JMI 11th Science Entrance Paper 2025 Answer Key

71. Question: If the ratio of the radius of a cone and a cylinder of equal volume is 3:5, find the ratio of their heights.

(a) 25/3

(b) 28/3

(c) 23/3

(d) 7

71. Explanation: Click Here

    Given Vcone​=Vcyl​ and rco​/rcy​=3/5. This leads to 31​π(rco​)2hco​=π(rcy​)2hcy​, which simplifies to hco​/hcy​=3×(rcy​/rco​)2=3×(5/3)2=25/3.

72. Question: A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

(a) 3:1:2

(b) 3:2:1

(c) 1:2:3

(d) 1:3:2

72. Explanation: Click Here

    Let radius be r and height be h=r. The volumes are Cylinder:πr3, Cone:31​πr3, Hemisphere:32​πr3. The ratio simplifies to 3:1:2.

73. Question: The relationship between mean, median and mode for a moderately skewed distribution is.

(a) mode = median – 2 mean

(b) mode = 3 median – 2 mean

(c) mode = 2 median – 3 mean

(d) mode = median – mean

73. Explanation: Click Here

    This is the standard empirical formula proposed by Karl Pearson to relate the three measures of central tendency.

74. Question: If P(A) denotes the probability of an event then:

(a) P(A) < 0

(b) P(A) > 0

(c) 0 ≤ P(A) ≤ 1

(d) -1 ≤ P(A) ≤ 0

74. Explanation: Click Here

    The probability of any event is always a value between 0 (impossible) and 1 (certain), inclusive.

75. Question: A card is drawn from a deck of 52 cards. The event E is that card is not an ace of hearts. The number of outcomes favorable to E is:

(a) 4

(b) 13

(c) 48

(d) 51

75. Explanation: Click Here

    There is only one ace of hearts. The number of cards that are not the ace of hearts is the total deck minus that one card: 52−1=51.