JMI 11th Science Entrance Paper 2026 Answer Key

96. If $x = \sqrt{3 + \sqrt{3 + \sqrt{3 + \dots \infty}}}$ and $x$ is a natural number, then

(a) $x^2+x-3=0$

(b) $x^2+2x+3=0$

(d) $x^2-x+3=0$

Answer:

(c)

x^2-x-3=0

Explanation:

Squaring both sides gives

x^2 = 3 + \sqrt{3 + \sqrt{3 + \dots}}

. The infinitely repeating term is identically

x

, so we get

x^2 = 3 + x

. Rearranging gives

x^2 – x – 3 = 0

97. The curved surface area of a cone having height 24cm and radius 10cm, is

(a) $528 \text{ cm}^2$

(b) $1056 \text{ cm}^2$

(d) $500 \text{ cm}^2$

Answer:

(c)

817.14 \text{ cm}^2

Explanation:

First, find the slant height

l

\sqrt{h^2 + r^2}

\sqrt{24^2 + 10^2}

\sqrt{576 + 100}

\sqrt{676}

26 \text{ cm}

. The curved surface area (CSA) is

\pi r l

\frac{22}{7} \times 10 \times 26 \approx 817.14 \text{ cm}^2

98. From a point on the ground, which is 15m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be $30^\circ$ . The height of the tower is

(a) $10\sqrt{3} \text{ m}$

(b) $5\sqrt{3} \text{ m}$

(d) 30 m

Answer:

(b)

5\sqrt{3} \text{ m}

Explanation:

In the right-angled triangle formed, $

\tan(30^\circ

) =

\frac{\text{height}}{\text{base distance}}

. Therefore,

\frac{1}{\sqrt{3}}

\frac{h}{15}

. Solving for

h

yields

h

\frac{15}{\sqrt{3}}

\frac{15\sqrt{3}}{3}

5\sqrt{3} \text{ m}

99. The next term of the A.P. $\sqrt{18}$ , $\sqrt{50}$ , $\sqrt{98}$ , … is,

(a) $\sqrt{146}$

(b) $\sqrt{128}$

(d) $\sqrt{200}$

Answer:

(c)

\sqrt{162}

Explanation:

We can simplify the sequence:

\sqrt{18}

3\sqrt{2}

\sqrt{50}

5\sqrt{2}

\sqrt{98}

7\sqrt{2}

. The common difference is $2\sqrt{2}$. The next term is

7\sqrt{2}

2\sqrt{2}

9\sqrt{2}

. Entering the 9 back into the root: $

\sqrt{9^2 \times 2}

\sqrt{81 \times 2}

\sqrt{162}

100. The probability of occurrence of an event can never be

(a) 1

(b) greater than 1

(d) None of these

Answer:

Explanation:

In probability theory, probability (

P

) is bound strictly between 0 and 1 inclusive (

0 \le P \le 1

). It can never be greater than 1 or negative.

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JMI 11th Science Entrance Paper 2026 Answer Key

JMI 11 SCIENCE ENTRANCE 2025 Solved paper with explanation is uploaded on our YouTube channel

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