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14 results found for "cubes" in Class 10.

Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-7x-18=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-7x-18=0\)?

Explanation opens after your attempt
Correct Answer

A. (721)

Step 1

Concept

The sum of roots is (7) and the product is (-18). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=343+378=721).

Step 2

Why this answer is correct

The correct answer is A. (721). The sum of roots is (7) and the product is (-18). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=343+378=721).

Step 3

Exam Tip

मूलों का योग (7) और गुणनफल (-18) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=343+378=721)।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण \(x^2-6x-16=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-6x-16=0\)?

Explanation opens after your attempt
Correct Answer

A. (504)

Step 1

Concept

The sum of roots is (6) and the product is (-16). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=216+288=504).

Step 2

Why this answer is correct

The correct answer is A. (504). The sum of roots is (6) and the product is (-16). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=216+288=504).

Step 3

Exam Tip

मूलों का योग (6) और गुणनफल (-16) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=216+288=504)।

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Question Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(x^2-5x-14=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-5x-14=0\)?

Explanation opens after your attempt
Correct Answer

A. (335)

Step 1

Concept

The sum of roots is (5) and the product is (-14). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=125+210=335).

Step 2

Why this answer is correct

The correct answer is A. (335). The sum of roots is (5) and the product is (-14). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=125+210=335).

Step 3

Exam Tip

मूलों का योग (5) और गुणनफल (-14) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=125+210=335)।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2-3x-10=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-3x-10=0\)?

Explanation opens after your attempt
Correct Answer

A. (117)

Step 1

Concept

The sum of roots is (3) and the product is (-10). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=27+90=117).

Step 2

Why this answer is correct

The correct answer is A. (117). The sum of roots is (3) and the product is (-10). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=27+90=117).

Step 3

Exam Tip

मूलों का योग (3) और गुणनफल (-10) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=27+90=117)।

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Question Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण \(x^2-2x-3=0\) के मूलों के घनों का योग क्या है?

What is the sum of cubes of the roots of \(x^2-2x-3=0\)?

Explanation opens after your attempt
Correct Answer

A. (26)

Step 1

Concept

The sum of roots is (2) and the product is (-3). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=8+18=26).

Step 2

Why this answer is correct

The correct answer is A. (26). The sum of roots is (2) and the product is (-3). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=8+18=26).

Step 3

Exam Tip

मूलों का योग (2) और गुणनफल (-3) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=8+18=26)।

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Question Expert Mathematics Real Numbers Prime factorisation Class 10 Level 7

यदि \(540=2^2\times3^3\times5\), तो (540) के ऐसे गुणनखंडों की संख्या कितनी है जो पूर्ण घन हैं?

If \(540=2^2\times3^3\times5\), how many factors of (540) are perfect cubes?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

A cube factor must have exponents that are multiples of (3).

Step 2

Why this answer is correct

For (2), only (0); for (3), (0) or (3); for (5), only (0). Total (=2).

Step 3

Exam Tip

Remember that (0) is also a multiple of (3). चरण 1: पूर्ण घन गुणनखंड में हर अभाज्य घात (3) की गुणज होनी चाहिए। चरण 2: (2) की घात केवल (0), (3) की घात (0) या (3), और (5) की घात केवल (0) हो सकती है। कुल \(1\times2\times1=2\)। चरण 3: घन गुणनखंडों में (0) भी (3) की गुणज माना जाता है।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(y \neq 0\), तो (\dfrac{(x+y)3-(x-y)3}{2y}) का सरल रूप क्या है?

If \(y \neq 0\), what is the simplified form of (\dfrac{(x+y)3-(x-y)3}{2y})?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The numerator difference is (6x-2y+2y-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 2

Why this answer is correct

The correct answer is A. \(,3x^2+y^2,\). The numerator difference is (6x-2y+2y-3=2y\(3x^2+y^2\)), so division gives \(3x^2+y^2\). In exams, take out the common factor.

Step 3

Exam Tip

ऊपर का अंतर (6x-2y+2y-3=2y\(3x^2+y^2\)) है, इसलिए भाग देने पर \(3x^2+y^2\) मिलता है। परीक्षा में common factor निकालें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x+1)3-(x-1)3) का सरल रूप क्या है?

What is the simplified form of ((x+1)3-(x-1)3)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

On expansion, ((x+1)3=x-3+3x-2+3x+1) and ((x-1)3=x-3-3x-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,6x^2+2,\). On expansion, ((x+1)3=x-3+3x-2+3x+1) and ((x-1)3=x-3-3x-2+3x-1), so the difference is \(6x^2+2\). In exams, expand cubes carefully.

Step 3

Exam Tip

विस्तार करने पर ((x+1)3=x-3+3x-2+3x+1) और ((x-1)3=x-3-3x-2+3x-1), इसलिए अंतर \(6x^2+2\) है। परीक्षा में cube expansion ध्यान से करें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(8x^3+1\)) को ((2x+1)) से भाग देने पर भागफल क्या है?

What is the quotient when (\(8x^3+1\)) is divided by ((2x+1))?

Explanation opens after your attempt
Correct Answer

A. \(,4x^2-2x+1,\)

Step 1

Concept

Because (8x-3+1=(2x)3+13=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,4x^2-2x+1,\). Because (8x-3+1=(2x)3+13=(2x+1)\(4x^2-2x+1\)). In exams, remember the identity for sum of cubes.

Step 3

Exam Tip

क्योंकि (8x-3+1=(2x)3+13=(2x+1)\(4x^2-2x+1\))। परीक्षा में sum of cubes की identity याद रखें।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

((x-2)\(x^2+2x+4\)) का विस्तार क्या है?

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

Explanation opens after your attempt
Correct Answer

A. \(,x^3-8,\)

Step 1

Concept

This matches ((a-b)\(a^2+ab+b^2\)=a-3-b-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 2

Why this answer is correct

The correct answer is A. \(,x^3-8,\). This matches ((a-b)\(a^2+ab+b^2\)=a-3-b-3), so the answer is \(x^3-8\). In exams, identifying the identity makes expansion faster.

Step 3

Exam Tip

यह ((a-b)\(a^2+ab+b^2\)=a-3-b-3) का रूप है, इसलिए उत्तर \(x^3-8\) है। परीक्षा में identity पहचानने से विस्तार जल्दी होता है।

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(x^3-27\)) को ((x-3)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-27\)) is divided by ((x-3))?

Explanation opens after your attempt
Correct Answer

A. \(,x^2+3x+9,\)

Step 1

Concept

Because (x-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+3x+9,\). Because (x-3-27=(x-3)\(x^2+3x+9\)), the quotient is \(x^2+3x+9\). In exams, identify the difference of cubes.

Step 3

Exam Tip

क्योंकि (x-3-27=(x-3)\(x^2+3x+9\)), इसलिए भागफल \(x^2+3x+9\) है। परीक्षा में घन के अंतर की पहचान करें।

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

(\(x^3-8\)) को ((x-2)) से भाग देने पर भागफल क्या होगा?

What is the quotient when (\(x^3-8\)) is divided by ((x-2))?

Explanation opens after your attempt
Correct Answer

A. \(,x^2+2x+4,\)

Step 1

Concept

Because (x-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 2

Why this answer is correct

The correct answer is A. \(,x^2+2x+4,\). Because (x-3-8=(x-2)\(x^2+2x+4\)), the quotient is \(x^2+2x+4\). In exams, remember the identity for cubes.

Step 3

Exam Tip

क्योंकि (x-3-8=(x-2)\(x^2+2x+4\)), इसलिए भागफल \(x^2+2x+4\) है। परीक्षा में cubes की identity याद रखें।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32

यदि \(x^2-10x+21=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha^3+\beta^3\) का मान क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-10x+21=0\), what is the value of \(\alpha^3+\beta^3\)?

Explanation opens after your attempt
Correct Answer

A. (370)

Step 1

Concept

\(\alpha+\beta=10\) and \(\alpha\beta=21\). (\alpha-3+\beta-3=103-3(21)(10)=370).

Step 2

Why this answer is correct

The correct answer is A. (370). \(\alpha+\beta=10\) and \(\alpha\beta=21\). (\alpha-3+\beta-3=103-3(21)(10)=370).

Step 3

Exam Tip

\(\alpha+\beta=10\) और \(\alpha\beta=21\) है। (\alpha-3+\beta-3=103-3(21)(10)=370) होगा।

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Question Hard Mathematics Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31

यदि \(x^2-9x+20=0\) के मूल \(\alpha\) और \(\beta\) हैं तो \(\alpha^3+\beta^3\) का मान क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-9x+20=0\), what is the value of \(\alpha^3+\beta^3\)?

Explanation opens after your attempt
Correct Answer

A. (369)

Step 1

Concept

\(\alpha+\beta=9\) and \(\alpha\beta=20\). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=729-540=189).

Step 2

Why this answer is correct

The correct answer is A. (369). \(\alpha+\beta=9\) and \(\alpha\beta=20\). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=729-540=189).

Step 3

Exam Tip

\(\alpha+\beta=9\) और \(\alpha\beta=20\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=729-540=189) नहीं बल्कि (189) होगा।

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