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Class 10 Mathematics Medium Quiz

Mathematics Medium Class 10 Level 45

Level 45 • 50/50 questions • 35 seconds per question.

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Question 1/50 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 2/50 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 3/50 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 4/50 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 5/50 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 6/50 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 7/50 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 8/50 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 9/50 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 10/50 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 11/50 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 12/50 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 13/50 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 14/50 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 15/50 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 16/50 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 17/50 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 18/50 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 19/50 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 20/50 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 21/50 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 22/50 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 23/50 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 24/50 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 25/50 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 26/50 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 27/50 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 28/50 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 29/50 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 30/50 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 31/50 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 32/50 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 33/50 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 34/50 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 35/50 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 36/50 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 37/50 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 38/50 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 39/50 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 40/50 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 41/50 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 42/50 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 43/50 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 44/50 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 45/50 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)?

Explanation opens after your attempt
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 46/50 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)?

Explanation opens after your attempt
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 47/50 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})?

Explanation opens after your attempt
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 48/50 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 \(100x^2-121y^2\)?

Explanation opens after your attempt
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 49/50 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 \(y\neq0\)?

Explanation opens after your attempt
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 50/50 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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