Class 10 perfect-square MCQ Questions

Question 31/260 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(9x^2-6x+1=0\) में समान मूल का मान क्या है?

What is the equal root in \(9x^2-6x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{1}{3}\)

Step 1

Concept

Here (9x^-2-6x+1=(3x-1)²). Therefore the equal root is \(x=\frac{1}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{1}{3}\). Here (9x^-2-6x+1=(3x-1)²). Therefore the equal root is \(x=\frac{1}{3}\).

Step 3

Exam Tip

यहाँ (9x^-2-6x+1=(3x-1)²) है। इसलिए समान मूल \(x=\frac{1}{3}\) है।

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Question 32/260 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(4x^2-4wx+w^2=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(4x^2-4wx+w^2=0\)?

Explanation opens after your attempt

Correct Answer

A. हमेशा वास्तविक और समानAlways real and equal

Step 1

Concept

Here (D=(-4w)²-4(4)\(w^2\)=0). Therefore roots are equal for every real (w).

Step 2

Why this answer is correct

The correct answer is A. हमेशा वास्तविक और समान / Always real and equal. Here (D=(-4w)²-4(4)\(w^2\)=0). Therefore roots are equal for every real (w).

Step 3

Exam Tip

यहाँ (D=(-4w)²-4(4)\(w^2\)=0) है। इसलिए हर वास्तविक (w) पर मूल समान हैं।

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Question 33/260 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(5x^2-30x+45=0\) में मूलों की प्रकृति क्या है?

What is the nature of roots in \(5x^2-30x+45=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समान ((D=0))Two real and equal ((D=0))

Step 1

Concept

Here (D=(-30)²-4(5)(45)=0). It can also be seen as (5(x-3)²=0).

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान ((D=0)) / Two real and equal ((D=0)). Here (D=(-30)²-4(5)(45)=0). It can also be seen as (5(x-3)²=0).

Step 3

Exam Tip

यहाँ (D=(-30)²-4(5)(45)=0) है। इसे (5(x-3)²=0) के रूप में भी देख सकते हैं।

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Question 34/260 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(4x^2-20x+25=0\) में समान मूल का मान क्या है?

What is the equal root in \(4x^2-20x+25=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{5}{2}\)

Step 1

Concept

Here (D=(-20)²-4(4)(25)=0), and ((2x-5)²=0). So the equal root is \(x=\frac{5}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{5}{2}\). Here (D=(-20)²-4(4)(25)=0), and ((2x-5)²=0). So the equal root is \(x=\frac{5}{2}\).

Step 3

Exam Tip

यहाँ (D=(-20)²-4(4)(25)=0) और ((2x-5)²=0) है। इसलिए समान मूल \(x=\frac{5}{2}\) है।

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Question 35/260 Hard Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2-2px+p^2=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(x^2-2px+p^2=0\)?

Explanation opens after your attempt

Correct Answer

A. हमेशा वास्तविक और समानAlways real and equal

Step 1

Concept

Here (D=(-2p)²-4p^-2=0). Hence the roots are equal for every real (p).

Step 2

Why this answer is correct

The correct answer is A. हमेशा वास्तविक और समान / Always real and equal. Here (D=(-2p)²-4p^-2=0). Hence the roots are equal for every real (p).

Step 3

Exam Tip

यहाँ (D=(-2p)²-4p^-2=0) है। इसलिए हर वास्तविक (p) के लिए मूल समान हैं।

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Question 36/260 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(4x^2-4x+1=0\) के लिए सही कथन कौन सा है?

Which statement is correct for \(4x^2-4x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. मूल समान हैं और \(x=\frac{1}{2}\)Roots are equal and \(x=\frac{1}{2}\)

Step 1

Concept

Here (D=(-4)²-4(4)(1)=0), and the equation is ((2x-1)²=0). So the equal root is \(x=\frac{1}{2}\).

Step 2

Why this answer is correct

The correct answer is A. मूल समान हैं और \(x=\frac{1}{2}\) / Roots are equal and \(x=\frac{1}{2}\). Here (D=(-4)²-4(4)(1)=0), and the equation is ((2x-1)²=0). So the equal root is \(x=\frac{1}{2}\).

Step 3

Exam Tip

यहाँ (D=(-4)²-4(4)(1)=0) और समीकरण ((2x-1)²=0) है। इसलिए समान मूल \(x=\frac{1}{2}\) है।

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Question 37/260 Medium Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(9x^2+12x+4=0\) के मूलों की प्रकृति क्या है?

What is the nature of roots of \(9x^2+12x+4=0\)?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समान ((D=0))Two real and equal ((D=0))

Step 1

Concept

Here (D=12²-4(9)(4)=0). It is also the perfect-square form ((3x+2)²=0).

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान ((D=0)) / Two real and equal ((D=0)). Here (D=12²-4(9)(4)=0). It is also the perfect-square form ((3x+2)²=0).

Step 3

Exam Tip

यहाँ (D=12²-4(9)(4)=0) है। यह पूर्ण वर्ग रूप ((3x+2)²=0) भी है।

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Question 38/260 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 39

समीकरण \(x^2-6x+8=0\) के लिए (D) कौन सा है?

Which is (D) for the equation \(x^2-6x+8=0\)?

Explanation opens after your attempt

Correct Answer

A. (4)

Step 1

Concept

Here (D=(-6)²-4(1)(8)=4). (4) is a positive perfect square.

Step 2

Why this answer is correct

The correct answer is A. (4). Here (D=(-6)²-4(1)(8)=4). (4) is a positive perfect square.

Step 3

Exam Tip

यहाँ (D=(-6)²-4(1)(8)=4) है। (4) धनात्मक पूर्ण वर्ग है।

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Question 39/260 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 38

समीकरण \(9x^2-6x+1=0\) में मूलों की प्रकृति कौन सी है?

Which is the nature of roots in the equation \(9x^2-6x+1=0\)?

Explanation opens after your attempt

Correct Answer

A. वास्तविक और समानReal and equal

Step 1

Concept

Here (D=(-6)²-4(9)(1)=0). Hence the roots are equal.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और समान / Real and equal. Here (D=(-6)²-4(9)(1)=0). Hence the roots are equal.

Step 3

Exam Tip

यहाँ (D=(-6)²-4(9)(1)=0) है। इसलिए मूल समान हैं।

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Question 40/260 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(x^2+12x+36=0\) के बारे में सही कथन कौन सा है?

Which statement is correct about \(x^2+12x+36=0\)?

Explanation opens after your attempt

Correct Answer

A. यह समान वास्तविक मूल रखता हैit has equal real roots

Step 1

Concept

(x^-2+12x+36=(x+6)²). Being a perfect square, it has equal real roots.

Step 2

Why this answer is correct

The correct answer is A. यह समान वास्तविक मूल रखता है / it has equal real roots. (x^-2+12x+36=(x+6)²). Being a perfect square, it has equal real roots.

Step 3

Exam Tip

(x^-2+12x+36=(x+6)²) है। पूर्ण वर्ग होने से मूल समान वास्तविक हैं।

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Question 41/260 Easy Mathematics Quadratic Equations Nature of Roots Class 10 Level 37

समीकरण \(4x^2-12x+9=0\) को देखकर मूलों की प्रकृति क्या होगी?

By observing \(4x^2-12x+9=0\), what will be the nature of roots?

Explanation opens after your attempt

Correct Answer

A. दो वास्तविक और समानtwo real and equal

Step 1

Concept

\(4x^2-12x+9\) is a perfect square ((2x-3)²). So the roots are equal and real.

Step 2

Why this answer is correct

The correct answer is A. दो वास्तविक और समान / two real and equal. \(4x^2-12x+9\) is a perfect square ((2x-3)²). So the roots are equal and real.

Step 3

Exam Tip

\(4x^2-12x+9\) एक पूर्ण वर्ग ((2x-3)²) है। इसलिए मूल समान वास्तविक हैं।

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Question 42/260 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(x^2-2\sqrt{17}x+17=0\) को किस रूप में लिखा जा सकता है?

In which form can \(x^2-2\sqrt{17}x+17=0\) be written?

Explanation opens after your attempt

Correct Answer

A. (\(x-\sqrt{17}\)²=0)

Step 1

Concept

Since (17=\(\sqrt{17}\)²) and the middle term is \(-2\sqrt{17}x\), it is (\(x-\sqrt{17}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 2

Why this answer is correct

The correct answer is A. (\(x-\sqrt{17}\)²=0). Since (17=\(\sqrt{17}\)²) and the middle term is \(-2\sqrt{17}x\), it is (\(x-\sqrt{17}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 3

Exam Tip

क्योंकि (17=\(\sqrt{17}\)²) और मध्य पद \(-2\sqrt{17}x\) है, इसलिए यह (\(x-\sqrt{17}\)²) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।

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Question 43/260 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(x^2+2\sqrt{13}x+13=0\) को किस रूप में लिखा जा सकता है?

In which form can \(x^2+2\sqrt{13}x+13=0\) be written?

Explanation opens after your attempt

Correct Answer

A. (\(x+\sqrt{13}\)²=0)

Step 1

Concept

Since (13=\(\sqrt{13}\)²) and the middle term is \(2\sqrt{13}x\), it is (\(x+\sqrt{13}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 2

Why this answer is correct

The correct answer is A. (\(x+\sqrt{13}\)²=0). Since (13=\(\sqrt{13}\)²) and the middle term is \(2\sqrt{13}x\), it is (\(x+\sqrt{13}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 3

Exam Tip

क्योंकि (13=\(\sqrt{13}\)²) और मध्य पद \(2\sqrt{13}x\) है, इसलिए यह (\(x+\sqrt{13}\)²) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।

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Question 44/260 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(x^2-2\sqrt{11}x+11=0\) को किस रूप में लिखा जा सकता है?

In which form can \(x^2-2\sqrt{11}x+11=0\) be written?

Explanation opens after your attempt

Correct Answer

A. (\(x-\sqrt{11}\)²=0)

Step 1

Concept

Since (11=\(\sqrt{11}\)²) and the middle term is \(-2\sqrt{11}x\), it is (\(x-\sqrt{11}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 2

Why this answer is correct

The correct answer is A. (\(x-\sqrt{11}\)²=0). Since (11=\(\sqrt{11}\)²) and the middle term is \(-2\sqrt{11}x\), it is (\(x-\sqrt{11}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 3

Exam Tip

क्योंकि (11=\(\sqrt{11}\)²) और मध्य पद \(-2\sqrt{11}x\) है, इसलिए यह (\(x-\sqrt{11}\)²) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।

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Question 45/260 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(x^2+2\sqrt{7}x+7=0\) को किस रूप में लिखा जा सकता है?

In which form can \(x^2+2\sqrt{7}x+7=0\) be written?

Explanation opens after your attempt

Correct Answer

A. (\(x+\sqrt{7}\)²=0)

Step 1

Concept

Since (7=\(\sqrt{7}\)²) and the middle term is \(2\sqrt{7}x\), it is (\(x+\sqrt{7}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 2

Why this answer is correct

The correct answer is A. (\(x+\sqrt{7}\)²=0). Since (7=\(\sqrt{7}\)²) and the middle term is \(2\sqrt{7}x\), it is (\(x+\sqrt{7}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 3

Exam Tip

क्योंकि (7=\(\sqrt{7}\)²) और मध्य पद \(2\sqrt{7}x\) है, इसलिए यह (\(x+\sqrt{7}\)²) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।

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Question 46/260 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(x^2-2\sqrt{5}x+5=0\) को किस रूप में लिखा जा सकता है?

In which form can \(x^2-2\sqrt{5}x+5=0\) be written?

Explanation opens after your attempt

Correct Answer

A. (\(x-\sqrt{5}\)²=0)

Step 1

Concept

Since (5=\(\sqrt{5}\)²) and the middle term is \(-2\sqrt{5}x\), it is (\(x-\sqrt{5}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 2

Why this answer is correct

The correct answer is A. (\(x-\sqrt{5}\)²=0). Since (5=\(\sqrt{5}\)²) and the middle term is \(-2\sqrt{5}x\), it is (\(x-\sqrt{5}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 3

Exam Tip

क्योंकि (5=\(\sqrt{5}\)²) और मध्य पद \(-2\sqrt{5}x\) है, इसलिए यह (\(x-\sqrt{5}\)²) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।

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Question 47/260 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(x^2+2\sqrt{3}x+3=0\) को किस रूप में लिखा जा सकता है?

In which form can \(x^2+2\sqrt{3}x+3=0\) be written?

Explanation opens after your attempt

Correct Answer

A. (\(x+\sqrt{3}\)²=0)

Step 1

Concept

Since (3=\(\sqrt{3}\)²) and the middle term is \(2\sqrt{3}x\), it is (\(x+\sqrt{3}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 2

Why this answer is correct

The correct answer is A. (\(x+\sqrt{3}\)²=0). Since (3=\(\sqrt{3}\)²) and the middle term is \(2\sqrt{3}x\), it is (\(x+\sqrt{3}\)²). In exams, identify perfect squares even with irrational coefficients.

Step 3

Exam Tip

क्योंकि (3=\(\sqrt{3}\)²) और मध्य पद \(2\sqrt{3}x\) है, इसलिए यह (\(x+\sqrt{3}\)²) है। परीक्षा में अपरिमेय गुणांक में भी पूर्ण वर्ग पहचानें।

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Question 48/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(49x^2-42x+9=0\) का मूल क्या है?

What is the root of \(49x^2-42x+9=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{3}{7}\)

Step 1

Concept

((7x-3)²=0), so (7x-3=0) and \(x=\frac{3}{7}\). In exams, solve the linear equation after square form.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{7}\). ((7x-3)²=0), so (7x-3=0) and \(x=\frac{3}{7}\). In exams, solve the linear equation after square form.

Step 3

Exam Tip

((7x-3)²=0), इसलिए (7x-3=0) और \(x=\frac{3}{7}\) है। परीक्षा में वर्ग रूप के बाद रैखिक समीकरण हल करें।

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Question 49/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(49x^2-42x+9=0\) को किस पूर्ण वर्ग रूप में लिखा जाएगा?

In which perfect square form will \(49x^2-42x+9=0\) be written?

Explanation opens after your attempt

Correct Answer

A. ((7x-3)²=0)

Step 1

Concept

(49x^-2-42x+9=(7x-3)²), so it is a perfect square. In exams, check \(2\cdot7x\cdot3=42x\).

Step 2

Why this answer is correct

The correct answer is A. ((7x-3)²=0). (49x^-2-42x+9=(7x-3)²), so it is a perfect square. In exams, check \(2\cdot7x\cdot3=42x\).

Step 3

Exam Tip

(49x^-2-42x+9=(7x-3)²), इसलिए यह पूर्ण वर्ग है। परीक्षा में \(2\cdot7x\cdot3=42x\) जांचें।

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Question 50/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(36x^2-60x+25=0\) का दोहराया हुआ मूल क्या है?

What is the repeated root of \(36x^2-60x+25=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{5}{6}\)

Step 1

Concept

((6x-5)²=0), so (6x-5=0) and \(x=\frac{5}{6}\). In exams, write the repeated root as a correct fraction.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{5}{6}\). ((6x-5)²=0), so (6x-5=0) and \(x=\frac{5}{6}\). In exams, write the repeated root as a correct fraction.

Step 3

Exam Tip

((6x-5)²=0), इसलिए (6x-5=0) और \(x=\frac{5}{6}\) है। परीक्षा में दोहराए हुए मूल को सही भिन्न में लिखें।

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Question 51/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(36x^2-60x+25=0\) किस पूर्ण वर्ग रूप में लिखा जाएगा?

In which perfect square form will \(36x^2-60x+25=0\) be written?

Explanation opens after your attempt

Correct Answer

A. ((6x-5)²=0)

Step 1

Concept

(36x^-2-60x+25=(6x-5)²), so it is a perfect square. In exams, recognize the pattern ((a-b)²).

Step 2

Why this answer is correct

The correct answer is A. ((6x-5)²=0). (36x^-2-60x+25=(6x-5)²), so it is a perfect square. In exams, recognize the pattern ((a-b)²).

Step 3

Exam Tip

(36x^-2-60x+25=(6x-5)²), इसलिए यह पूर्ण वर्ग है। परीक्षा में ((a-b)²) का पैटर्न पहचानें।

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Question 52/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(25x^2-20x+4=0\) का मूल क्या है?

What is the root of \(25x^2-20x+4=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{2}{5}\)

Step 1

Concept

((5x-2)²=0), so (5x-2=0) and \(x=\frac{2}{5}\). In exams, solve the linear equation after square form.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{2}{5}\). ((5x-2)²=0), so (5x-2=0) and \(x=\frac{2}{5}\). In exams, solve the linear equation after square form.

Step 3

Exam Tip

((5x-2)²=0), इसलिए (5x-2=0) और \(x=\frac{2}{5}\) है। परीक्षा में वर्ग रूप के बाद रैखिक समीकरण हल करें।

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Question 53/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(25x^2-20x+4=0\) को किस पूर्ण वर्ग रूप में लिखा जाएगा?

In which perfect square form will \(25x^2-20x+4=0\) be written?

Explanation opens after your attempt

Correct Answer

A. ((5x-2)²=0)

Step 1

Concept

(25x^-2-20x+4=(5x-2)²), so it is a perfect square. In exams, check \(2\cdot5x\cdot2=20x\).

Step 2

Why this answer is correct

The correct answer is A. ((5x-2)²=0). (25x^-2-20x+4=(5x-2)²), so it is a perfect square. In exams, check \(2\cdot5x\cdot2=20x\).

Step 3

Exam Tip

(25x^-2-20x+4=(5x-2)²), इसलिए यह पूर्ण वर्ग है। परीक्षा में \(2\cdot5x\cdot2=20x\) जांचें।

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Question 54/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(16x^2-24x+9=0\) का दोहराया हुआ मूल क्या है?

What is the repeated root of \(16x^2-24x+9=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{3}{4}\)

Step 1

Concept

((4x-3)²=0), so (4x-3=0) and \(x=\frac{3}{4}\). In exams, write the repeated root as a correct fraction.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{4}\). ((4x-3)²=0), so (4x-3=0) and \(x=\frac{3}{4}\). In exams, write the repeated root as a correct fraction.

Step 3

Exam Tip

((4x-3)²=0), इसलिए (4x-3=0) और \(x=\frac{3}{4}\) है। परीक्षा में दोहराए हुए मूल को भी सही भिन्न में लिखें।

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Question 55/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(16x^2-24x+9=0\) किस पूर्ण वर्ग रूप में लिखा जाएगा?

In which perfect square form will \(16x^2-24x+9=0\) be written?

Explanation opens after your attempt

Correct Answer

A. ((4x-3)²=0)

Step 1

Concept

(16x^-2-24x+9=(4x-3)²), so it is a perfect square. In exams, recognize the pattern ((a-b)²).

Step 2

Why this answer is correct

The correct answer is A. ((4x-3)²=0). (16x^-2-24x+9=(4x-3)²), so it is a perfect square. In exams, recognize the pattern ((a-b)²).

Step 3

Exam Tip

(16x^-2-24x+9=(4x-3)²), इसलिए यह पूर्ण वर्ग है। परीक्षा में ((a-b)²) का पैटर्न पहचानें।

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Question 56/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(9x^2-30x+25=0\) का मूल क्या है?

What is the root of \(9x^2-30x+25=0\)?

Explanation opens after your attempt

Correct Answer

A. \(x=\frac{5}{3}\)

Step 1

Concept

((3x-5)²=0), so (3x-5=0) and \(x=\frac{5}{3}\). In exams, solve the linear equation after square form.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{5}{3}\). ((3x-5)²=0), so (3x-5=0) and \(x=\frac{5}{3}\). In exams, solve the linear equation after square form.

Step 3

Exam Tip

((3x-5)²=0), इसलिए (3x-5=0) और \(x=\frac{5}{3}\) है। परीक्षा में वर्ग रूप के बाद रैखिक समीकरण हल करें।

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Question 57/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(9x^2-30x+25=0\) को किस पूर्ण वर्ग रूप में लिखा जाएगा?

In which perfect square form will \(9x^2-30x+25=0\) be written?

Explanation opens after your attempt

Correct Answer

A. ((3x-5)²=0)

Step 1

Concept

(9x^-2-30x+25=(3x-5)²). In exams, check the pattern using \(2\cdot3x\cdot5=30x\).

Step 2

Why this answer is correct

The correct answer is A. ((3x-5)²=0). (9x^-2-30x+25=(3x-5)²). In exams, check the pattern using \(2\cdot3x\cdot5=30x\).

Step 3

Exam Tip

(9x^-2-30x+25=(3x-5)²) है। परीक्षा में \(2\cdot3x\cdot5=30x\) से पैटर्न जांचें।

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Question 58/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(4x^2-12x+9=0\) का दोहराया हुआ मूल क्या है?

What is the repeated root of \(4x^2-12x+9=0\)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

((2x-3)²=0), so (2x-3=0) and \(x=\frac{3}{2}\). In exams, write the repeated root with the correct value.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{2}\). ((2x-3)²=0), so (2x-3=0) and \(x=\frac{3}{2}\). In exams, write the repeated root with the correct value.

Step 3

Exam Tip

((2x-3)²=0), इसलिए (2x-3=0) और \(x=\frac{3}{2}\) है। परीक्षा में दोहराए हुए मूल को भी सही मान से लिखें।

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Question 59/260 Medium Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(4x^2-12x+9=0\) किस पूर्ण वर्ग रूप में लिखा जाएगा?

In which perfect square form will \(4x^2-12x+9=0\) be written?

Explanation opens after your attempt

Correct Answer

A. ((2x-3)²=0)

Step 1

Concept

(4x^-2-12x+9=(2x-3)²), so it is a perfect square. In exams, recognize the pattern ((a-b)²).

Step 2

Why this answer is correct

The correct answer is A. ((2x-3)²=0). (4x^-2-12x+9=(2x-3)²), so it is a perfect square. In exams, recognize the pattern ((a-b)²).

Step 3

Exam Tip

(4x^-2-12x+9=(2x-3)²), इसलिए यह पूर्ण वर्ग है। परीक्षा में ((a-b)²) का पैटर्न पहचानें।

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Question 60/260 Easy Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

यदि \(x^2+10x+k\) एक पूर्ण वर्ग हो और उसका रूप ((x+5)²) हो, तो (k) क्या होगा?

If \(x^2+10x+k\) is a perfect square and its form is ((x+5)²), what is (k)?

Explanation opens after your attempt

Correct Answer

A. (25)

Step 1

Concept

((x+5)²=x^-2+10x+25), so (k=25). In exams, remember perfect square expansion.

Step 2

Why this answer is correct

The correct answer is A. (25). ((x+5)²=x^-2+10x+25), so (k=25). In exams, remember perfect square expansion.

Step 3

Exam Tip

((x+5)²=x^-2+10x+25), इसलिए (k=25) है। परीक्षा में पूर्ण वर्ग विस्तार याद रखें।

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perfect-square MCQ Questions for Class 10

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यदि \(x^2+10x+k\) एक पूर्ण वर्ग हो और उसका रूप ((x+5)²) हो, तो (k) क्या होगा?