JMI 11th Science Entrance Paper 2025 Answer Key

Question: 54 is divided into two parts such that the sum of 10 times the first part and 22 times the second part is 780. What is the bigger part?

(a) 34

(b) 32

(d) 24

(a) 34

Explanation:

Let parts be x and (54-x). Then 10x+22(54−x)=780. Solving this equation gives x=34. The parts are 34 and 20.

(a) x(2x+3)=x2+1

(b) x(x+1)+8=(x+2)(x−2)

(d) (x−2)2+1=2x−3

(b) x(x+1)+8=(x+2)(x−2)

Simplifying option (b) gives x2+x+8=x2−4⟹x+12=0,
which is a linear equation because the x2 terms cancel out.

(a) 5n+2

(b) 5n+3

(d) 5n−3

Explanation:

Here, first term a=7 and common difference d=5. The (n−1)th term is an−1=a+((n−1)−1)d=7+(n−2)5=5n−3.

(a) 7.5 cm

(b) 3 cm

(d) 6 cm

By the Basic Proportionality Theorem, CD/DA=CE/EB. So,
3/DA=4/6⟹DA=(3×6)/4=4.5 cm.

Question: The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is.

(a) 63

(b) 35

(d) 36

Using the determinant formula for area, Area = 0.5∣x1(y2−y3)+x2(y3−y1)+x3(y1−y2)∣=0.5∣50+8+48∣=53
sq. units.

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