MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 1

From the official CBSE sample question paper for 2023-24, section A, question 1, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q1 · 1 mark · MCQReal Numbers

If two positive integers $a$ and $b$ are written as $a = x^{3} y^{2}$ and $b = x y^{3}$ , where $x, y$ are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM $(a, b)$ is

(A) $x y$
(B) $x y^{2}$
(C) $x^{3} y^{3}$
(D) $x^{2} y^{2}$

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

Open one hint at a time and try again before the next.

Hint 1

Recall the relation between product, HCF and LCM of two numbers.

Hint 2

Product ÷ LCM equals the HCF. Take the lowest power of each prime.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Product: $ab = x^{3} y^{2} \cdot x y^{3} = x^{4} y^{5}$ .
LCM takes the highest power of each prime: $LCM (a, b) = x^{3} y^{3}$ .
$\frac{ab}{LCM} = \frac{x ^{4} y ^{5}}{x ^{3} y ^{3}} = x y^{2}$ . This is the HCF, as expected. Option (B).
1 mark

Answer: $x y^{2}$ , option (B)

Where the marks are

Uses product ÷ LCM (= HCF) to get $x y^{2}$ , option (B) (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 1

Hints

Step-by-step solution

Revise the chapter

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