Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A circular garden is divided into 4 equal parts. If the total area is 314 \( \text{m}^2 \), what is the central angle of one part and its area?
\( 60^\circ, 78.5 \text{ m}^2 \)
\( 90^\circ, 78.5 \text{ m}^2 \)
\( 120^\circ, 75 \text{ m}^2 \)
\( 90^\circ, 80 \text{ m}^2 \)
Correct answer
\( 60^\circ, 78.5 \text{ m}^2 \)
A running track is comprised of a rectangular shape with semicircles at each of its shorter ends. The combined area of the two semicircles is 50% of the area of the central rectangular section. What is the approximate ratio of the length of the rectangular section to its width? (Use \(\pi \approx 3.14\))
1 : 1
1.57 : 1
2 : 1
3.14 : 1
Correct answer
1 : 1
A sector having a radius of 9 cm and has a central angle of 60°. What is the area of the sector?
\( \frac{27\pi}{2} \text{ cm}^2 \)
\( 14.5\pi \text{ cm}^2 \)
\( 82.4 \text{ cm}^2 \)
\( \frac{80\pi}{6} \text{ cm}^2 \)
Correct answer
\( \frac{27\pi}{2} \text{ cm}^2 \)
Two lines are perpendicular if their slopes multiply to:
0
1
-1
\(\infty\)
Correct answer
0
Choose the incorrect relation from the following:
I. \(\sqrt{6} + \sqrt{2} = \sqrt{5} + \sqrt{3}\)
II. \(\sqrt{6} + \sqrt{2} < \sqrt{5} + \sqrt{3}\)
III. \(\sqrt{6} + \sqrt{2} > \sqrt{5} + \sqrt{3}\)
I
I and III
II
II and III
Correct answer
I
How many numbers less than 1,000 are multiples of both 7 and 11?
13
11
12
10
Correct answer
13
A shopkeeper gives a discount of 15% on the marked price of an article. If the selling price is ₹8,500, then the discount on it will be ________.
₹1,200
₹1,600
₹1,500
₹1,800
Correct answer
₹1,200
Reena makes a profit of 20% by selling pens at a certain price. If she charges ₹5 more on each pen, she will gain 40%. The initial selling price of one pen was:
₹30
₹20
₹35
₹25
Correct answer
₹30
Four numbers are in the ratio of 2 : 3 : 4 : 5, and their sum is 56. Find the sum of the first and third numbers.
16
24
20
12
Correct answer
16
Rama sold a car costing ₹4,00,000 to Sansar at a loss of 20%. What is the selling price (in ₹)?
3,50,000
3,20,000
4,80,000
3,80,000
Correct answer
3,50,000
₹50,000 is deposited in a bank account. There was already some money in the account. Now the bank gives ₹7,500 as simple interest in a year. The rate of simple interest is 4.5% per annum. How much money (in ₹) was already there in the account?
1,33,333.33
1,66,666.67
1,16,666.67
1,13,333.33
Correct answer
1,33,333.33
A person crosses a road 350 metres wide in 70 seconds. His speed (in km/h) is:
18
17
19
15
Correct answer
18
A policeman chases a thief on a straight road. The policeman catches the thief in 15 minutes if he drives with a speed of 60 km/h and catches the thief in 0.5 hours if he drives with a speed 45 km/h. What should be his driving speed (in km/h) to catch the thief in just 10 minutes?
70
75
65
90
Correct answer
70
Three solid iron cubes of edges 8 cm, 10 cm and 12 cm are melted together to make a new cube. It is observed that 496 cm3 of the melted material is lost due to improper handling. The area (in cm2) of the whole surface of the newly formed cube is:
1331
1176
2197
3375
Correct answer
1331
If the surface areas of two spheres are in the ratio of 9 : 49, then the ratio of their volumes is:
81 ∶ 311
27 ∶ 143
27 ∶ 343
343 ∶ 81
Correct answer
81 ∶ 311
In nine games, A wins five games with score differences of 12, 3, 8, 4 and 1, while in the remaining four games, he loses with score differences of –4, –1, –2 and –3. The average score difference of A in all the nine games is:
2
3
4
1
Correct answer
2
Reshma covers 45 km at a speed of 15 km/h by bicycle, 80 km at a speed of 40 km/h by car, and another 6 km at a speed of 2 km/h on foot. Find her average speed for the whole journey (correct to 2 decimal places).
18.36 km/h
43.50 km/h
16.38 km/h
15.25 km/h
Correct answer
18.36 km/h
Find the area of a right angle whose base is 15 cm and hypotenuse is 17 cm.
40 cm2
55 cm2
60 cm2
75 cm2
Correct answer
40 cm2
In an examination, there were two papers, A and B, and the maximum mark in each of the two papers was 10. However, the weightage assigned to papers A and B were in the ratio 2 : 1, respectively. Jonathan scored 8 out of 10 in Paper A and an overall 70% in the examination. How much did he score in Paper B out of 10?
5.5
6.5
6
5
Correct answer
5.5
What annual installment will discharge a debt of ₹5,460 due in 5 years at 10% simple interest per annum?
₹1,200
₹1,092
₹910
₹950
Correct answer
₹1,200
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.