JMI 11th Science Entrance Paper 2023 Answer Key

41. Line formed by joining (-1, 1) and (5,7) is divided by a line x+y=4 in the ratio of:

(A) 1:4

(B) 1:3

(D) 3:4

Answer:

Explanation:

Using the section formula for ratio

k: 1

,
the intersection point is

(\frac{5k-1}{k+1}, \frac{7k+1}{k+1})

.
Substituting these into

x+y = 4

gives

\frac{12k}{k+1} =4

12k=4k+4

.
Ratio is 1:2.

42. The ratio of the length of a rod and its shadow is $1: \sqrt3$ . The angle of elevation of the sun is:

(A) 30°

(B) 60°

(D) None of these

Answer:

Explanation:

Let the angle of elevation be

\theta

tan\theta = \frac{height}{shadow length} =\frac{1}{\sqrt3}

Therefore ,

\theta = 30°

43. A circle is inscribed in a quadrilateral ABCD in which . If AD=23 cm, AB=29 cm and DS=5 cm, then the radius of the circle is:

(A) 10

(B) 11

(D) 09

Answer:

(B) 11

Explanation:

44. If P(, 4) is the mid point of the line segment joining the points Q(-6,5) and R(-2,3) then the value of “a” is:

(A) -4

(B) -12

(D) 6

Answer:

Explanation:

By the midpoint formula, the x-coordinate of P is

\frac{-6+(-2)}{2} = -4

. Setting this equal to the given x-coordinate:

a/3 = -4

a= -12

45. If x=1 is a common root of the equations $ax^2 + ax +3 = 0$ and $x^2 +x +b =0$ then ab=?

(A) 6

(B) 3

(D)

Answer:

Explanation:

Substituting

x=1

into the first equation:

a(1)^2 + a(1) +3 =0

2a = -3

a = -3/2

Substituting into the second:

1^2 + 1 + b = 0

b = -2

The product

ab = (-3/2)*(-2) =3

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