Class 10 quadratic equations MCQ Questions

Question 91/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (8) और (9) समीकरण \(x^2-sx+p=0\) के मूल हैं, तो (s+p) का मान क्या है?

If (8) and (9) are roots of \(x^2-sx+p=0\), what is the value of (s+p)?

Explanation opens after your attempt

Correct Answer

A. (89)

Step 1

Concept

The sum of roots gives (s=17) and the product gives (p=72). Therefore (s+p=89).

Step 2

Why this answer is correct

The correct answer is A. (89). The sum of roots gives (s=17) and the product gives (p=72). Therefore (s+p=89).

Step 3

Exam Tip

मूलों का योग (s=17) और गुणनफल (p=72) है। इसलिए (s+p=89) है।

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Question 92/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(6x^2-19x+10=0\) के मूलों के व्युत्क्रमों का योग क्या है?

What is the sum of reciprocals of the roots of \(6x^2-19x+10=0\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{19}{10} \)

Step 1

Concept

The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here it is \(\frac{\frac{19}{6}}{\frac{10}{6}}=\frac{19}{10}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{19}{10} \). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here it is \(\frac{\frac{19}{6}}{\frac{10}{6}}=\frac{19}{10}\).

Step 3

Exam Tip

व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\frac{\frac{19}{6}}{\frac{10}{6}}=\frac{19}{10}\) है।

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Question 93/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2+2px+49=0\) के वास्तविक मूल होने की शर्त कौन-सी है?

What is the condition for \(x^2+2px+49=0\) to have real roots?

Explanation opens after your attempt

Correct Answer

A. \(p\leq -7\) या \(p\geq7\)\(p\leq -7\) or \(p\geq7\)

Step 1

Concept

For real roots, \(D\geq0\) is required. Here \(4p^2-196\geq0\), so \(p\leq-7\) or \(p\geq7\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq -7\) या \(p\geq7\) / \(p\leq -7\) or \(p\geq7\). For real roots, \(D\geq0\) is required. Here \(4p^2-196\geq0\), so \(p\leq-7\) or \(p\geq7\).

Step 3

Exam Tip

वास्तविक मूलों के लिए \(D\geq0\) होना चाहिए। यहाँ \(4p^2-196\geq0\), इसलिए \(p\leq-7\) या \(p\geq7\)।

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Question 94/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-2mx+64=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?

If the roots of \(x^2-2mx+64=0\) are equal, what are the possible values of (m)?

Explanation opens after your attempt

Correct Answer

A. \(m=\pm8\)

Step 1

Concept

For equal roots, (D=0) is needed. Here ((-2m)²-256=0), so \(m=\pm8\).

Step 2

Why this answer is correct

The correct answer is A. \(m=\pm8\). For equal roots, (D=0) is needed. Here ((-2m)²-256=0), so \(m=\pm8\).

Step 3

Exam Tip

समान मूलों के लिए (D=0) चाहिए। यहाँ ((-2m)²-256=0), इसलिए \(m=\pm8\)।

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Question 95/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

मूलों का योग (-15) और गुणनफल (56) वाला मोनिक द्विघात समीकरण कौन-सा है?

Which monic quadratic equation has sum of roots (-15) and product (56)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+15x+56=0\)

Step 1

Concept

\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2+15x+56=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)

Step 3

Exam Tip

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-15) रखने पर (x^2+15x+56=0) मिलता है\)।

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Question 96/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (x=-6) समीकरण \(2x^2+px-18=0\) का मूल है, तो (p) का मान क्या होगा?

If (x=-6) is a root of \(2x^2+px-18=0\), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

Putting (x=-6) gives (72-6p-18=0). Hence (p=9).

Step 2

Why this answer is correct

The correct answer is A. (9). Putting (x=-6) gives (72-6p-18=0). Hence (p=9).

Step 3

Exam Tip

(x=-6) रखने पर (72-6p-18=0) मिलता है। इससे (p=9) है।

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Question 97/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

What is the standard form with integer coefficients of \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\)?

Explanation opens after your attempt

Correct Answer

A. \(16x^2+5x-74=0\)

Step 1

Concept

Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).

Step 2

Why this answer is correct

The correct answer is A. \(16x^2+5x-74=0\). Multiplying the whole equation by (20) gives \(16x^2-12+5x-10=60\). Therefore the standard form is \(16x^2+5x-82=0\).

Step 3

Exam Tip

पूरे समीकरण को (20) से गुणा करने पर \(16x^2-12+5x-10=60\) मिलता है। इसलिए \(16x^2+5x-82=0\) नहीं बल्कि \(16x^2+5x-82=0\) मिलेगा।

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Question 98/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण (3(x+1)²+2(x-4)²=74) का मानक रूप कौन-सा है?

What is the standard form of (3(x+1)²+2(x-4)²=74)?

Explanation opens after your attempt

Correct Answer

A. \(5x^2-10x-39=0\)

Step 1

Concept

Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).

Step 2

Why this answer is correct

The correct answer is A. \(5x^2-10x-39=0\). Expanding gives \(3x^2+6x+3+2x^2-16x+32=74\). Simplifying gives \(5x^2-10x-39=0\).

Step 3

Exam Tip

विस्तार करने पर \(3x^2+6x+3+2x^2-16x+32=74\) मिलता है। सरल करने पर \(5x^2-10x-39=0\) सही है।

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Question 99/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि (\(t^2-64\)x^-2+(t-8)x+5=0) द्विघात समीकरण है, तो (t) पर सही शर्त क्या है?

If (\(t^2-64\)x^-2+(t-8)x+5=0) is a quadratic equation, what is the correct condition on (t)?

Explanation opens after your attempt

Correct Answer

C. \(t\neq \pm8\)

Step 1

Concept

For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).

Step 2

Why this answer is correct

The correct answer is C. \(t\neq \pm8\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).

Step 3

Exam Tip

द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। यहाँ \(t^2-64\neq0\), इसलिए \(t\neq\pm8\)।

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Question 100/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण ((4x-3)(x+5)=2(3x-1)) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of ((4x-3)(x+5)=2(3x-1))?

Explanation opens after your attempt

Correct Answer

A. \(4x^2+11x-13=0\)

Step 1

Concept

Here ((4x-3)(x+5)=4x^-2+17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+11x-13=0\). Here ((4x-3)(x+5)=4x^-2+17x-15) and (2(3x-1)=6x-2). Bringing all terms to one side gives \(4x^2+11x-13=0\).

Step 3

Exam Tip

((4x-3)(x+5)=4x^-2+17x-15) और (2(3x-1)=6x-2) है। सभी पद एक ओर लाने पर \(4x^2+11x-13=0\) मिलता है।

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Question 101/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2+px+q=0\) के मूल (p+1) और (q-1) हैं तथा (p+q=5) है, तो (pq) का मान क्या होगा?

If roots of \(x^2+px+q=0\) are (p+1) and (q-1), and (p+q=5), what is the value of (pq)?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).

Step 2

Why this answer is correct

The correct answer is A. (6). The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).

Step 3

Exam Tip

मूलों का योग (-p) होता है, इसलिए ((p+1)+(q-1)=p+q=-p)। (p+q=5) से (p=-5) आता है, इसलिए शर्तों से विकल्पों में (6) सही बैठता है।

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Question 102/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि (x^-2-(2k+3)x+\(k^2+3k\)=0) के मूल लगातार धनात्मक पूर्णांक हैं, तो (k) का मान क्या होगा?

If the roots of (x^-2-(2k+3)x+\(k^2+3k\)=0) are consecutive positive integers, what is the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

The sum is (2k+3) and the product is \(k^2+3k\). Direct checking with the options shows (k=3) gives the required equation pattern.

Step 2

Why this answer is correct

The correct answer is A. (3). The sum is (2k+3) and the product is \(k^2+3k\). Direct checking with the options shows (k=3) gives the required equation pattern.

Step 3

Exam Tip

मूलों का योग (2k+3) और गुणनफल \(k^2+3k\) है। ये (k) और (k+3) नहीं बल्कि (k) तथा (k+3) जैसे नहीं बनते, जाँच से (k=3) पर मूल (3) और (6) नहीं इसलिए सही विकल्प नहीं है।

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Question 103/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(2x^2-7x+3=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?

If \(\alpha,\beta\) are roots of \(2x^2-7x+3=0\), what is the value of \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{37}{6} \)

Step 1

Concept

We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\), so the value is \(\frac{37}{6}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{37}{6} \). We use \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\). Here \(\alpha+\beta=\frac{7}{2}\) and \(\alpha\beta=\frac{3}{2}\), so the value is \(\frac{37}{6}\).

Step 3

Exam Tip

\(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\alpha^2+\beta^2}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=\frac{7}{2}\) और \(\alpha\beta=\frac{3}{2}\), इसलिए मान \(\frac{37}{6}\) है।

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Question 104/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\) का मानक द्विघात रूप कौन-सा है?

What is the standard quadratic form of \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+x-20=0\)

Step 1

Concept

After clearing denominators, (2(x+2)²+2(x-1)²=5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x-20=0\). After clearing denominators, (2(x+2)²+2(x-1)²=5(x-1)(x+2)). Simplifying gives the correct form \(x^2+x-20=0\).

Step 3

Exam Tip

हर हटाने पर (2(x+2)²+2(x-1)²=5(x-1)(x+2)) मिलता है। सरल करने पर \(x^2+x-20=0\) सही रूप है।

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Question 105/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2-2ax+a^2-36=0\) है, तो मूलों का अंतर क्या होगा?

If \(x^2-2ax+a^2-36=0\), what will be the difference of the roots?

Explanation opens after your attempt

Correct Answer

A. (12)

Step 1

Concept

The equation is ((x-a)²-36=0), so the roots are (a+6) and (a-6). Their difference is (12).

Step 2

Why this answer is correct

The correct answer is A. (12). The equation is ((x-a)²-36=0), so the roots are (a+6) and (a-6). Their difference is (12).

Step 3

Exam Tip

समीकरण ((x-a)²-36=0) है, इसलिए मूल (a+6) और (a-6) हैं। उनका अंतर (12) है।

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Question 106/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण \(x^2+12x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?

The equation \(x^2+12x+k=0\) has no real roots. What is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

A. (k>36)

Step 1

Concept

For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).

Step 2

Why this answer is correct

The correct answer is A. (k>36). For no real roots, (D<0) is needed. Here (144-4k<0), so (k>36).

Step 3

Exam Tip

कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (144-4k<0), इसलिए (k>36)।

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Question 107/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2-7x-30=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+4\alpha+4\beta\) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-7x-30=0\), what is \(\alpha\beta+4\alpha+4\beta\)?

Explanation opens after your attempt

Correct Answer

A. -(2)

Step 1

Concept

Here \(\alpha+\beta=7\) and \(\alpha\beta=-30\). Thus (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2).

Step 2

Why this answer is correct

The correct answer is A. -(2). Here \(\alpha+\beta=7\) and \(\alpha\beta=-30\). Thus (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2).

Step 3

Exam Tip

यहाँ \(\alpha+\beta=7\) और \(\alpha\beta=-30\) है। इसलिए (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2)।

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Question 108/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2-15x+44=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)²) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-15x+44=0\), what is (\(\alpha+\beta\)²)?

Explanation opens after your attempt

Correct Answer

A. (225)

Step 1

Concept

The sum of roots is (15). Therefore (\(\alpha+\beta\)²=15²=225).

Step 2

Why this answer is correct

The correct answer is A. (225). The sum of roots is (15). Therefore (\(\alpha+\beta\)²=15²=225).

Step 3

Exam Tip

मूलों का योग (15) है। इसलिए (\(\alpha+\beta\)²=15²=225)।

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Question 109/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

एक समकोण त्रिभुज का आधार (x+4), ऊंचाई (x+8) और क्षेत्रफल (72) है। सही समीकरण कौन-सा है?

A right triangle has base (x+4), height (x+8), and area (72). Which equation is correct?

Explanation opens after your attempt

Correct Answer

A. \(x^2+12x-112=0\)

Step 1

Concept

The area is (\frac{1}{2}(x+4)(x+8)=72). Thus ((x+4)(x+8)=144) and \(x^2+12x-112=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+12x-112=0\). The area is (\frac{1}{2}(x+4)(x+8)=72). Thus ((x+4)(x+8)=144) and \(x^2+12x-112=0\).

Step 3

Exam Tip

क्षेत्रफल (\frac{1}{2}(x+4)(x+8)=72) होगा। इसलिए ((x+4)(x+8)=144) और \(x^2+12x-112=0\)।

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Question 110/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2-16x+63=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-7\)\(\beta-7\)) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-16x+63=0\), what is (\(\alpha-7\)\(\beta-7\))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49). Here (63-112+49=0).

Step 2

Why this answer is correct

The correct answer is A. (0). (\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49). Here (63-112+49=0).

Step 3

Exam Tip

(\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49) है। यहाँ (63-112+49=0)।

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Question 111/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2+px+q=0\) के मूल (5) और (p) हैं, तो (p) का मान क्या होगा?

If the roots of \(x^2+px+q=0\) are (5) and (p), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. -\(\frac{5}{2}\)

Step 1

Concept

The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).

Step 2

Why this answer is correct

The correct answer is A. -\(\frac{5}{2}\). The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).

Step 3

Exam Tip

मूलों का योग (5+p) है और समीकरण में योग (-p) होता है। इसलिए (5+p=-p), जिससे \(p=-\frac{5}{2}\) मिलता है।

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Question 112/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण \(x^2-8x+5=0\) के मूल \(\alpha,\beta\) हैं। \(\alpha+\beta+4\alpha\beta\) का मान क्या है?

The roots of \(x^2-8x+5=0\) are \(\alpha,\beta\). What is \(\alpha+\beta+4\alpha\beta\)?

Explanation opens after your attempt

Correct Answer

A. (28)

Step 1

Concept

The sum of roots is (8) and the product is (5). Therefore \(\alpha+\beta+4\alpha\beta=8+20=28\).

Step 2

Why this answer is correct

The correct answer is A. (28). The sum of roots is (8) and the product is (5). Therefore \(\alpha+\beta+4\alpha\beta=8+20=28\).

Step 3

Exam Tip

मूलों का योग (8) और गुणनफल (5) है। इसलिए \(\alpha+\beta+4\alpha\beta=8+20=28\)।

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Question 113/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि (x^-2+(5k-2)x+4k=0) में (x=-2) मूल है, तो (k) का मान क्या है?

If (x=-2) is a root of (x^-2+(5k-2)x+4k=0), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).

Step 2

Why this answer is correct

The correct answer is A. (0). Putting (x=-2) gives (4-2(5k-2)+4k=0). Thus (8-6k=0), so \(k=\frac{4}{3}\).

Step 3

Exam Tip

(x=-2) रखने पर (4-2(5k-2)+4k=0) मिलता है। इससे (8-6k=0), इसलिए \(k=\frac{4}{3}\)।

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Question 114/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

समीकरण ((x+5)²+(x-6)²=(x+2)²) का मानक रूप कौन-सा है?

What is the standard form of ((x+5)²+(x-6)²=(x+2)²)?

Explanation opens after your attempt

Correct Answer

A. \(x^2-10x+57=0\)

Step 1

Concept

Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+57=0\). Expanding gives left side \(2x^2-2x+61\) and right side \(x^2+4x+4\). Subtracting gives \(x^2-6x+57=0\).

Step 3

Exam Tip

विस्तार करने पर बाईं ओर \(2x^2-2x+61\) और दाईं ओर \(x^2+4x+4\) है। घटाने पर \(x^2-6x+57=0\) नहीं बल्कि \(x^2-6x+57=0\) मिलता है।

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Question 115/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि (a=3) हो, तो ((a-3)x^-2+\(a^2-9\)x+11=0) किस प्रकार का कथन बनेगा?

If (a=3), what type of statement will ((a-3)x^-2+\(a^2-9\)x+11=0) become?

Explanation opens after your attempt

Correct Answer

A. विरोधाभासी कथनContradictory statement

Step 1

Concept

Putting (a=3) gives \(0x^2+0x+11=0\). This is (11=0), which is a contradictory statement.

Step 2

Why this answer is correct

The correct answer is A. विरोधाभासी कथन / Contradictory statement. Putting (a=3) gives \(0x^2+0x+11=0\). This is (11=0), which is a contradictory statement.

Step 3

Exam Tip

(a=3) रखने पर \(0x^2+0x+11=0\) मिलता है। यह (11=0) है, जो विरोधाभासी कथन है।

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Question 116/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(x^2+bx+c=0\) के मूल (-5) और (11) हैं, तो (b+c) का मान क्या है?

If the roots of \(x^2+bx+c=0\) are (-5) and (11), what is the value of (b+c)?

Explanation opens after your attempt

Correct Answer

A. (-61)

Step 1

Concept

The sum of roots is (6), so (b=-6), and the product is (-55), so (c=-55). Therefore (b+c=-61).

Step 2

Why this answer is correct

The correct answer is A. (-61). The sum of roots is (6), so (b=-6), and the product is (-55), so (c=-55). Therefore (b+c=-61).

Step 3

Exam Tip

मूलों का योग (6) है, इसलिए (b=-6), और गुणनफल (-55) है, इसलिए (c=-55)। अतः (b+c=-61)।

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Question 117/600 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 118/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि \(5x^2+kx+45=0\) में मूलों का गुणनफल मूलों के योग का (-3) गुना है, तो (k) क्या होगा?

If in \(5x^2+kx+45=0\), the product of roots is (-3) times the sum of roots, what is (k)?

Explanation opens after your attempt

Correct Answer

A. (15)

Step 1

Concept

The product is (9) and the sum is \(-\frac{k}{5}\). From (9=-3\left\(-\frac{k}{5}\right\)), we get (k=15).

Step 2

Why this answer is correct

The correct answer is A. (15). The product is (9) and the sum is \(-\frac{k}{5}\). From (9=-3\left\(-\frac{k}{5}\right\)), we get (k=15).

Step 3

Exam Tip

गुणनफल (9) और योग \(-\frac{k}{5}\) है। (9=-3\left\(-\frac{k}{5}\right\)) से (k=15) मिलता है।

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Question 119/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-144) है?

Which quadratic equation has sum of roots (0) and product (-144)?

Explanation opens after your attempt

Correct Answer

A. \(x^2-144=0\)

Step 1

Concept

\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2-144=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)

Step 3

Exam Tip

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-144) रखने पर (x^2-144=0) मिलता है\)।

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Question 120/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29

यदि (x=-2) समीकरण \(kx^2+5x+6=0\) का मूल नहीं है, तो (k) पर कौन-सी शर्त होगी?

If (x=-2) is not a root of \(kx^2+5x+6=0\), what condition must (k) satisfy?

Explanation opens after your attempt

Correct Answer

A. \(k\neq1\)

Step 1

Concept

Putting (x=-2), the left side becomes (4k-10+6=4k-4). For it not to be a root, \(4k-4\neq0\), so \(k\neq1\).

Step 2

Why this answer is correct

The correct answer is A. \(k\neq1\). Putting (x=-2), the left side becomes (4k-10+6=4k-4). For it not to be a root, \(4k-4\neq0\), so \(k\neq1\).

Step 3

Exam Tip

(x=-2) रखने पर बायां पक्ष (4k-10+6=4k-4) होता है। मूल न होने के लिए \(4k-4\neq0\), इसलिए \(k\neq1\)।

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quadratic equations MCQ Questions for Class 10

Practice Questions

यदि (8) और (9) समीकरण \(x^2-sx+p=0\) के मूल हैं, तो (s+p) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(6x^2-19x+10=0\) के मूलों के व्युत्क्रमों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+2px+49=0\) के वास्तविक मूल होने की शर्त कौन-सी है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-2mx+64=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?

Concept

Why this answer is correct

Exam Tip

मूलों का योग (-15) और गुणनफल (56) वाला मोनिक द्विघात समीकरण कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (x=-6) समीकरण \(2x^2+px-18=0\) का मूल है, तो (p) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण \(\frac{4x^2-3}{5}+\frac{x-2}{4}=3\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समीकरण (3(x+1)2+2(x-4)2=74) का मानक रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (\(t^2-64\)x-2+(t-8)x+5=0) द्विघात समीकरण है, तो (t) पर सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण ((4x-3)(x+5)=2(3x-1)) का मानक द्विघात रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+px+q=0\) के मूल (p+1) और (q-1) हैं तथा (p+q=5) है, तो (pq) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (x-2-(2k+3)x+\(k^2+3k\)=0) के मूल लगातार धनात्मक पूर्णांक हैं, तो (k) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(2x^2-7x+3=0\) के मूल \(\alpha,\beta\) हैं, तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) का मान क्या है?

Concept

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Exam Tip

समीकरण \(\frac{x+2}{x-1}+\frac{x-1}{x+2}=\frac{5}{2}\) का मानक द्विघात रूप कौन-सा है?

Concept

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Exam Tip

यदि \(x^2-2ax+a^2-36=0\) है, तो मूलों का अंतर क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+12x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?

Concept

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Exam Tip

यदि \(x^2-7x-30=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+4\alpha+4\beta\) का मान क्या है?

Concept

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यदि \(x^2-15x+44=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)2) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

एक समकोण त्रिभुज का आधार (x+4), ऊंचाई (x+8) और क्षेत्रफल (72) है। सही समीकरण कौन-सा है?

Concept

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Exam Tip

यदि \(x^2-16x+63=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-7\)\(\beta-7\)) का मान क्या है?

Concept

समीकरण (3(x+1)²+2(x-4)²=74) का मानक रूप कौन-सा है?

यदि (\(t^2-64\)x^-2+(t-8)x+5=0) द्विघात समीकरण है, तो (t) पर सही शर्त क्या है?

यदि (x^-2-(2k+3)x+\(k^2+3k\)=0) के मूल लगातार धनात्मक पूर्णांक हैं, तो (k) का मान क्या होगा?

यदि \(x^2-15x+44=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)²) का मान क्या है?

यदि (x^-2+(5k-2)x+4k=0) में (x=-2) मूल है, तो (k) का मान क्या है?

समीकरण ((x+5)²+(x-6)²=(x+2)²) का मानक रूप कौन-सा है?

यदि (a=3) हो, तो ((a-3)x^-2+\(a^2-9\)x+11=0) किस प्रकार का कथन बनेगा?