Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A travels for 8 hours at the rate of 4 km/h and for 4 hours at the rate of 8 km/h. The average speed of the journey (in km/h) is:
\(4 \frac{2}{3}\)
\(5 \frac{1}{3}\)
\(4 \frac{1}{3}\)
\(5\frac{2}{3}\)
Correct answer
\(4 \frac{2}{3}\)
Two trains are moving in the same direction at 60 km/h and 42 km/h. The faster train crosses a man in the slower train in 36 seconds. Find the length of the faster train.
185 m
195 m
180 m
175 m
Correct answer
185 m
Let a be a positive number and \(b=\frac{4}{a}\). What is the mean proportional of a and b ?
a
3
2
4
Correct answer
a
A gear 15 cm in diameter is turning a gear 21 cm in diameter. When the smaller gear has 105 revolutions, how many has the larger one made?
100
75
85
90
Correct answer
100
If the polynomial (2x3 + ax2 + 3x - 5) and (x3 + x2 - 2x + a) leave the same remainder when divided by (x-2), find the remainder.
4
2
3
5
Correct answer
4
Simplify the given expression.
\(\frac{13 \div{6-6 \div(7-9) \times 8+9}}{5+5 \times 5 \div 5 \text { of } 5}\)
\(\frac{1}{18}\)
13
39
\(\frac{1}{2}\)
Correct answer
\(\frac{1}{18}\)
The value of \(\left(\frac{2 \cos ^3 \theta-\cos \theta}{\sin \theta-2 \sin ^3 \theta}\right)^2+1 \), θ ≠ 45° is:
sec2 θ
cot2 θ
cosec2 θ
sin2 θ
Correct answer
sec2 θ
If \(\rm \frac{a}{b}+\frac{b}{a}=1, a \neq 0, b \neq 0\), then find the value of \(\rm \frac{a^3+b^3}{3 a b}\).
3
2
-3
0
Correct answer
3
If x = 11, then the value of (x5 - 12x4 + 12x3 - 12x2 + 12x - 1) is:
14
9
8
10
Correct answer
14
A trader sells pulses at a 32% profit and uses weights 20% less than the actual measure. Find his gain percentage.
72%
62%
58%
65%
Correct answer
72%
Consider the data of a certain number of activities of type P, Q, and R in the percentage of the total activities of the cities B, C, D, and K in the table below.
| City → | B | C | D | K |
|---|---|---|---|---|
| Activity ↓ | ||||
| P | 45 | 30 | 25 | 35 |
| Q | 25 | 30 | 35 | 30 |
| R | 30 | 40 | 40 | 35 |
If the total activities of B and C are 500 and 400, respectively, then what is the difference in activity R of B and C?
15
10
30
20
Correct answer
15
The following table shows the number of new employees added to different categories of employees in a university and also the number of employees from these categories who left the university every year:
| Professor | Assistant Professor | Associate Professor | Peon | |||||
|---|---|---|---|---|---|---|---|---|
| New | Left | New | Left | New | Left | New | Left | |
| 2018 | 80 | - | 100 | - | 90 | - | 60 | - |
| 2019 | 100 | 60 | 150 | 40 | 110 | 30 | 80 | 10 |
| 2020 | 150 | 40 | 160 | 30 | 140 | 40 | 70 | 20 |
| 2021 | 180 | 60 | 200 | 50 | 190 | 50 | 80 | 30 |
| 2022 | 200 | 80 | 220 | 60 | 220 | 60 | 90 | 40 |
What is the difference between the total number of professors added to the university and the total number of associate professors added to the university during the years 2019 to 2022 ?
40
50
120
Correct answer
What is the ratio between S and T if S is 75% of T?
2 ∶ 3
4 ∶ 3
75 ∶ 1
3 ∶ 4
Correct answer
2 ∶ 3
The area of the canvas cloth needed to erect a right conical tent of height 20ft. and circular base of circumference 30π ft. is:
375π sq.ft.
589π sq.ft.
470π sq.ft.
455π sq.ft.
Correct answer
375π sq.ft.
In an election between P, R and S, \(\frac{1}{10}\) of the total votes polled are invalid. Votes polled in favour of R and S are half of the total votes polled, and they get equal votes. Due to a fault in the machine, half of the votes of S and half of the invalid votes are counted additionally in favour of R. What is the overall percentage of votes secured by R due to the fault?
42.5%
38.5%
41.55%
37.55%
Correct answer
42.5%
P can do a piece of work in 30 days and Q in 40 days. They work together for 4 days and then Q leaves. The number of days taken by P to finish the remaining work is:
28 days
23 days
30 days
7 days
Correct answer
28 days
Find the perimeter of a triangle with sides equal to 13 cm, 12 cm and 5 cm.
5 cm
25 cm
30 cm
15 cm
Correct answer
5 cm
The cost of Compressed Natural Gas (CNG) per litre is increased by 65%. By what percentage must Manish reduce his consumption of CNG so as not to increase his expenditure? (correct up to two decimal places)
25.39%
45.13%
39.39%
30.13%
Correct answer
25.39%
Arrange the following ratios in ascending order.
3 ∶ 4, 3 ∶ 5, 2 ∶ 11, 7 ∶ 2
3 ∶ 5 < 2 ∶ 11 < 3 ∶ 4 < 7 ∶ 2
2 ∶ 11 < 3 ∶ 5 < 3 ∶ 4 < 7 ∶ 2
7 ∶ 2 < 3 ∶ 4 < 3 ∶ 5 < 2 ∶ 11
3 ∶ 4 < 3 ∶ 5 < 2 ∶ 11 < 7 ∶ 2
Correct answer
3 ∶ 5 < 2 ∶ 11 < 3 ∶ 4 < 7 ∶ 2
Three circles each of radius 5 cm touch one another. The area (in cm2) subtended between them is:
\(25\left(\sqrt{3}+\frac{\pi}{2}\right) \)
\(25\left(2 \sqrt{3}-\frac{\pi}{2}\right)\)
\(50\left(\sqrt{3}-\frac{\pi}{2}\right) \)
\(25\left(\sqrt{3}-\frac{\pi}{2}\right)\)
Correct answer
\(25\left(\sqrt{3}+\frac{\pi}{2}\right) \)
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.