2021.
Two circles with centres M and N have radii 5 cm and 8 cm, respectively. The circles touch each other externally at point T. A
line PR is drawn such that the points M, T and N lie on PR, P being closer to M. From P, a tangent PQ = 12 cm is drawn to the
circle with centre M touching at Q, and from R, another tangent RS = 15 cm is drawn to the circle with centre N touching at
S. What is the length (in cm) of PR?
(A)
37
(B)
43
(C)
53
(D)
26
2022.
A car covers a certain distance in 85 minutes, if it runs at a speed of 36 km/hr. The speed at which the car must run to
reduce the time of journey to 51 minutes will be:
(A)
70 km/hr
(B)
80 km/hr
(C)
60 km/hr
(D)
50 km/hr
2023.
The diameter of a cylinder is 14 cm and its height is 9 cm. Find the total surface area of the cylinder.
(A)
(B)
(C)
(D)
2024.
Express the following as decimals, respectively.
20%,0.5%,0.03%
(A)
0.02,0.005,0.0003
(B)
0.02,0.005,0.003
(C)
0.2,0.005,0.0003
(D)
0.2,0.0005,0.0003
2025.
How much time (in years) will it take for an amount of ₹4,50,000 to yield ₹45,000 as simple interest at a 5% per annum rate of
interest?
(A)
5
(B)
4
(C)
2
(D)
3
2026.
The measures of the three angles of a triangle are such that the smallest angle measures 42° less than the greatest angle,
while the measure of the remaining angle is 24° more than the measure of the smallest angle. Find the measure of the
smallest angle of the triangle.
(A)
42°
(B)
40°
(C)
38°
(D)
36°
2027.
In right triangle ABC with right angle at C, M is the mid-point of hypotenuse AB. C is joined to M and produced to a point D,
such that DM = CM. Point D is joined to B. If CD = 10 cm, and BD = 6 cm, find the value of CM.
(A)
8 cm
(B)
5 cm
(C)
9.5 cm
(D)
11.4 cm
2028.
The centers of two circles of radii 25 cm and 35 cm are 80 cm apart. What is the ratio of the lengths of the transverse
common tangent to the direct common tangent to these circles?
(A)
(B)
(C)
(D)
2029.
Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm.
(A)
43 cm2
(B)
41 cm2
(C)
40 cm2
(D)
42 cm2
2030.
10 years ago, a man’s age was 5 times of his son’s age. 2 years hence, twice his age will be equal to 4 times the age of his
son. What is the present age (in years) of the son?
