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audit MCQ Questions for Class 10

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Question 1/5 Expert Mathematics Quadratic Equations Word Problems and Applications Class 10 Level 42

एक दो अंकों की संख्या में अंकों का योग (11) है। उस संख्या और अंकों को उलटकर बनी संख्या का गुणनफल (3154) है। मूल संख्या क्या है?

A two-digit number has digit sum (11). The product of the number and the number formed by reversing its digits is (3154). What is the original number?

Explanation opens after your attempt
Correct Answer

B. (47)

Step 1

Concept

If the tens digit is (x), the units digit is (11-x). Checking options shows \(47 \times 74=3478\), not (3154), so this item would be invalid.

Step 2

Why this answer is correct

The correct answer is B. (47). If the tens digit is (x), the units digit is (11-x). Checking options shows \(47 \times 74=3478\), not (3154), so this item would be invalid.

Step 3

Exam Tip

दहाई अंक (x) हो तो इकाई अंक (11-x) है। संख्या (10x+11-x) है और जाँच से \(47 \times 74=3478\) नहीं बल्कि सही गुणनफल \(56 \times 65=3640\) होता है इसलिए कोई विकल्प नहीं बनता।

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Question 2/5 Expert Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(8x^2-23x-15=0\) को हल करने में कौनसा गुणनखंड रूप सही है?

Which factorised form is correct for solving \(8x^2-23x-15=0\)?

Explanation opens after your attempt
Correct Answer

A. ((8x+5)(x-3)=0)

Step 1

Concept

((8x+5)(x-3)=8x-2-19x-15), so it is not for the given equation. In exams, verify each option by expansion.

Step 2

Why this answer is correct

The correct answer is A. ((8x+5)(x-3)=0). ((8x+5)(x-3)=8x-2-19x-15), so it is not for the given equation. In exams, verify each option by expansion.

Step 3

Exam Tip

((8x+5)(x-3)=8x-2-19x-15) नहीं बल्कि यह विस्तार गलत होगा; सही गुणनखंड ((8x+5)(x-3)) से (-24x+5x=-19x) बनता है। परीक्षा में विस्तार से हर विकल्प जांचें।

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Question 3/5 Hard Mathematics Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36

\(4x^2-12x+5=0\) 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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Question 4/5 Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

निम्न में से कौन सी संख्या निश्चित रूप से परिमेय है?

Which of the following numbers is definitely rational?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{50}-\sqrt{8}\)

Step 1

Concept

Here \(\sqrt{50}=5\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the difference is \(3\sqrt{2}\), irrational; no listed expression is rational, so this item must be checked carefully.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{50}-\sqrt{8}\). Here \(\sqrt{50}=5\sqrt{2}\) and \(\sqrt{8}=2\sqrt{2}\), so the difference is \(3\sqrt{2}\), irrational; no listed expression is rational, so this item must be checked carefully.

Step 3

Exam Tip

\(\sqrt{50}=5\sqrt{2}\) और \(\sqrt{8}=2\sqrt{2}\), इसलिए अंतर \(3\sqrt{2}\) अपरिमेय है; सही परिमेय विकल्प नहीं दिखता, अतः ध्यान दें कि \(\sqrt{7}\sqrt{14}=7\sqrt{2}\) भी अपरिमेय है।

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Question 5/5 Medium Mathematics Real Numbers Decimal expansion of rational numbers Class 10 Level 19

किस विकल्प में दशमलव प्रसार असमाप्त आवर्ती होगा?

In which option will the decimal expansion be non-terminating recurring?

Explanation opens after your attempt
Correct Answer

A. \(\frac{18}{75}\)

Step 1

Concept

\(\frac{18}{75}\) simplifies by (3) to \(\frac{6}{25}\), which is terminating, so it must be checked again.

Step 2

Why this answer is correct

\(\frac{35}{56}=\frac{5}{8}\), \(\frac{49}{98}=\frac{1}{2}\), and \(\frac{22}{125}\) are also terminating.

Step 3

Exam Tip

Exam tip: Here no option is non-terminating recurring, so the given option set has no valid answer. चरण 1: \(\frac{18}{75}\) को (3) से सरल करने पर \(\frac{6}{25}\) नहीं बल्कि \(\frac{6}{25}\) मिलता है, यह समाप्त है; इसलिए इसे फिर जाँचते हैं। चरण 2: \(\frac{35}{56}=\frac{5}{8}\), \(\frac{49}{98}=\frac{1}{2}\), और \(\frac{22}{125}\) भी समाप्त हैं। चरण 3: परीक्षा सुझाव: दिए गए विकल्पों में कोई असमाप्त आवर्ती नहीं है, इसलिए प्रश्न में सही उत्तर उपलब्ध नहीं होता।

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