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rational-equation MCQ Questions for Class 10

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12 questions tagged with rational-equation.

Question 1/12 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(\frac{x+6}{x}=\frac{49}{x+6}\), \(x\neq0,-6\), के हल क्या हैं?

What are the solutions of \(\frac{x+6}{x}=\frac{49}{x+6}\), \(x\neq0,-6\)?

Explanation opens after your attempt
Correct Answer

A. (x=1,36)

Step 1

Concept

(x-2-37x+36=(x-1)(x-36)), so (x=1) and (x=36). In exams, check solutions against excluded denominator values.

Step 2

Why this answer is correct

The correct answer is A. (x=1,36). (x-2-37x+36=(x-1)(x-36)), so (x=1) and (x=36). In exams, check solutions against excluded denominator values.

Step 3

Exam Tip

(x-2-37x+36=(x-1)(x-36)), इसलिए (x=1) और (x=36) हैं। परीक्षा में हर के निषिद्ध मानों से हलों की जांच करें।

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Question 2/12 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(\frac{x+6}{x}=\frac{49}{x+6}\), \(x\neq0,-6\), का सही द्विघात रूप कौनसा है?

What is the correct quadratic form of \(\frac{x+6}{x}=\frac{49}{x+6}\), \(x\neq0,-6\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-37x+36=0\)

Step 1

Concept

Cross multiplication gives ((x+6)2=49x), so \(x^2+12x+36-49x=0\), and \(x^2-37x+36=0\). In exams, cross multiply carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-37x+36=0\). Cross multiplication gives ((x+6)2=49x), so \(x^2+12x+36-49x=0\), and \(x^2-37x+36=0\). In exams, cross multiply carefully.

Step 3

Exam Tip

क्रॉस गुणा करने पर ((x+6)2=49x), इसलिए \(x^2+12x+36-49x=0\) और \(x^2-37x+36=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।

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Question 3/12 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(\frac{x+5}{x}=\frac{36}{x+5}\), \(x\neq0,-5\), के हल क्या हैं?

What are the solutions of \(\frac{x+5}{x}=\frac{36}{x+5}\), \(x\neq0,-5\)?

Explanation opens after your attempt
Correct Answer

A. (x=1,25)

Step 1

Concept

(x-2-26x+25=(x-1)(x-25)), so (x=1) and (x=25). In exams, check solutions against excluded denominator values.

Step 2

Why this answer is correct

The correct answer is A. (x=1,25). (x-2-26x+25=(x-1)(x-25)), so (x=1) and (x=25). In exams, check solutions against excluded denominator values.

Step 3

Exam Tip

(x-2-26x+25=(x-1)(x-25)), इसलिए (x=1) और (x=25) हैं। परीक्षा में हर के निषिद्ध मानों से हलों की जांच करें।

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Question 4/12 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(\frac{x+5}{x}=\frac{36}{x+5}\), \(x\neq0,-5\), का सही द्विघात रूप कौनसा है?

What is the correct quadratic form of \(\frac{x+5}{x}=\frac{36}{x+5}\), \(x\neq0,-5\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-26x+25=0\)

Step 1

Concept

Cross multiplication gives ((x+5)2=36x), so \(x^2+10x+25-36x=0\), and \(x^2-26x+25=0\). In exams, cross multiply carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-26x+25=0\). Cross multiplication gives ((x+5)2=36x), so \(x^2+10x+25-36x=0\), and \(x^2-26x+25=0\). In exams, cross multiply carefully.

Step 3

Exam Tip

क्रॉस गुणा करने पर ((x+5)2=36x), इसलिए \(x^2+10x+25-36x=0\) और \(x^2-26x+25=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।

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Question 5/12 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(\frac{x+4}{x}=\frac{25}{x+4}\), \(x\neq0,-4\), के हल क्या हैं?

What are the solutions of \(\frac{x+4}{x}=\frac{25}{x+4}\), \(x\neq0,-4\)?

Explanation opens after your attempt
Correct Answer

A. (x=1,16)

Step 1

Concept

(x-2-17x+16=(x-1)(x-16)), so (x=1) and (x=16). In exams, check solutions against excluded denominator values.

Step 2

Why this answer is correct

The correct answer is A. (x=1,16). (x-2-17x+16=(x-1)(x-16)), so (x=1) and (x=16). In exams, check solutions against excluded denominator values.

Step 3

Exam Tip

(x-2-17x+16=(x-1)(x-16)), इसलिए (x=1) और (x=16) हैं। परीक्षा में हर के निषिद्ध मानों से हलों की जांच करें।

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Question 6/12 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(\frac{x+4}{x}=\frac{25}{x+4}\), \(x\neq0,-4\), का सही द्विघात रूप कौनसा है?

What is the correct quadratic form of \(\frac{x+4}{x}=\frac{25}{x+4}\), \(x\neq0,-4\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-17x+16=0\)

Step 1

Concept

Cross multiplication gives ((x+4)2=25x), so \(x^2+8x+16-25x=0\), and \(x^2-17x+16=0\). In exams, cross multiply carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-17x+16=0\). Cross multiplication gives ((x+4)2=25x), so \(x^2+8x+16-25x=0\), and \(x^2-17x+16=0\). In exams, cross multiply carefully.

Step 3

Exam Tip

क्रॉस गुणा करने पर ((x+4)2=25x), इसलिए \(x^2+8x+16-25x=0\) और \(x^2-17x+16=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।

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Question 7/12 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(\frac{x+3}{x}=\frac{16}{x+3}\), \(x\neq0,-3\), के हल क्या हैं?

What are the solutions of \(\frac{x+3}{x}=\frac{16}{x+3}\), \(x\neq0,-3\)?

Explanation opens after your attempt
Correct Answer

A. (x=1,9)

Step 1

Concept

(x-2-10x+9=(x-1)(x-9)), so (x=1) and (x=9). In exams, check solutions against excluded denominator values.

Step 2

Why this answer is correct

The correct answer is A. (x=1,9). (x-2-10x+9=(x-1)(x-9)), so (x=1) and (x=9). In exams, check solutions against excluded denominator values.

Step 3

Exam Tip

(x-2-10x+9=(x-1)(x-9)), इसलिए (x=1) और (x=9) हैं। परीक्षा में हर के निषिद्ध मानों से हलों की जांच करें।

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Question 8/12 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(\frac{x+3}{x}=\frac{16}{x+3}\), \(x\neq0,-3\), का सही द्विघात रूप कौनसा है?

What is the correct quadratic form of \(\frac{x+3}{x}=\frac{16}{x+3}\), \(x\neq0,-3\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+9=0\)

Step 1

Concept

Cross multiplication gives ((x+3)2=16x), so \(x^2+6x+9-16x=0\), and \(x^2-10x+9=0\). In exams, cross multiply carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+9=0\). Cross multiplication gives ((x+3)2=16x), so \(x^2+6x+9-16x=0\), and \(x^2-10x+9=0\). In exams, cross multiply carefully.

Step 3

Exam Tip

क्रॉस गुणा करने पर ((x+3)2=16x), इसलिए \(x^2+6x+9-16x=0\) और \(x^2-10x+9=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।

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Question 9/12 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(\frac{x+2}{x}=\frac{9}{x+2}\), \(x\neq0,-2\), के हल क्या हैं?

What are the solutions of \(\frac{x+2}{x}=\frac{9}{x+2}\), \(x\neq0,-2\)?

Explanation opens after your attempt
Correct Answer

A. (x=1,4)

Step 1

Concept

(x-2-5x+4=(x-1)(x-4)), so (x=1) and (x=4). In exams, check solutions against excluded denominator values.

Step 2

Why this answer is correct

The correct answer is A. (x=1,4). (x-2-5x+4=(x-1)(x-4)), so (x=1) and (x=4). In exams, check solutions against excluded denominator values.

Step 3

Exam Tip

(x-2-5x+4=(x-1)(x-4)), इसलिए (x=1) और (x=4) हैं। परीक्षा में हर वाले निषिद्ध मानों से हलों की जांच करें।

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Question 10/12 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35

\(\frac{x+2}{x}=\frac{9}{x+2}\), \(x\neq0,-2\), का सही द्विघात रूप कौनसा है?

What is the correct quadratic form of \(\frac{x+2}{x}=\frac{9}{x+2}\), \(x\neq0,-2\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Cross multiplication gives ((x+2)2=9x), so \(x^2+4x+4-9x=0\), and \(x^2-5x+4=0\). In exams, cross multiply carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-5x+4=0\). Cross multiplication gives ((x+2)2=9x), so \(x^2+4x+4-9x=0\), and \(x^2-5x+4=0\). In exams, cross multiply carefully.

Step 3

Exam Tip

क्रॉस गुणा करने पर ((x+2)2=9x), इसलिए \(x^2+4x+4-9x=0\) और \(x^2-5x+4=0\) है। परीक्षा में क्रॉस गुणा सावधानी से करें।

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Question 11/12 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(\frac{x+1}{x}=\frac{6}{x+1}\), \(x\neq0,-1\), का सही द्विघात रूप कौनसा है?

What is the correct quadratic form of \(\frac{x+1}{x}=\frac{6}{x+1}\), \(x\neq0,-1\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x+1=0\)

Step 1

Concept

From ((x+1)2=6x), we get \(x^2+2x+1-6x=0\), that is \(x^2-4x+1=0\). In exams, avoid a wrong middle term.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+1=0\). From ((x+1)2=6x), we get \(x^2+2x+1-6x=0\), that is \(x^2-4x+1=0\). In exams, avoid a wrong middle term.

Step 3

Exam Tip

((x+1)2=6x) से \(x^2+2x+1-6x=0\), यानी \(x^2-4x+1=0\) मिलता है। परीक्षा में गलत मध्य पद से बचें।

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Question 12/12 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34

\(\frac{x+1}{x}=\frac{6}{x+1}\), \(x\neq0,-1\), को द्विघात रूप में बदलने पर क्या मिलेगा?

For \(\frac{x+1}{x}=\frac{6}{x+1}\), \(x\neq0,-1\), what quadratic form is obtained?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Cross multiplication gives ((x+1)2=6x), so \(x^2+2x+1=6x\), and the correct form is \(x^2-4x+1=0\). In exams, cross multiply very carefully.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2x-5=0\). Cross multiplication gives ((x+1)2=6x), so \(x^2+2x+1=6x\), and the correct form is \(x^2-4x+1=0\). In exams, cross multiply very carefully.

Step 3

Exam Tip

क्रॉस गुणा करने पर ((x+1)2=6x), इसलिए \(x^2+2x+1=6x\) और \(x^2-4x+1=0\) नहीं बल्कि जांच करने पर सही रूप ((x+1)2=6x) से \(x^2-4x+1=0\) बनता है। परीक्षा में क्रॉस गुणा बहुत सावधानी से करें।

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