Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Simplify: \(\sqrt{75} + \sqrt{48} - \sqrt{27}\)
\(8\sqrt{3}\)
\(7\sqrt{3}\)
\(6\sqrt{3}\)
\(9\sqrt{3}\)
Correct answer
\(8\sqrt{3}\)
Find the least number which leaves remainder 3 when divided by 5, 7, and 8.
280
283
313
275
Correct answer
280
The value of: \( (3 + \sqrt{8}) + \left( \frac{1}{3 - \sqrt{8}} \right) - (6 + 4\sqrt{2}) \) is:
0
1
8
\( \sqrt{2} \)
Correct answer
0
P and Q invest ₹1,00,000 and ₹50,000, respectively. After one year, the total profit, which includes a 10% interest, amounts to ₹20,000. Determine Q's share of the profit.
₹6,666.67
₹5,667.67
₹6,000.67
₹5,000.67
Correct answer
₹6,666.67
The mean of five consecutive odd numbers is 61. What is the smallest of these numbers?
57
67
97
87
Correct answer
57
The sum of 25% of a number and 40% of the same number is 325. What is 120% of that number?
500
550
600
650
Correct answer
500
What is the compound interest on a sum of ₹37,500 for \( 1 \frac{1}{3} \) years at 12% p.a., compounded every 8 months?
₹6,500
₹6,000
₹6,240
₹7,000
Correct answer
₹6,500
A baker made 100 cakes for ₹3000. Due to an accident, 10 cakes were damaged. At what price per cake should he sell the remaining cakes to make an overall profit of 15%?
₹63.62
₹28.43
₹39.62
₹38.33
Correct answer
₹63.62
A can finish a task in 15 days and B in 20 days. They take a contract for ₹ 18,000. Assisted by C, they complete the job in 6 days. What is C's share of the money?
₹ 6,000
₹ 5,000
₹ 5,400
₹ 4,800
Correct answer
₹ 6,000
A 90-litre mixture of petrol and kerosene is in the ratio 4:5. Some of it is removed and replaced with pure petrol. The final ratio becomes 7:5. How much of the mixture was replaced?
20.6 litres
22.5 litres
19.4 litres
18.5 litres
Correct answer
20.6 litres
A train crosses a 180-meter-long platform in 20 seconds and a man standing on the platform in 12 seconds. What is the length of the train?
270 m
180 m
150 m
250 m
Correct answer
270 m
If \( a^2 + \frac{1}{a^2} = 14 \), find the value of \( a^4 + \frac{1}{a^4} \)
190
194
186
188
Correct answer
190
An item is produced by one of three machines, A, B, or C. Machine A produces 50% of the items, B produces 30%, and C produces 20%. The defect rates are 1% for A, 2% for B, and 3% for C. If an item is chosen at random, what is the probability that it is defective?
0.015
0.017
0.019
0.021
Correct answer
0.015
From the top of a 150 m high cliff, an observer notices a car moving away from the base of the cliff. The angle of depression of the car changes from 45° to 30° in 15 seconds. What is the approximate speed of the car?
6.8 m/s
7.3 m/s
8.1 m/s
9.0 m/s
Correct answer
6.8 m/s
A solid hemisphere is melted into a smaller hemisphere and a sphere of equal radii. If the smaller hemisphere's radius is r, find the radius R of the original hemisphere.
\(\sqrt[3]{3} \times r\)
\(\sqrt[3]{5} \times r\)
\(\sqrt[3]{7} \times r\)
\(\sqrt[3]{11} \times r\)
Correct answer
\(\sqrt[3]{3} \times r\)
The base of a right prism is a rectangle with sides 8 cm and 5 cm. The height of the prism is 12 cm. What is the total surface area?
392 cm2
456 cm2
528 cm2
600 cm2
Correct answer
392 cm2
Two semicircles of radius 7 cm are attached to opposite ends of a rectangle of 14 cm × 7 cm. What is the total area of the figure?
251.94 cm2
269.5 cm2
285.52 cm2
301.5 cm2
Correct answer
251.94 cm2
Complement of angle x is equal to (x + 10). Find the angle.
35°
40°
45°
50°
Correct answer
35°
If secA + tanA = x, express secA in terms of x.
(x2 + 1) / 2x
(x2 + 1) / x
2
j
Correct answer
(x2 + 1) / 2x
In a triangle, the distances from the incenter to the vertices are 5 cm, 6 cm, and 7 cm. Find the inradius.
2 cm
3 cm
4 cm
Cannot be determined
Correct answer
2 cm
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.