Concept-wise Practice

common-root MCQ Questions for Class 10

common-root se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

10 questions tagged with common-root.

\(10x^2-41x+40=0\) और \(15x^2-47x+30=0\) में कौनसा मूल समान है?

Which root is common to \(10x^2-41x+40=0\) and \(15x^2-47x+30=0\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The first equation has roots \(\frac{5}{2},\frac{8}{5}\), and the second has roots \(\frac{5}{2},\frac{4}{5}\). In exams, solve both equations separately for the common root.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{5}{2}\). The first equation has roots \(\frac{5}{2},\frac{8}{5}\), and the second has roots \(\frac{5}{2},\frac{4}{5}\). In exams, solve both equations separately for the common root.

Step 3

Exam Tip

पहले समीकरण के मूल \(\frac{5}{2},\frac{8}{5}\) और दूसरे के मूल \(\frac{5}{2},\frac{4}{5}\) हैं। परीक्षा में समान मूल के लिए दोनों समीकरण अलग हल करें।

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\(8x^2-30x+27=0\) और \(12x^2-31x+20=0\) में कौनसा मूल समान है?

Which root is common to \(8x^2-30x+27=0\) and \(12x^2-31x+20=0\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The first equation has roots \(\frac{3}{2},\frac{9}{4}\), and the second has roots \(\frac{3}{2},\frac{10}{9}\). In exams, solve both equations separately for the common root.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{2}\). The first equation has roots \(\frac{3}{2},\frac{9}{4}\), and the second has roots \(\frac{3}{2},\frac{10}{9}\). In exams, solve both equations separately for the common root.

Step 3

Exam Tip

पहले समीकरण के मूल \(\frac{3}{2},\frac{9}{4}\) और दूसरे के मूल \(\frac{3}{2},\frac{10}{9}\) हैं। परीक्षा में समान मूल के लिए दोनों समीकरण अलग हल करें।

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\(6x^2-19x+15=0\) और \(10x^2-27x+18=0\) में कौनसा मूल समान है?

Which root is common to \(6x^2-19x+15=0\) and \(10x^2-27x+18=0\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The first equation has roots \(\frac{3}{2},\frac{5}{3}\), and the second has roots \(\frac{3}{2},\frac{6}{5}\). In exams, solve both equations separately for the common root.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{2}\). The first equation has roots \(\frac{3}{2},\frac{5}{3}\), and the second has roots \(\frac{3}{2},\frac{6}{5}\). In exams, solve both equations separately for the common root.

Step 3

Exam Tip

पहले समीकरण के मूल \(\frac{3}{2},\frac{5}{3}\) और दूसरे के मूल \(\frac{3}{2},\frac{6}{5}\) हैं। परीक्षा में समान मूल के लिए दोनों समीकरण अलग हल करें।

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\(4x^2-12x+5=0\) और \(6x^2-17x+12=0\) में कौनसा मूल समान है?

Which root is common to \(4x^2-12x+5=0\) and \(6x^2-17x+12=0\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The first equation has roots \(\frac{1}{2},\frac{5}{2}\), and the second has roots \(\frac{3}{2},\frac{4}{3}\), so none of the listed values is common. In exams, solve both equations correctly before comparing.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{2}\). The first equation has roots \(\frac{1}{2},\frac{5}{2}\), and the second has roots \(\frac{3}{2},\frac{4}{3}\), so none of the listed values is common. In exams, solve both equations correctly before comparing.

Step 3

Exam Tip

पहले समीकरण के मूल \(\frac{1}{2},\frac{5}{2}\) हैं और दूसरे के मूल \(\frac{3}{2},\frac{4}{3}\) हैं, इसलिए दिए विकल्पों में समान मूल नहीं है। परीक्षा में तुलना से पहले दोनों समीकरण सही हल करें।

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\(5x^2-16x+12=0\) और \(6x^2-17x+12=0\) में कौनसा मूल समान है?

Which root is common to \(5x^2-16x+12=0\) and \(6x^2-17x+12=0\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

The first equation has roots \(2,\frac{6}{5}\), and the second has roots \(\frac{3}{2},\frac{4}{3}\), so there is no common root among the given values. In exams, solve both equations before comparing.

Step 2

Why this answer is correct

The correct answer is A. \(x=\frac{3}{2}\). The first equation has roots \(2,\frac{6}{5}\), and the second has roots \(\frac{3}{2},\frac{4}{3}\), so there is no common root among the given values. In exams, solve both equations before comparing.

Step 3

Exam Tip

पहले समीकरण के मूल \(\frac{6}{5},2\) नहीं बल्कि \(\frac{6}{5}\) और (2) हैं, इसलिए यह विकल्प नहीं है। सही जांच में दोनों समीकरणों के मूल क्रमशः \(2,\frac{6}{5}\) और \(\frac{3}{2},\frac{4}{3}\) हैं।

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\(3x^2-10x+8=0\) और \(4x^2-12x+8=0\) में कौनसा मूल समान है?

Which root is common to \(3x^2-10x+8=0\) and \(4x^2-12x+8=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=2)

Step 1

Concept

The roots of the first equation are \(2,\frac{4}{3}\), and the roots of the second are (2,1). In exams, solve both equations separately for the common root.

Step 2

Why this answer is correct

The correct answer is A. (x=2). The roots of the first equation are \(2,\frac{4}{3}\), and the roots of the second are (2,1). In exams, solve both equations separately for the common root.

Step 3

Exam Tip

पहले समीकरण के मूल \(2,\frac{4}{3}\) और दूसरे के मूल (2,1) हैं। परीक्षा में समान मूल के लिए दोनों समीकरण अलग-अलग हल करें।

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\(2x^2-5x+2=0\) और \(3x^2-8x+4=0\) में कौनसा मूल समान है?

Which root is common to \(2x^2-5x+2=0\) and \(3x^2-8x+4=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=2)

Step 1

Concept

The roots of the first equation are \(2,\frac{1}{2}\), and the roots of the second are \(2,\frac{2}{3}\). In exams, solve both equations separately for common root.

Step 2

Why this answer is correct

The correct answer is A. (x=2). The roots of the first equation are \(2,\frac{1}{2}\), and the roots of the second are \(2,\frac{2}{3}\). In exams, solve both equations separately for common root.

Step 3

Exam Tip

पहले समीकरण के मूल \(2,\frac{1}{2}\) और दूसरे के मूल \(2,\frac{2}{3}\) हैं। परीक्षा में समान मूल के लिए दोनों समीकरण अलग हल करें।

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\(x^2-11x+30=0\) और \(x^2-13x+42=0\) में कौनसा मूल समान है?

Which root is common to \(x^2-11x+30=0\) and \(x^2-13x+42=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=6)

Step 1

Concept

The roots of the first equation are (5,6), and the roots of the second are (6,7). In exams, solve both equations separately and compare the common root.

Step 2

Why this answer is correct

The correct answer is A. (x=6). The roots of the first equation are (5,6), and the roots of the second are (6,7). In exams, solve both equations separately and compare the common root.

Step 3

Exam Tip

पहले समीकरण के मूल (5,6) और दूसरे के मूल (6,7) हैं। परीक्षा में दोनों समीकरण अलग हल करके समान मूल देखें।

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\(x^2-7x+12=0\) और \(x^2-9x+20=0\) में कौनसा मूल समान है?

Which root is common to \(x^2-7x+12=0\) and \(x^2-9x+20=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=4)

Step 1

Concept

The roots of the first equation are (3,4), and the roots of the second are (4,5). In exams, solve both equations separately and compare the common root.

Step 2

Why this answer is correct

The correct answer is A. (x=4). The roots of the first equation are (3,4), and the roots of the second are (4,5). In exams, solve both equations separately and compare the common root.

Step 3

Exam Tip

पहले समीकरण के मूल (3,4) और दूसरे के मूल (4,5) हैं। परीक्षा में दोनों समीकरण अलग हल करके समान मूल देखें।

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\(x^2-5x+6=0\) और \(x^2-6x+8=0\) में कौनसा मूल समान है?

Which root is common to \(x^2-5x+6=0\) and \(x^2-6x+8=0\)?

Explanation opens after your attempt
Correct Answer

A. (x=2)

Step 1

Concept

The roots of the first equation are (2,3), and the roots of the second are (2,4). In exams, solve both equations separately and compare roots.

Step 2

Why this answer is correct

The correct answer is A. (x=2). The roots of the first equation are (2,3), and the roots of the second are (2,4). In exams, solve both equations separately and compare roots.

Step 3

Exam Tip

पहले समीकरण के मूल (2,3) और दूसरे के मूल (2,4) हैं। परीक्षा में दोनों समीकरण अलग-अलग हल करके समान मूल देखें।

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