NIMCET 2020 Previous Year Questions (PYQs) – Page 2 of 12

Let mother’s present age = \(M\), person’s present age = \(P\).
Given:
\(P = \frac{2}{5} M\) ...(1)
After 8 years:
\(P + 8 = \frac{1}{2} (M + 8)\) ...(2)

Substitute \(P\) from (1) into (2):
\[ \frac{2}{5}M + 8 = \frac{1}{2}(M + 8) \] Multiply both sides by 10 to clear denominators:
\[ 4M + 80 = 5M + 40 \] \[ 80 - 40 = 5M - 4M \] \[ 40 = M \]

Answer: The mother’s present age is 40 years

Answer: The members of Team X are B, H, C and G.

Correct Option: 4) B, H, C and G

Seating (one valid arrangement):

A – C – E – H – F – B – D – G (circular)

Here, E is sitting between C and H.

Answer: C and H

Given: Total marbles = 30, each student gets between 5 and 10 marbles, all different.

A and C got odd marbles. B and D got even marbles.

A > B, C > D, and B > D.

Step 1: Possible distinct sets (5 to 10) with sum 30:

{5, 6, 9, 10}, {5, 7, 8, 10}, {6, 7, 8, 9}

Step 2: Check parity and conditions:

In {6, 7, 8, 9}:
Evens: 6, 8 → B > D ⇒ B = 8, D = 6
Odds: 7, 9 → A > B ⇒ A = 9, C = 7

Verify:

A > B ⇒ 9 > 8 ✔
C > D ⇒ 7 > 6 ✔
B > D ⇒ 8 > 6 ✔

Final Distribution:

A = 9, B = 8, C = 7, D = 6

Given: Total marbles = 30, each student gets between 5 and 10 marbles, all different.

A and C got odd marbles. B and D got even marbles.

A > B, C > D, and B > D.

Step 1: Possible distinct sets (5 to 10) with sum 30:

{5, 6, 9, 10}, {5, 7, 8, 10}, {6, 7, 8, 9}

Step 2: Check parity and conditions:

In {6, 7, 8, 9}:
Evens: 6, 8 → B > D ⇒ B = 8, D = 6
Odds: 7, 9 → A > B ⇒ A = 9, C = 7

Verify:

A > B ⇒ 9 > 8 ✔
C > D ⇒ 7 > 6 ✔
B > D ⇒ 8 > 6 ✔

Final Distribution:

A = 9, B = 8, C = 7, D = 6

mean(B,C,D)=$\dfrac{8+7+6}{3}$=7