JMI 11th Science Entrance Paper 2023 Answer Key

31. ABC is an isosceles triangle right-angled at C. The side AB is equal to:

(A) $\sqrt2AC^2$

(B) $AC$

(D) $AC + \sqrt2$

Answer:

(C)

\sqrt2AC

Explanation:

By the Pythagorean theorem,

AB^2 = AC^2 + BC^2

. Because it’s an isosceles triangle at C,

AC = BC

. So,

AB^2 = 2AC ^2

, which simplifies to

AB = \sqrt2AC

32. Five years ago, A was thrice as old as B and ten years later A shall be twice as old as B, then the present age of A is:

(A) 20

(B) 50

(D) None of these

Answer:

Explanation:

33. If the mean of frequency distribution is 7.5 and $\sum f_i x_i = 120 +3k$ and $\sum f_i = 30$ , then k is equal to:

(A) 40

(B) 35

(D) 45

Answer:

Explanation:

The formula for mean is

\frac{\sum f_i x_i}{\sum f_i}

. So,

7.5 = \frac{120+3k}{30}

. Multiplying gives

225 = 120 +3k

3k = 105

k=35

34. In a cylinder, if radius is doubled and height is halved then curved surface area will be:

(A) halved

(B) doubled

(D) four times

Answer:

Explanation:

The Curved Surface Area (CSA) of a cylinder is

2\pi rh

.
The new CSA is

2\pi (2r)(h/2) = 2\pi rh

. The area remains exactly the same.

35. Two dice are rolled together. The probability of getting an even number on both the dice is:

(A) 1/2

(B) 1/3

(D) 1/5

Answer:

Explanation:

The total number of outcomes is 36. Getting an even number on one die has 3 possibilities (2,4,6). Thus, there are favorable outcomes

3*3 = 9

. The probability is

\frac{9}{36} = \frac{1}{4}

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