. \(16x^2-40x+25\)

Explanation

Simple Explanation

((a-b)2=a-2-2ab+b-2) लगाएँ। यहाँ (a=4x) और (b=5) हैं। / Use ((a-b)2=a-2-2ab+b-2). Here (a=4x) and (b=5).

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Question 143/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((5x+2)2) का विस्तार क्या है?

What is the expansion of ((5x+2)2)?

Explanation opens after your attempt
Correct Answer

A. \(25x^2+20x+4\)

Explanation

Simple Explanation

((a+b)2) में (a=5x) और (b=2) लें। मध्य पद \(2\cdot5x\cdot2=20x\) है। / Take (a=5x) and (b=2) in ((a+b)2). The middle term is \(2\cdot5x\cdot2=20x\).

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Question 144/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

((7x+6)(7x-6)) का सरल रूप क्या है?

What is the simplified form of ((7x+6)(7x-6))?

Explanation opens after your attempt
Correct Answer

A. \(49x^2-36\)

Explanation

Simple Explanation

((a+b)(a-b)=a-2-b-2) है। यहाँ (a=7x) और (b=6) हैं। / ((a+b)(a-b)=a-2-b-2). Here (a=7x) and (b=6).

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Question 145/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(3^{x+2}=243\) है तो (x) का मान क्या है?

If \(3^{x+2}=243\), what is the value of (x)?

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Correct Answer

B. (3)

Explanation

Simple Explanation

क्योंकि \(243=3^5\), इसलिए (x+2=5) है। इससे (x=3) मिलता है। / Since \(243=3^5\), (x+2=5). This gives (x=3).

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Question 146/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(2^{x-1}=32\) है तो (x) का मान क्या है?

If \(2^{x-1}=32\), what is the value of (x)?

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Correct Answer

C. (6)

Explanation

Simple Explanation

\(32=2^5\), इसलिए (x-1=5) है। इससे (x=6) मिलता है। / \(32=2^5\), so (x-1=5). This gives (x=6).

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Question 147/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\frac{\(2^4\)2\cdot8^{-1}}{4}) का सरल रूप क्या है?

What is the simplified form of (\frac{\(2^4\)2\cdot8^{-1}}{4})?

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Correct Answer

A. \(2^3\)

Explanation

Simple Explanation

(\(2^4\)2=28), \(8^{-1}=2^{-3}\) और \(4=2^2\) है। कुल घात (8-3-2=3) है। / (\(2^4\)2=28), \(8^{-1}=2^{-3}\), and \(4=2^2\). The total exponent is (8-3-2=3).

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Question 148/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(100x^2-121y^2\) का गुणनखंड रूप क्या है?

What is the factorized form of \(100x^2-121y^2\)?

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Correct Answer

A. ((10x-11y)(10x+11y))

Explanation

Simple Explanation

(100x-2-121y-2=(10x)2-(11y)2) है। अंतर के वर्ग का नियम (\(a^2-b^2\)=(a-b)(a+b)) लगाएँ। / (100x-2-121y-2=(10x)2-(11y)2). Apply the difference of squares rule (\(a^2-b^2\)=(a-b)(a+b)).

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Question 149/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\frac{\(2x^2y^{-2}\)3}{8x-3y^{-7}}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?

What is the simplified form of (\frac{\(2x^2y^{-2}\)3}{8x-3y^{-7}}) if \(x\neq0\) and \(y\neq0\)?

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Correct Answer

A. \(x^3y\)

Explanation

Simple Explanation

ऊपर (\(2x^2y^{-2}\)3=8x-6y^{-6}) है। भाग देने पर \(x^{6-3}y^{-6-(-7)}=x^3y\) मिलता है। / The numerator is (\(2x^2y^{-2}\)3=8x-6y^{-6}). Dividing gives \(x^{6-3}y^{-6-(-7)}=x^3y\).

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Question 150/150 Medium Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (x+y=10) और \(x^2+y^2=58\) है तो (xy) का मान क्या है?

If (x+y=10) and \(x^2+y^2=58\), what is the value of (xy)?

Explanation opens after your attempt
Correct Answer

A. (21)

Explanation

Simple Explanation

((x+y)2=x-2+y-2+2xy) से (100=58+2xy) है। इसलिए (2xy=42) और (xy=21) है। / From ((x+y)2=x-2+y-2+2xy), (100=58+2xy). Thus (2xy=42) and (xy=21).

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