Class 10 quadratic equations MCQ Questions

Question 181/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(3x^2-14x+16=0\) में मूलों का अंतर क्या है?

What is the difference between the roots of \(3x^2-14x+16=0\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{2}{3} \)

Step 1

Concept

The roots are (2) and \(\frac{8}{3}\). Their difference is \(\frac{8}{3}-2=\frac{2}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{2}{3} \). The roots are (2) and \(\frac{8}{3}\). Their difference is \(\frac{8}{3}-2=\frac{2}{3}\).

Step 3

Exam Tip

मूल (2) और \(\frac{8}{3}\) हैं। उनका अंतर \(\frac{8}{3}-2=\frac{2}{3}\) है।

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Question 182/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि (x^-2-(m+5)x+5m=0) का एक मूल (5) है, तो दूसरा मूल क्या है?

If one root of (x^-2-(m+5)x+5m=0) is (5), what is the other root?

Explanation opens after your attempt

Correct Answer

A. (m)

Step 1

Concept

The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).

Step 2

Why this answer is correct

The correct answer is A. (m). The product of roots is (5m) and one root is (5). Hence the other root is \(\frac{5m}{5}=m\).

Step 3

Exam Tip

मूलों का गुणनफल (5m) है और एक मूल (5) है। इसलिए दूसरा मूल \(\frac{5m}{5}=m\) है।

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Question 183/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(x^2-8x+17=0\) के लिए कौन-सा कथन सही है?

Which statement is correct for \(x^2-8x+17=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक मूल नहीं हैंIt has no real roots

Step 1

Concept

Here (D=(-8)²-4\cdot1\cdot17=-4<0). Therefore it has no real roots.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक मूल नहीं हैं / It has no real roots. Here (D=(-8)²-4\cdot1\cdot17=-4<0). Therefore it has no real roots.

Step 3

Exam Tip

यहाँ (D=(-8)²-4\cdot1\cdot17=-4<0) है। इसलिए वास्तविक मूल नहीं होंगे।

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Question 184/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि किसी मोनिक द्विघात समीकरण के मूल (r) और (3r) हैं तथा उनका योग (16) है, तो उस समीकरण का स्थिर पद क्या होगा?

If the roots of a monic quadratic equation are (r) and (3r), and their sum is (16), what will be the constant term?

Explanation opens after your attempt

Correct Answer

A. (48)

Step 1

Concept

From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).

Step 2

Why this answer is correct

The correct answer is A. (48). From (r+3r=16), we get (r=4), so the roots are (4) and (12). The constant term is the product of roots (48).

Step 3

Exam Tip

(r+3r=16) से (r=4) मिलता है, इसलिए मूल (4) और (12) हैं। स्थिर पद मूलों का गुणनफल (48) होगा।

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Question 185/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण ((x+3)(x+6)+(x-2)(x+5)=70) का मानक रूप कौन-सा है?

What is the standard form of ((x+3)(x+6)+(x-2)(x+5)=70)?

Explanation opens after your attempt

Correct Answer

A. \(2x^2+12x-62=0\)

Step 1

Concept

The left side is \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\). Subtracting (70) gives \(2x^2+12x-62=0\).

Step 2

Why this answer is correct

The correct answer is A. \(2x^2+12x-62=0\). The left side is \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\). Subtracting (70) gives \(2x^2+12x-62=0\).

Step 3

Exam Tip

बाईं ओर \(x^2+9x+18+x^2+3x-10=2x^2+12x+8\) है। (70) घटाने पर \(2x^2+12x-62=0\) मिलता है।

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Question 186/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि \(x^2-9x+18=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-3\)\(\beta-3\)) का मान क्या है?

If \(\alpha\) and \(\beta\) are roots of \(x^2-9x+18=0\), what is (\(\alpha-3\)\(\beta-3\))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9). Here (18-27+9=0).

Step 2

Why this answer is correct

The correct answer is A. (0). (\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9). Here (18-27+9=0).

Step 3

Exam Tip

(\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9) है। यहाँ (18-27+9=0)।

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Question 187/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(5x^2+6x+1=0\) में मूलों के वर्गों का योग क्या है?

What is the sum of squares of the roots of \(5x^2+6x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{26}{25} \)

Step 1

Concept

(\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta). Here (\left\(-\frac{6}{5}\right\)²-2\cdot\frac{1}{5}=\frac{26}{25}).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{26}{25} \). (\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta). Here (\left\(-\frac{6}{5}\right\)²-2\cdot\frac{1}{5}=\frac{26}{25}).

Step 3

Exam Tip

(\alpha^-2+\beta^-2=\(\alpha+\beta\)²-2\alpha\beta) होता है। यहाँ (\left\(-\frac{6}{5}\right\)²-2\cdot\frac{1}{5}=\frac{26}{25})।

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Question 188/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि \(x^2+ax+24=0\) का एक मूल (4) है, तो दूसरा मूल और (a) कौन-से हैं?

If one root of \(x^2+ax+24=0\) is (4), what are the other root and (a)?

Explanation opens after your attempt

Correct Answer

A. दूसरा मूल (6), (a=-10)other root (6), (a=-10)

Step 1

Concept

The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).

Step 2

Why this answer is correct

The correct answer is A. दूसरा मूल (6), (a=-10) / other root (6), (a=-10). The product of roots is (24), so the other root is (6). The sum is (10), and (-a=10), so (a=-10).

Step 3

Exam Tip

मूलों का गुणनफल (24) है, इसलिए दूसरा मूल (6) होगा। योग (10) है और (-a=10), इसलिए (a=-10)।

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Question 189/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

किस समीकरण का विवेचक (-23) है?

Which equation has discriminant (-23)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+x+6=0\)

Step 1

Concept

For \(x^2+x+6=0\), \(D=1^2-4\cdot1\cdot6=-23\). Subtract the full (4ac) in the discriminant.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x+6=0\). For \(x^2+x+6=0\), \(D=1^2-4\cdot1\cdot6=-23\). Subtract the full (4ac) in the discriminant.

Step 3

Exam Tip

\(x^2+x+6=0\) के लिए \(D=1^2-4\cdot1\cdot6=-23\) है। विवेचक में (4ac) पूरा घटाएं।

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Question 190/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(x^2-12x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?

If the roots of \(x^2-12x+k=0\) are real and distinct, what is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

A. (k<36)

Step 1

Concept

For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).

Step 2

Why this answer is correct

The correct answer is A. (k<36). For real and distinct roots, (D>0) is required. Here (144-4k>0), so (k<36).

Step 3

Exam Tip

भिन्न वास्तविक मूलों के लिए (D>0) चाहिए। यहाँ (144-4k>0), इसलिए (k<36)।

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Question 191/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि (5) और (6) समीकरण \(x^2-sx+p=0\) के मूल हैं, तो (s+p) का मान क्या है?

If (5) and (6) are roots of \(x^2-sx+p=0\), what is the value of (s+p)?

Explanation opens after your attempt

Correct Answer

A. (41)

Step 1

Concept

The sum of roots gives (s=11) and the product gives (p=30). Therefore (s+p=41).

Step 2

Why this answer is correct

The correct answer is A. (41). The sum of roots gives (s=11) and the product gives (p=30). Therefore (s+p=41).

Step 3

Exam Tip

मूलों का योग (s=11) और गुणनफल (p=30) है। इसलिए (s+p=41) है।

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Question 192/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(4x^2-13x+9=0\) के मूलों के व्युत्क्रमों का योग क्या है?

What is the sum of reciprocals of the roots of \(4x^2-13x+9=0\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{13}{9} \)

Step 1

Concept

The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here it is \(\frac{\frac{13}{4}}{\frac{9}{4}}=\frac{13}{9}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{13}{9} \). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here it is \(\frac{\frac{13}{4}}{\frac{9}{4}}=\frac{13}{9}\).

Step 3

Exam Tip

व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\frac{\frac{13}{4}}{\frac{9}{4}}=\frac{13}{9}\) है।

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Question 193/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(x^2+2px+25=0\) के वास्तविक मूल होने की शर्त कौन-सी है?

What is the condition for \(x^2+2px+25=0\) to have real roots?

Explanation opens after your attempt

Correct Answer

A. \(p\leq -5\) या \(p\geq5\)\(p\leq -5\) or \(p\geq5\)

Step 1

Concept

For real roots, \(D\geq0\) is needed. Here \(4p^2-100\geq0\), so \(p\leq-5\) or \(p\geq5\).

Step 2

Why this answer is correct

The correct answer is A. \(p\leq -5\) या \(p\geq5\) / \(p\leq -5\) or \(p\geq5\). For real roots, \(D\geq0\) is needed. Here \(4p^2-100\geq0\), so \(p\leq-5\) or \(p\geq5\).

Step 3

Exam Tip

वास्तविक मूलों के लिए \(D\geq0\) चाहिए। यहाँ \(4p^2-100\geq0\), इसलिए \(p\leq-5\) या \(p\geq5\)।

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Question 194/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि \(x^2-2mx+36=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?

If the roots of \(x^2-2mx+36=0\) are equal, what are the possible values of (m)?

Explanation opens after your attempt

Correct Answer

A. \(m=\pm6\)

Step 1

Concept

For equal roots, (D=0), so ((-2m)²-144=0). This gives \(m^2=36\) and \(m=\pm6\).

Step 2

Why this answer is correct

The correct answer is A. \(m=\pm6\). For equal roots, (D=0), so ((-2m)²-144=0). This gives \(m^2=36\) and \(m=\pm6\).

Step 3

Exam Tip

समान मूलों के लिए (D=0), अतः ((-2m)²-144=0) होगा। इससे \(m^2=36\) और \(m=\pm6\) है।

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Question 195/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

मूलों का योग (-11) और गुणनफल (30) वाला मोनिक द्विघात समीकरण कौन-सा है?

Which monic quadratic equation has sum of roots (-11) and product (30)?

Explanation opens after your attempt

Correct Answer

A. \(x^2+11x+30=0\)

Step 1

Concept

\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-11) gives (x^2+11x+30=0).\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2+11x+30=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-11) gives (x^2+11x+30=0).\)

Step 3

Exam Tip

\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-11) रखने पर (x^2+11x+30=0) मिलता है\)।

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Question 196/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि (x=-3) समीकरण \(4x^2+px-9=0\) का मूल है, तो (p) का मान क्या होगा?

If (x=-3) is a root of \(4x^2+px-9=0\), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

Putting (x=-3) gives (36-3p-9=0). Hence (p=9).

Step 2

Why this answer is correct

The correct answer is A. (9). Putting (x=-3) gives (36-3p-9=0). Hence (p=9).

Step 3

Exam Tip

(x=-3) रखने पर (36-3p-9=0) मिलता है। इससे (p=9) है।

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Question 197/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

What is the standard form with integer coefficients of \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\)?

Explanation opens after your attempt

Correct Answer

A. \(4x^2+5x-59=0\)

Step 1

Concept

Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+5x-59=0\). Multiplying the whole equation by (10) gives \(4x^2-2+5x+15=70\). Therefore the standard form is \(4x^2+5x-57=0\).

Step 3

Exam Tip

पूरे समीकरण को (10) से गुणा करने पर \(4x^2-2+5x+15=70\) मिलता है। इसलिए \(4x^2+5x-57=0\) नहीं बल्कि \(4x^2+5x-57=0\) मिलेगा।

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Question 198/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

समीकरण ((x+2)²+2(x-3)²=35) का मानक रूप कौन-सा है?

What is the standard form of ((x+2)²+2(x-3)²=35)?

Explanation opens after your attempt

Correct Answer

A. \(3x^2-8x-13=0\)

Step 1

Concept

Expanding gives \(x^2+4x+4+2x^2-12x+18=35\). Hence \(3x^2-8x-13=0\) is correct.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-8x-13=0\). Expanding gives \(x^2+4x+4+2x^2-12x+18=35\). Hence \(3x^2-8x-13=0\) is correct.

Step 3

Exam Tip

विस्तार करने पर \(x^2+4x+4+2x^2-12x+18=35\) मिलता है। इसलिए \(3x^2-8x-13=0\) सही है।

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Question 199/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

यदि (\(k^2-25\)x^-2+(k-5)x+1=0) द्विघात समीकरण है, तो (k) पर सही शर्त क्या है?

If (\(k^2-25\)x^-2+(k-5)x+1=0) is a quadratic equation, what is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

C. \(k\neq \pm5\)

Step 1

Concept

For the equation to be quadratic, \(k^2-25\neq0\) is required. So both \(k\neq5\) and \(k\neq-5\) are necessary.

Step 2

Why this answer is correct

The correct answer is C. \(k\neq \pm5\). For the equation to be quadratic, \(k^2-25\neq0\) is required. So both \(k\neq5\) and \(k\neq-5\) are necessary.

Step 3

Exam Tip

द्विघात होने के लिए \(k^2-25\neq0\) होना चाहिए। इसलिए \(k\neq5\) और \(k\neq-5\) दोनों शर्तें जरूरी हैं।

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Question 200/600 Expert Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28

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

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

Explanation opens after your attempt

Correct Answer

A. \(6x^2+7x-16=0\)

Step 1

Concept

Here ((2x+5)(3x-4)=6x^-2+7x-20) and (4(x-1)=4x-4). Bringing all terms to one side gives \(6x^2+3x-16=0\).

Step 2

Why this answer is correct

The correct answer is A. \(6x^2+7x-16=0\). Here ((2x+5)(3x-4)=6x^-2+7x-20) and (4(x-1)=4x-4). Bringing all terms to one side gives \(6x^2+3x-16=0\).

Step 3

Exam Tip

((2x+5)(3x-4)=6x^-2+7x-20) और (4(x-1)=4x-4) है। सभी पद एक ओर लाने पर \(6x^2+3x-16=0\) नहीं बल्कि सही रूप \(6x^2+3x-16=0\) मिलता है।

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Question 201/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण ((x-2)(x+3)+(2x-1)(x-4)=0) का मानक रूप कौन-सा है?

What is the standard form of ((x-2)(x+3)+(2x-1)(x-4)=0)?

Explanation opens after your attempt

Correct Answer

A. \(3x^2-8x-2=0\)

Step 1

Concept

Here ((x-2)(x+3)=x^-2+x-6) and ((2x-1)(x-4)=2x^-2-9x+4). Adding them gives \(3x^2-8x-2=0\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-8x-2=0\). Here ((x-2)(x+3)=x^-2+x-6) and ((2x-1)(x-4)=2x^-2-9x+4). Adding them gives \(3x^2-8x-2=0\).

Step 3

Exam Tip

((x-2)(x+3)=x^-2+x-6) और ((2x-1)(x-4)=2x^-2-9x+4) है। जोड़ने पर \(3x^2-8x-2=0\) मिलता है।

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Question 202/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+px+q=0\) के मूल (3) और (p) हैं, तो (p) का संभावित मान क्या होगा?

If the roots of \(x^2+px+q=0\) are (3) and (p), what is a possible value of (p)?

Explanation opens after your attempt

Correct Answer

A. \(-\frac{3}{2}\)

Step 1

Concept

The sum of roots is (3+p), and in the equation the sum is (-p). Thus (3+p=-p), giving \(p=-\frac{3}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(-\frac{3}{2}\). The sum of roots is (3+p), and in the equation the sum is (-p). Thus (3+p=-p), giving \(p=-\frac{3}{2}\).

Step 3

Exam Tip

मूलों का योग (3+p) है और समीकरण में योग (-p) होता है। इसलिए (3+p=-p), जिससे \(p=-\frac{3}{2}\) मिलता है।

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Question 203/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-2ax+a^2-16=0\) है, तो मूलों का अंतर क्या होगा?

If \(x^2-2ax+a^2-16=0\), what will be the difference of the roots?

Explanation opens after your attempt

Correct Answer

A. (8)

Step 1

Concept

The equation is ((x-a)²-16=0), so the roots are (a+4) and (a-4). Their difference is (8).

Step 2

Why this answer is correct

The correct answer is A. (8). The equation is ((x-a)²-16=0), so the roots are (a+4) and (a-4). Their difference is (8).

Step 3

Exam Tip

समीकरण ((x-a)²-16=0) है, इसलिए मूल (a+4) और (a-4) हैं। उनका अंतर (8) है।

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Question 204/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

समीकरण \(x^2+8x+k=0\) के कोई वास्तविक मूल नहीं हैं। (k) पर सही शर्त क्या है?

The equation \(x^2+8x+k=0\) has no real roots. What is the correct condition on (k)?

Explanation opens after your attempt

Correct Answer

A. (k>16)

Step 1

Concept

For no real roots, (D<0) is needed. Here (64-4k<0), so (k>16).

Step 2

Why this answer is correct

The correct answer is A. (k>16). For no real roots, (D<0) is needed. Here (64-4k<0), so (k>16).

Step 3

Exam Tip

कोई वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (64-4k<0), इसलिए (k>16)।

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Question 205/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-4x-21=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+2\alpha+2\beta\) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-4x-21=0\), what is \(\alpha\beta+2\alpha+2\beta\)?

Explanation opens after your attempt

Correct Answer

A. (-13)

Step 1

Concept

Here \(\alpha+\beta=4\) and \(\alpha\beta=-21\). Thus (\alpha\beta+2\alpha+2\beta=-21+2(4)=-13).

Step 2

Why this answer is correct

The correct answer is A. (-13). Here \(\alpha+\beta=4\) and \(\alpha\beta=-21\). Thus (\alpha\beta+2\alpha+2\beta=-21+2(4)=-13).

Step 3

Exam Tip

यहाँ \(\alpha+\beta=4\) और \(\alpha\beta=-21\) है। इसलिए (\alpha\beta+2\alpha+2\beta=-21+2(4)=-13)।

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Question 206/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-9x+14=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)²) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-9x+14=0\), what is (\(\alpha+\beta\)²)?

Explanation opens after your attempt

Correct Answer

A. (81)

Step 1

Concept

The sum of roots is (9). Therefore (\(\alpha+\beta\)²=9²=81).

Step 2

Why this answer is correct

The correct answer is A. (81). The sum of roots is (9). Therefore (\(\alpha+\beta\)²=9²=81).

Step 3

Exam Tip

मूलों का योग (9) है। इसलिए (\(\alpha+\beta\)²=9²=81)।

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Question 207/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

एक समकोण त्रिभुज का आधार (x+2), ऊंचाई (x+6) और क्षेत्रफल (40) है। सही समीकरण कौन-सा है?

A right triangle has base (x+2), height (x+6), and area (40). Which equation is correct?

Explanation opens after your attempt

Correct Answer

A. \(x^2+8x-68=0\)

Step 1

Concept

The area is (\frac{1}{2}(x+2)(x+6)=40). Thus ((x+2)(x+6)=80) and \(x^2+8x-68=0\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+8x-68=0\). The area is (\frac{1}{2}(x+2)(x+6)=40). Thus ((x+2)(x+6)=80) and \(x^2+8x-68=0\).

Step 3

Exam Tip

क्षेत्रफल (\frac{1}{2}(x+2)(x+6)=40) होगा। इसलिए ((x+2)(x+6)=80) और \(x^2+8x-68=0\)।

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Question 208/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2-9x+20=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-4\)\(\beta-4\)) का मान क्या है?

If \(\alpha,\beta\) are roots of \(x^2-9x+20=0\), what is (\(\alpha-4\)\(\beta-4\))?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Here (20-36+16=0).

Step 2

Why this answer is correct

The correct answer is A. (0). (\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Here (20-36+16=0).

Step 3

Exam Tip

(\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16) है। यहाँ (20-36+16=0)।

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Question 209/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

यदि \(x^2+px+q=0\) के मूल (2) और (p) हैं, तो (q) के लिए कौन-सा संबंध सही है?

If the roots of \(x^2+px+q=0\) are (2) and (p), which relation is correct for (q)?

Explanation opens after your attempt

Correct Answer

A. (q=2p)

Step 1

Concept

The product of roots is (q). The given roots are (2) and (p), so (q=2p).

Step 2

Why this answer is correct

The correct answer is A. (q=2p). The product of roots is (q). The given roots are (2) and (p), so (q=2p).

Step 3

Exam Tip

मूलों का गुणनफल (q) होता है। दिए मूल (2) और (p) हैं, इसलिए (q=2p)।

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Question 210/600 Hard Mathematics Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30

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

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

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

The sum of roots is (5) and the product is (2). Therefore \(\alpha+\beta+2\alpha\beta=5+4=9\).

Step 2

Why this answer is correct

The correct answer is A. (9). The sum of roots is (5) and the product is (2). Therefore \(\alpha+\beta+2\alpha\beta=5+4=9\).

Step 3

Exam Tip

मूलों का योग (5) और गुणनफल (2) है। इसलिए \(\alpha+\beta+2\alpha\beta=5+4=9\)।

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quadratic equations MCQ Questions for Class 10

Practice Questions

समीकरण \(3x^2-14x+16=0\) में मूलों का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (x-2-(m+5)x+5m=0) का एक मूल (5) है, तो दूसरा मूल क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-8x+17=0\) के लिए कौन-सा कथन सही है?

Concept

Why this answer is correct

Exam Tip

यदि किसी मोनिक द्विघात समीकरण के मूल (r) और (3r) हैं तथा उनका योग (16) है, तो उस समीकरण का स्थिर पद क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण ((x+3)(x+6)+(x-2)(x+5)=70) का मानक रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-9x+18=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-3\)\(\beta-3\)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(5x^2+6x+1=0\) में मूलों के वर्गों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2+ax+24=0\) का एक मूल (4) है, तो दूसरा मूल और (a) कौन-से हैं?

Concept

Why this answer is correct

Exam Tip

किस समीकरण का विवेचक (-23) है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2-12x+k=0\) के मूल वास्तविक और भिन्न हों, तो (k) पर सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (5) और (6) 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 \(4x^2-13x+9=0\) के मूलों के व्युत्क्रमों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

समीकरण \(x^2+2px+25=0\) के वास्तविक मूल होने की शर्त कौन-सी है?

Concept

Why this answer is correct

Exam Tip

यदि \(x^2-2mx+36=0\) के मूल समान हैं, तो (m) के संभावित मान क्या हैं?

Concept

Why this answer is correct

Exam Tip

मूलों का योग (-11) और गुणनफल (30) वाला मोनिक द्विघात समीकरण कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (x=-3) समीकरण \(4x^2+px-9=0\) का मूल है, तो (p) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

समीकरण \(\frac{2x^2-1}{5}+\frac{x+3}{2}=7\) का पूर्णांक गुणांकों वाला मानक रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

समीकरण ((x+2)2+2(x-3)2=35) का मानक रूप कौन-सा है?

Concept

Why this answer is correct

Exam Tip

यदि (\(k^2-25\)x-2+(k-5)x+1=0) द्विघात समीकरण है, तो (k) पर सही शर्त क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

यदि (x^-2-(m+5)x+5m=0) का एक मूल (5) है, तो दूसरा मूल क्या है?

समीकरण ((x+2)²+2(x-3)²=35) का मानक रूप कौन-सा है?

यदि (\(k^2-25\)x^-2+(k-5)x+1=0) द्विघात समीकरण है, तो (k) पर सही शर्त क्या है?

यदि \(x^2-9x+14=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha+\beta\)²) का मान क्या है?