A machine costing ₹ 1,00,000 has a… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Statistics & Applications

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A machine costing ₹ 1,00,000 has a useful life of 5 years. The estimated scrap value is ₹ 20,000. Using straight line method the annual depreciation is

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Held on 22 May 2025 · Verified 13 Jul 2026.

Options

A
₹ 12,000
B
₹ 16,000
C
₹ 20,000
D
₹ 10,000

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Solution

Given $n(A) = 5$ and $n(B) = 7$ .

A one-one function assigns each element in set A to a different element in set B. No two elements from A can map to the same element in B.

For the 1st element of A: 7 choices from B

For the 2nd element of A: 6 remaining choices

For the 3rd element of A: 5 remaining choices

For the 4th element of A: 4 remaining choices

For the 5th element of A: 3 remaining choices

Total number of one-one functions:

$7 \times 6 \times 5 \times 4 \times 3$

$= 42 \times 5$

$= 210 \times 4$

$= 840 \times 3$

$= 2520$

This can also be calculated using the permutation formula:

$^nP_r = \dfrac{n!}{(n-r)!}$

Where $n = 7$ and $r = 5$ :

$^7P_5 = \dfrac{7!}{(7-5)!}$

$= \dfrac{7!}{2!}$

$= 2520$

Therefore, the number of one-one functions from A to B is $2520$ .

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