Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Solve the following equation
\(\sec^2\theta(\sqrt{1-\sin^2\theta})=\) _______.
tan θ
cosec θ
sec θ
1
Correct answer
tan θ
Swati sold a bag to Ankita at a gain of 15%. Aashi bought this bag from Ankita for Rs. 24,840. Ankita earned a profit of 20%. At what price would Swati have bought the bag?
Rs. 18,500
Rs. 18,000
Rs. 16,000
Rs. 20,000
Correct answer
Rs. 18,500
If a 4 digit number x58y is exactly divisible by 9, then the least value of (x + y) is:
4
5
3
2
Correct answer
4
The simplified value of (0.2)3 × 400 ÷ 2000 of (0.2)2 is:
\(\frac{1}{25}\)
\(\frac{3}{25}\)
\(\frac{2}{25}\)
\(\frac{1}{50}\)
Correct answer
\(\frac{1}{25}\)
At a construction site, Raju can paint a wall in 36 hours, while Angad can do the same work in 18 hours. Sumit can paint the same wall in 24 hours. In how much time can they paint the wall if they all work together?
9 hours
12 hours
6 hours
8 hours
Correct answer
9 hours
What are the values of R and M, respectively, if the given number is perfectly divisible by 16 and 11 ?
34R05030M6
4 and 6
7 and 5
5 and 5
5 and 7
Correct answer
4 and 6
Find the HCF of 238 and 832.
16
8
2
14
Correct answer
16
Which of the following is the smallest ratio?
41 ∶ 92
33 ∶ 41
42 ∶ 49
35 ∶ 47
Correct answer
41 ∶ 92
Two trains, running between Bangalore and Chennai, start at the same time from their respective locations and proceed towards each other at the speed of 80 km/h and 95km/h. When they meet, it is found that one train has travelled 180 km more than the other. The distance between Bangalore and Chennai is ______
1200 km
2100 km
345 km
400 km
Correct answer
1200 km
The value of \(\frac{2\cos^3 \theta-\cos\theta}{\sin \theta-2\sin^3\theta}\) is:
sec θ
sin θ
cot θ
tan θ
Correct answer
sec θ
The population of four villages in 4 years is presented in the following table.
| Village/Year | 2018 | 2019 | 2020 | 2021 |
|---|---|---|---|---|
| A | 12381 | 12800 | 13045 | 13256 |
| B | 10089 | 11478 | 11502 | 11931 |
| C | 7896 | 7942 | 8069 | 8275 |
| D | 5152 | 5230 | 5346 | 5500 |
What is the average population of village D during all the 4 years?
5295
5300
5307
5315
Correct answer
5295
The curved surface area and circumference of the base of a solid right circular cylinder are 2200 cm2 and 110 cm, respectively. Find the height of the cylinder.
24 cm
22 cm
20 cm
18 cm
Correct answer
24 cm
If a car covers 75.5 km in 3.5 litres of petrol, how much distance (in km) will it cover in 28 litres of petrol?
603
602
604
600
Correct answer
603
The table shows the percentage of total population of a city in different age groups. Study the table and answer the question.
| Age group | percentage |
|---|---|
| Up to 15 | 15.00 |
| 16-25 | 20.25 |
| 26-35 | 16.75 |
| 36-45 | 26.25 |
| 46-55 | 15.00 |
| 56-65 | 5.50 |
| 66 and above | 1.25 |
If there are 30 million people below 36 years, then the number of people (in millions) in the age group (56-65) is: (consider up to two decimals)
1.16 million
3.17 million
1.87 million
2.17 million
Correct answer
1.16 million
The simplified form of (7x + 4y)2 + (7x − 4y)2 is:
98x2 + 32y2
98x2 + 32y2 – 5xy
32x2 + 98y2
98x2 − 32y2
Correct answer
98x2 + 32y2
How many metallic spheres, each of diameter 6 cm can be melted to mould into a solid cylinder of diameter 8 cm and height of 18 cm?
6
12
8
10
Correct answer
6
A sphere is of radius 5 cm. What is the surface area of the sphere?
100 π cm2
150 π cm2
200 π cm2
120 π cm2
Correct answer
100 π cm2
What is the simplified value of (0.00243)(0.2)
0.3
0.03
0.003
0.0003
Correct answer
0.3
The least common multiple of 48 and 64 is _____ times the highest common factor of 12 and 18.
28
32
24
16
Correct answer
28
Geeta runs 5/2 times as fast as Babita. In a race, if Geeta gives a lead of 40 m to Babita, find the distance from the starting point where both of them will meet (correct up to two decimal places).
66.67 m
65 m
65.33 m
66 m
Correct answer
66.67 m
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.