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Mathematics Quiz - Class 10 Mathematics Polynomials...

Question 1/50 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 2/50 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 3/50 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 4/50 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 5/50 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 6/50 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 7/50 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 8/50 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 9/50 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 10/50 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 11/50 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 12/50 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 13/50 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 14/50 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 15/50 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 16/50 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 17/50 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 18/50 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 19/50 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 20/50 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 21/50 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 22/50 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 23/50 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 24/50 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 25/50 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 26/50 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 27/50 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 28/50 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 29/50 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 30/50 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 31/50 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 32/50 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 33/50 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 34/50 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 35/50 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 36/50 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 37/50 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 38/50 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 39/50 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 40/50 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 41/50 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 42/50 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 43/50 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 44/50 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)?

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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 45/50 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 46/50 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 47/50 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 48/50 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 49/50 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 50/50 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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Class 10 Mathematics - Polynomials - Operations on real numbers and the laws of exponents Medium Quiz

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

((0.25)^{-2}) का मान क्या है?

Simple Explanation

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

Simple Explanation

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

Simple Explanation

(\(a^3b^2\)3) का सही सरल रूप क्या है?

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

((2x+3)+(4x-7)) का सरल रूप क्या है?

Simple Explanation

((7x-2)-(3x+5)) का सरल रूप क्या है?

Simple Explanation

(3x\(2x^2-5x+4\)) का विस्तार क्या है?

Simple Explanation

((x+4)(x+3)) का विस्तार क्या है?

Simple Explanation

((x-5)(x+2)) का विस्तार क्या है?

Simple Explanation

((3x+1)(x-4)) का विस्तार क्या है?

Simple Explanation

((x+8)2) का सही विस्तार क्या है?

Simple Explanation

((x-9)2) का सही विस्तार क्या है?

Simple Explanation

((x+9)(x-9)) का सरल रूप क्या है?

Simple Explanation

\(64x^2-81\) का गुणनखंड रूप क्या है?

Simple Explanation

\(x^2+18x+81\) किसके बराबर है?

Simple Explanation

\(x^2-20x+100\) किसके बराबर है?

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

\(103^2\) का मान क्या है?

Simple Explanation

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

Simple Explanation

\(2.5^2-1.5^2\) का मान क्या है?

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

Simple Explanation

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

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

(\(a^3b^2\)³) का सही सरल रूप क्या है?

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

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

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

((x+8)²) का सही विस्तार क्या है?

((x-9)²) का सही विस्तार क्या है?

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

((3x-4)²) का विस्तार क्या है?

((4x+3)²) का विस्तार क्या है?

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