Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
The number 150328 is divisible by 23. If the digits are rearranged in descending order and five times of 13 is subtracted from the new number thus formed, then the resultant number will be divisible by:
3
5
11
2
Correct answer
3
The LCM and HCF of two numbers are 126 and 9, respectively. If one of the numbers is 18, then what is the other number?
63
36
84
24
Correct answer
63
If cos 48° = \(\rm\frac{m}{n}\), then sec 48° - cot 42° is equal to:
\(\rm\frac{m-\sqrt{n^2-m^2}}{m}\)
\(\rm\frac{m-\sqrt{n^2-m^2}}{n}\)
\(\rm\frac{n-\sqrt{n^2-m^2}}{n}\)
\(\rm\frac{n-\sqrt{n^2-m^2}}{m}\)
Correct answer
\(\rm\frac{m-\sqrt{n^2-m^2}}{m}\)
The ratio of the number of boys to that of girls in a school is 5 ∶ 2. If 87% of the boys and 80% of the girls passed in the annual exams, then find the percentage of students who failed in the annual exams.
18%
16%
15%
17%
Correct answer
18%
As shown in the given figure, inside the large semicircle, three semicircles (with equal radii) are drawn so that their diameters all sit on the large semicircle's diameter. What is the ratio between the red and blue areas?
4 ∶ 3
1 ∶ 2
2 ∶ 1
3 ∶ 4
Correct answer
4 ∶ 3
The average marks of students in five subjects in class X in a school is given in the table.
| Year | History (Out of 200 marks) | Geography (Out of 100 marks) | Mathematics (Out of 200 marks) | Science (Out of 200 marks) | English (Out of 150 marks) |
|---|---|---|---|---|---|
| 1984 | 88 | 46 | 94 | 98 | 60 |
| 1985 | 90 | 35 | 88 | 120 | 90 |
| 1986 | 100 | 45 | 112 | 102 | 66 |
| 1987 | 120 | 38 | 96 | 112 | 45 |
| 1988 | 124 | 54 | 80 | 96 | 57 |
The average percentage marks of which of the following pairs of subjects was the same in 1985?
Geography, Mathematics
Science, Geography
Science, English
English, Mathematics
Correct answer
Geography, Mathematics
Two stations are 120 km apart on a straight line. A train starts from station A at 8 a.m. and moves towards station B at 20 km/h, and another train starts from station B at 9 a.m. and travels towards station A at a speed of 30 km/h. At what time will they meet?
10:30 a.m.
10:00 a.m.
11:00 a.m.
11:30 a.m.
Correct answer
10:30 a.m.
The value of the expression cos2 45° + cos2 135° + cos2 225° + cos2 315° is:
2
\(\frac{1}{2}\)
\(\frac{3}{2}\)
1
Correct answer
2
The given table represents the population of different villages.
| Name of village | Number of males | Number of females |
|---|---|---|
| A | 1500 | 1220 |
| B | 1460 | 1320 |
| C | 1105 | 1180 |
| D | 1305 | 1170 |
J : denotes the average number of males in villages A, B and C.
K : denotes the average number of females in villages B, C and D.
What is the average of J and K?
1289.17
1279.62
1278.36
1288.62
Correct answer
1289.17
Annual production of four different types of cold drinks has been tabulated below. Which of these cold-drinks has encountered maximum percentage increment in production?
| Cold drink | 2020 (units) | 2021 (units) |
|---|---|---|
| Sprite | 5400 | 5800 |
| Coca-cola | 5300 | 5600 |
| Pepsi | 6000 | 6800 |
| Fanta | 1800 | 2700 |
Coca-Cola
Pepsi
Fanta
Sprite
Correct answer
Coca-Cola
A chord of a circle is equal to its radius of length 9 cm. Find the angle subtended by it in major segment.
90°
60°
30°
120°
Correct answer
90°
The following table shows the number of centuries scored by given five cricketers in the past 5 years.
| Years → | 2021 | 2020 | 2019 | 2018 | 2017 |
|---|---|---|---|---|---|
| cricketers ↓ | |||||
| A | 1 | 0 | 1 | 0 | 1 |
| B | 1 | 0 | 2 | 1 | 1 |
| C | 1 | 2 | 0 | 0 | 1 |
| D | 0 | 0 | 1 | 1 | 0 |
| E | 0 | 1 | 1 | 0 | 1 |
Who scored the maximum number of centuries?
A
C
B
E
Correct answer
A
The following table shows the number of centuries scored by cricketers in the past 5 years.
| Years → | 2021 | 2020 | 2019 | 2018 | 2017 |
|---|---|---|---|---|---|
| cricketers ↓ | |||||
| A | 1 | 0 | 2 | 1 | 1 |
| B | 1 | 2 | 0 | 0 | 1 |
| C | 0 | 0 | 1 | 1 | 0 |
| D | 0 | 1 | 1 | 0 | 1 |
| E | 1 | 0 | 1 | 0 | 1 |
In which year the maximum number of centuries were scored?
2020
2018
2019
2021
Correct answer
2020
Study the following table and answer the question below.
| School name | Total number of students enrolled | Percentage of enrolled students, opted Biology | Ratio of male to female students who opted Biology |
|---|---|---|---|
| A | 900 | 30 | 7 ∶ 8 |
| B | 400 | 36 | 9 ∶ 10 |
| C | 1000 | 24 | 5 ∶ 19 |
| D | 800 | 18 | 5 ∶ 7 |
Find the ratio of the number of students who opted biology in school B and school D.
1 ∶ 4
1 ∶ 2
1 ∶ 1
2 ∶ 1
Correct answer
1 ∶ 4
Study the following data and answer the question below.
| Year | 2016 | 2017 | 2018 | 2019 | 2020 |
|---|---|---|---|---|---|
| Company's % profit | 30 | 20 | 25 | 15 | 10 |
What was the revenue of the company if its expenditure was ₹50 lakhs in the year when its profit percentage was the highest?
₹55 lakhs
₹70 lakhs
₹65 lakhs
₹60 lakhs
Correct answer
₹55 lakhs
A truck goes from Haryana to Bangalore with an average speed of 60 km/h. The journey takes 30 hours. It returns from Bangalore to Haryana on the same road with an average speed of 40 km/h. What was the average speed of the truck during the roundtrip?
60 km/h
40 km/h
50 km/h
48 km/h
Correct answer
60 km/h
If X, Y, Z and W are in fourth proportion. X = 3, Y = 13 and W = 39, determine Z.
5
20
15
9
Correct answer
5
What is the radius of a normal cylinder whose height is 21 cm and curved surface area is 1386 cm2?
10.5 cm
3.5 cm
7 cm
10 cm
Correct answer
10.5 cm
If a, b, c are all non-zero and a + b + c = 0, find the value of \(\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}\).
3
4
1
\(\frac{1}{2}\)
Correct answer
3
Three persons P, Q, R run along a circular track at speeds of 3 km/h, 4 km/h, 6 km/h, respectively. If the length of the track is 36 km, then after how much time will they meet again at the starting point?
38 hours
36 hours
24 hours
28 hours
Correct answer
38 hours
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.