NIMCET 2025 Previous Year Questions (PYQs) – Page 12 of 12

Answer: Both conclusions follow.

Why:
From “All apples are fruits” and “All fruits are tasty,” it follows that all apples are tasty (I).
And from “All apples are tasty,” we can validly infer the particular statement some tasty things are apples (II), via valid conversion of a universal affirmative (“All A are B ⟹ Some B are A”).

Odd man out: 2) Pampering 

Cannot be determined uniquely.

John’s mother’s father = John’s maternal grandfather.
His granddaughter could be:

• John’s sister (his mother’s daughter), or

• John’s maternal cousin (daughter of his mother’s sibling).

So Maria is either John’s sister or his maternal cousin; the statement doesn’t fix which.

A person walks $8$ km north. 

Mohan’s sister’s brother = Mohan himself. 

2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
Answer = 36

1-digit numbers: 1 to 9 → 9 digits
2-digit numbers: 10 to 99 → 90 × 2 = 180 digits
Total till 99 → 9 + 180 = 189 digits
Remaining → 2028 − 189 = 1839 digits (in 3-digit range)
Each 3-digit number has 3 digits → 1839 ÷ 3 = 613 numbers (approx.)
Last full number before 2028th digit → 100 + 612 = 712
712 → digits are 7, 1, 2
Hence, the 2028th digit = 2

Answer: Only Conclusion 1 follows.

Reasoning:
Given “All engineers are good at math” ($E \to M$):

• It implies some good-at-math people are engineers (since at least one engineer would then be in the math-good group) → Conclusion 1 follows.

• It does not imply everyone good at math is an engineer ($M \to E$ is not guaranteed) → Conclusion 2 does not follow.

Let distances from the lighthouse be $x$ (for $30^\circ$) and $y$ (for $45^\circ$). With height $h=100$ m:

$\tan 30^\circ=\dfrac{100}{x}\ \Rightarrow\ x=\dfrac{100}{\tan30^\circ}=100\sqrt{3}$,   $\tan 45^\circ=\dfrac{100}{y}\ \Rightarrow\ y=\dfrac{100}{\tan45^\circ}=100$.

Ships are on opposite sides ⇒ distance $=x+y=100\sqrt{3}+100=100(\sqrt{3}+1)\approx \boxed{273.2\ \text{m}}$.