Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A train departs from Station P for Station Q at 9:00 AM, traveling at a speed of 60 km/h. Another train departs from Station Q for Station P at 11:00 AM traveling at a speed of 75 km/h. The distance between the two stations is 585 km. At what time will the two trains cross each other?
1:00 PM
2:26 PM
3:00 PM
4:00 PM
Correct answer
1:00 PM
If \(\sqrt{(1 - a^2)(1 - b^2)} = \frac{3}{5}\) and \(b = \frac{2}{5}\), then evaluate: \([(4a^2 + 4b^2 + 8ab) + (4a^2 + 4b^2 - 8ab)]\)
\(\frac{1024}{175}\)
\(\frac{1028}{177}\)
\(\frac{1052}{280}\)
\(\frac{1050}{250}\)
Correct answer
\(\frac{1024}{175}\)
A fair coin is flipped repeatedly. What is the expected number of flips until you get two consecutive Heads (HH)?
4
5
6
8
Correct answer
4
A climber ascends a vertical rock face at 5 m/min for the first 3 minutes, then at 3 m/min thereafter. From the bottom of the cliff, the angle of elevation to the climber is measured every minute. If at t=0 the angle is 30° and at t=7 min it is 60°, determine the cliff's height.
40.5 m
45.8 m
52.6 m
56.2 m
Correct answer
40.5 m
The base of a right prism is a right-angled triangle with legs 7 cm and 24 cm. The height of the prism is 12 cm.
Find the lateral surface area of the prism.
640 cm2
660 cm2
672 cm2
684 cm2
Correct answer
640 cm2
A solid hemisphere is mounted on a cylinder of equal radius. The total height of the combined solid is 6R. Find the total surface area.
13πR2
15πR2
16πR2
18πR2
Correct answer
13πR2
A circular disc of radius 10 cm is divided into 6 equal sectors. What is the angle of each sector?
60°
30°
45°
90°
Correct answer
60°
The complement of an angle is one-fourth the angle. Find the angle.
72°
7°
42°
87°
Correct answer
72°
If cotθ = 3/4, find the value of 1 + tan2θ.
25/9
1
16/9
9/16
Correct answer
25/9
Calculate P15 for the data given below:
6, 24, 36, 12, 20, 10
5
5.1
5.45
6.2
Correct answer
5
The inradius of a triangle with sides 7 cm, 24 cm, 25 cm is:
3 cm
6 cm
7 cm
2 cm
Correct answer
3 cm
The angle bisectors of angles A, B and C meet its circumcircle at P, Q and R. If ∠P = 72°, what is the value of ∠CAB?
18°
36°
54°
72°
Correct answer
18°
Calculate coefficient of mean deviation from median for the following data:
100, 150, 200, 250, 360, 490, 500, 600, 671
0.48
0.55
0.35
0.85
Correct answer
0.48
A line passes through the point (2, -4) and is parallel to the line y = 4x + 1. What is its equation?
y = 4x - 11
y = 4x - 12
y = 4x - 10
y = 3x - 12
Correct answer
y = 4x - 11
A quadrilateral ABCD is inscribed around a circle. If AB=10 cm, BC=12 cm, and the perimeter of the quadrilateral is 40 cm, what is the length of side CD?
8 cm
10 cm
12 cm
18 cm
Correct answer
8 cm
Simplify \((\sqrt{3} + \sqrt{5})^2\).
\(2 - 2\sqrt{15}\)
\(8 - 2\sqrt{15}\)
\(2 + 2\sqrt{15}\)
\(8 + 2\sqrt{15}\)
Correct answer
\(2 - 2\sqrt{15}\)
Chords AB and CD intersect inside a circle at point O.
If \(AO = 8\) cm, \(OB = 12\) cm, and \(CO = 6\) cm, find OD.
(O is the origin)
16 cm
15 cm
14 cm
13 cm
Correct answer
16 cm
Which is the most significant 4-digit number exactly divisible by 88?
9999
9988
9960
9944
Correct answer
9999
Find the value of: \( (\frac{1}{(5-\sqrt{6})}) + (\frac{1}{(5+\sqrt{6})}) - (\frac{10}{(25-6)}) \)
0
1
\( \sqrt{6} \)
2
Correct answer
0
X and Y make investments of ₹40,000 and ₹60,000, respectively. After one year, the total profit, which includes a 10% interest, amounts to ₹16,000. What portion of this profit does X receive?
₹10,000
₹10,400
₹6,000
₹6,400
Correct answer
₹10,000
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.