Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Ram has 12 hens and 5 cows, Shyam has 18 hens and 9 cows, Preetham has 4 hens and 8 cows, and Vinay has 10 hens and 7 cows. Who has a greater ratio of hens to cows?
Preetham
Shyam
Ram
Vinay
Correct answer
Preetham
If tan θ + cot θ = 2, θ is an acute angle, then find the value of 2 tan25 θ + 3 cot20 θ + 5 tan30 θ cot15 θ.
8
6
10
12
Correct answer
8
The LCM of 96, 132 and 438 is:
86084
67055
85046
77088
Correct answer
86084
A runner runs a 750-metre race in 54 seconds. Find the runner’s speed (in km/h).
40
30
14
50
Correct answer
40
Vipin can do a piece of work in 2 days; Vaibhav can do the same work in 3 days and Chirag can do the same work in 6 days. If they start working together, how many days will they take to complete the work?
3
1
5
4
Correct answer
3
The greatest possible length that can be used to measure exactly the lengths of 3 m 15 cm, 5 m, and 6 m 85 cm is:
9 cm
11 cm
7 cm
5 cm
Correct answer
9 cm
A can do a certain piece of work in 2.4 times the number of days in which B and C together can do it. If A and B together can do the said piece of work in 27 days and C alone can do it in 75 days, then how many days will B take to do this piece of work alone?
54
48
45
42
Correct answer
54
Find the value of sin (50° + A) - cos (40° - A).
2
0
-1
1
Correct answer
2
Two metallic balls P and Q are such that the diameter of P is four times the diameter of Q. What is the ratio between the volumes of P and Q?
32 ∶ 1
16 ∶ 1
8 ∶ 1
64 ∶ 1
Correct answer
32 ∶ 1
Simplify the following.
9 × 2 ÷ 3 of 24 - 3 ÷ 2 × (6 - 7) × 2 + 3 ÷ 3 of 5
3
\(\frac{9}{20}\)
4
\(\frac{69}{20}\)
Correct answer
3
The following table gives the number of different types of batteries sold by a company over the years (numbers in hundreds).
| Type of battery → | 7 AH | 32 AH | 35 AH | 55 AH |
|---|---|---|---|---|
| Year ↓ | ||||
| 2018 | 20 | 30 | 40 | 50 |
| 2019 | 40 | 35 | 45 | 45 |
| 2020 | 50 | 40 | 40 | 40 |
| 2021 | 40 | 50 | 50 | 45 |
| 2022 | 45 | 45 | 35 | 55 |
What is the difference in the number of 7AH batteries sold in 2021 and 2022?
200
700
300
500
Correct answer
200
The LCM of 8, 12 and 18 is:
24
80
72
36
Correct answer
24
Rakesh runs a coaching institute having 50 faculty members. The average monthly salary of 35 faculty members is Rs. 37,500. What will be the average monthly salary (in Rs. ) of the other 15 faculty members, if the average monthly salary of all the 50 faculty members is found to be ₹Rs. 30,000?
13,000
13,500
12,500
12,000
Correct answer
13,000
A shopkeeper sells sugar at Rs. 40 per kg, which he purchased at Rs. 36 per kg. His weighing machine is faulty and it weighs only 800 gm while selling. His percentage profit (correct to 2 decimal places) is:
37.58%
40%
39.28%
38.89%
Correct answer
37.58%
Simplify the given expression.
(x - 2y)(y - 3x) + (x + y)(x - y) + (x - 3y)(2x + y)
2y(x - 3y)
2y(x + 3y)
2x(x - 3y)
2x(x + 3y)
Correct answer
2y(x - 3y)
The chord of a circle is equal to its radius. Find the difference between the angle subtended by this chord at the minor arc and major arc of the circle.
30°
120°
60°
150°
Correct answer
30°
In a store, Arun has two options to buy a mobile phone, either he can pay the full amount of Rs. 2,500 or he may buy at an instalment scheme, i.e. Rs. 520 in down payment and four equal instalments, rate of interest being charged at 25% p.a. simple interest. Arun buys a mobile phone on the instalment scheme. What is the monthly instalment for Arun?
Rs. 510
Rs. 530
Rs. 550
Rs. 520
Correct answer
Rs. 510
Find the fourth proportional of 22, 66 and 11.
23
33
17
39
Correct answer
23
If cot2θ = 1 - e2 , then the value of cosec θ + cot3 θ sec θ is:
\( \left(2-\mathrm{e}^2\right)^{\frac{1}{2}} \)
\( \left(1-\mathrm{e}^2\right)^{\frac{3}{2}}\)
\(\left(1-\mathrm{e}^2\right)\)
\( \left(2-\mathrm{e}^2\right)^{\frac{3}{2}}\)
Correct answer
\( \left(2-\mathrm{e}^2\right)^{\frac{1}{2}} \)
If Arun can complete \(2/3\)rd of a work in 12 days, then in how many days can he complete \(1/6\)th of the same work?
3
4
5
2
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.