JMI BEd PYQ 2025 || Jamia BEd Previous Year Question with Explanation

Q. 111. Determine the solution set for the system $5x – 15y = 8$ and $3x – 9y = 24/5$ .

(A) No solution

(B) Exactly one solution

(D) Two solutions

Answer:

Explanation:

Dividing the first equation by 5 gives

x – 3y = 8/5

. Dividing the second equation by 3 gives

x – 3y = 8/5

. Since they are identical lines, there are infinitely many solutions.

Q. 112. Solve the equation $3 + 30/x^2 = -21/x$.

(A) x = -5, -2

(B) x = -5, 2

(D) x = 2, 5

Answer:

Explanation:

Multiplying the entire equation by

x^2

gives

3x^2 + 30 = -21x

. Rearranging yields

3x^2 + 21x + 30 = 0

. Dividing by 3 yields

x^2 + 7x + 10 = 0

, which factors to

(x+5)(x+2) = 0

, so

x = -5, -2

Q. 113. If $\alpha$ and $\beta$ are roots of $x^2 – x – 1 = 0$ , find the equation with roots $\alpha/\beta$ and $\beta/\alpha$ .

(A) $x^2 + 3x – 1 = 0$

(B) $x^2 + x – 1 = 0$

(D) $x^2 + 3x + 1 = 0$

Answer:

(D)

x^2 + 3x + 1 = 0

Explanation:

For

x^2 – x – 1 = 0

, the sum of roots

\alpha+\beta=1

and product

\alpha\beta=-1

. The new roots

\alpha/\beta

and

\beta/\alpha

have a sum of

(\alpha^2+\beta^2)/(\alpha\beta) = ((\alpha+\beta)^2 – 2\alpha\beta)/(\alpha\beta) = (1 – 2(-1))/(-1) = -3

, and a product of 1. The new equation is

x^2 – (sum)x + (product) = 0

, or

x^2 + 3x + 1 = 0

Q. 114. If x, 12, 8, 32 are in continued proportion, what is x?

(A) 2

(B) 3

(D) 6

Answer:

Explanation:

In a continued proportion given as four values, the ratio between consecutive pairs remains constant.

x/12 = 8/32

. Solving for x gives

x = 12 \times (1/4) = 3

Q. 115. What is the area of $\triangle PQR$ with $P(0,1)$ , $Q(0,5)$ , $R(3,4)$ ?

(A) 4 sq units

(B) 6 sq units

(D) 16 sq units

Answer:

Explanation:

Using the vertices

P(0,1)

and

Q(0,5)

, the base PQ lying on the y-axis has a length of

5-1 = 4

. The height is the x-coordinate of R, which is 3. Area = 1/2 * base * height = 1/2 * 4 * 3 = 6 sq units.

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