Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A batsman has an average of 54 runs in 19 innings. How many runs should he score in the 20th innings to raise his average to 56?
94
84
78
54
Correct answer
94
What percent of 0.05 cubic meters is 25,000 cubic centimeters?
25%
50%
75%
100%
Correct answer
25%
The difference between the compound interest and simple interest on ₹18,000 for 2 years is ₹405. What is the rate of interest per annum?
10%
9%
15%
11%
Correct answer
10%
The profit obtained by selling a bicycle for ₹840 is the same as the loss incurred if it is sold for ₹760. What will be the percentage profit if the bicycle is sold for ₹900?
\( 16.28% \)
\( 12.5% \)
\( 20.62% \)
\( 19.25% \)
Correct answer
\( 16.28% \)
A shopkeeper mixes 40 kg of rice at ₹55 /kg with another grade at ₹85 /kg. He sells the mixture at ₹70 /kg, making a profit of \( 16 \frac{2}{3} % \). How many kg of the dearer rice did he use?
8 kg
9 kg
10 kg
11 kg
Correct answer
8 kg
A can lay a stretch of track in 8 days, B in 10 days. They undertake the work for ₹ 3,600. With C joining them, the job is finished in 4 days. How much should C receive?
₹ 300
₹ 360
₹ 400
₹ 460
Correct answer
₹ 300
Cities P and Q are 250 km apart. Two trains start from P and Q simultaneously. If they proceed in the same direction, they will encounter each other in 25 hours. If they travel towards each other, they meet in 5 hours. What is the speed of the slower train?
20 km/h
30 km/h
40 km/h
15 km/h
Correct answer
20 km/h
Determine the value of an expression \( (\frac{5}{a} + 5a) (\frac{25}{a^2} - 25 + 25a^2) \) if \( a = 3 \).
\( \frac{91250}{27} \)
\( \frac{82650}{27} \)
\( \frac{9800}{27} \)
\( \frac{92450}{27} \)
Correct answer
\( \frac{91250}{27} \)
A company has two machines, M1 and M2, producing widgets. M1 produces 60% of the widgets and M2 produces 40%. 3% of M1's widgets are defective, and 5% of M2's widgets are defective. If a randomly selected widget is found to be defective, what is the probability it came from M1?
0.36
0.47
0.53
0.64
Correct answer
0.36
A man on a lighthouse that stands 50 meters tall is observing a boat moving away from it. Over the course of 10 seconds, the angle of depression to the boat shifts from \( 60^\circ \) to \( 30^\circ \). What is the approximate speed of the boat?
5.0 m/s
5.8 m/s
6.5 m/s
7.2 m/s
Correct answer
5.0 m/s
A right prism has a regular pentagonal base of side length 7 cm and height 16 cm. Find the lateral surface area.
\( 260 \text{ cm}^2 \)
\( 280 \text{ cm}^2 \)
\( 300 \text{ cm}^2 \)
\( 560 \text{ cm}^2 \)
Correct answer
\( 260 \text{ cm}^2 \)
A hemisphere has radius \( R \). A sphere of maximum possible radius is inscribed in the hemisphere such that it touches the curved surface internally and rests on the hemisphere's base. Find the ratio of their surface areas.
3 : 1
7 : 4
6 : 5
3 : 5
Correct answer
3 : 1
A square and a regular hexagon share the same perimeter. What is the ratio of their areas?
2 : √3
√3 : 2
1 : √3
√3 : 1
Correct answer
2 : √3
An arc of a circle with radius 14 cm subtends an angle of 2 radians at the center. Find the length of the arc.
28 cm
14 cm
21 cm
25 cm
Correct answer
28 cm
If \(\tan A + \sec A = 5\) and \(A\) is acute, then find the value of \(\tan A\).
3
12/5
1
2
Correct answer
3
The mean of 2, 7, 5, 9, 14, 5 is \( m \). The numbers 12, 17, 19, 64, 9, -54, \( p \) have mean \( m + 5 \) and median \( q \). Then find the value of \( p + q \).
34
29
24
17
Correct answer
34
If the circumradius of triangle ABC is 12 cm, and its area is 48 \( \text{cm}^2 \), find the product of its sides.
48 \( \text{cm}^3 \)
192 \( \text{cm}^3 \)
2204 \( \text{cm}^3 \)
2304 \( \text{cm}^3 \)
Correct answer
48 \( \text{cm}^3 \)
Two tangents are drawn from an external point to a circle. What can be said about their lengths?
One is longer
Tangents are equal
One is shorter
Both are curved
Correct answer
One is longer
The x-intercept of the line \( 6x - 2y = 10 \) is = ?
\( 2/3 \)
\( 4/3 \)
\( 5/3 \)
\( 1/2 \)
Correct answer
\( 2/3 \)
Compute the Karl Pearson Coefficient of Skewness for the data given here 27, 3, 28, 40, 28, 30, 35, 27, 25, 27?
3
2
1
0
Correct answer
3
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.