Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Find the value of the following expression.
(1 + tan θ + sec θ) × ( 1 + cot θ - cosec θ)
cos θ sin θ
1
2
tan θ
Correct answer
cos θ sin θ
A hostel had food provision for 300 students for a month. After 20 days, 50 students left the hostel. How long would the remaining food last? (1 month = 30 days)
14 days
12 days
10 days
16 days
Correct answer
14 days
The breadth of a rectangular lawn is decreased by 8% and its length is increased by 15%. Find the percentage change in the lawn area.
8.5% decrease
8.5% increase
5.8%decrease
5.8% increase
Correct answer
8.5% decrease
A drink is made by mixing water and juice in the ratio 9 ∶ 7. If x litres of water and 2x litres of juice are mixed in 160 litres of drink, then the new ratio becomes 13 ∶ 15. The quantity of drink (in litres) is:
240
280
300
260
Correct answer
240
A dishonest dealer sells an article at a 10% loss on the cost price but uses a weight of 40 g instead of 50 g. What is his percentage of profit?
12.5%
10.0%
11.5%
18.4%
Correct answer
12.5%
The area of a triangle is 486 cm2 and its sides are in the ratio 3 ∶ 4 ∶ 5. The perimeter of the triangle is:
108 cm
308 cm
218 cm
105 cm
Correct answer
108 cm
The value of \(\frac{2 \cos 15^{\circ} \sin 15^{\circ}}{\cos ^2 15^{\circ}-\sin ^2 15^{\circ}}\) is:
\(\frac{1}{\sqrt{3}}\)
\(\sqrt{3}\)
\(\frac{\sqrt{5}-1}{\sqrt{5+1}}\)
∞
Correct answer
\(\frac{1}{\sqrt{3}}\)
If \(\frac{5 x+3 y}{5 x-3 y}=\frac{7}{3}\), then find x ∶ y.
2 ∶ 3
5 ∶ 3
3 ∶ 2
3 ∶ 5
Correct answer
2 ∶ 3
Simplify \(\frac{\tan 71^{\circ}+\tan 19^{\circ}}{1-\tan 71^{\circ} \tan 19^{\circ}}\).
0
\( \sqrt{3}\)
Not defined
1
Correct answer
0
If sin(x + y) = cos {3(x + y)}, then, the value of cot {2(x + y)} is _______.
2
1
-1
-2
Correct answer
2
A person bought two buffaloes for Rs. 11,520. One is sold at a loss of 15% and the other is sold at a gain of 19%. If the selling price of both buffaloes is equal, find the cost price of the first one.
Rs. 6,700
Rs. 6,720
Rs. 6,710
Rs. 6,715
Correct answer
Rs. 6,700
Simplify 63 - [15 + {17 - (9 - 7 + 1)}].
44
40
34
30
Correct answer
44
The value of 264 ÷ 8 − 1 − 32 × 2 + 80 ÷ 5 × 40 ÷ 20 is:
0
1
3
2
Correct answer
0
18 students of a class took part in a quiz. If the number of girls is 8 more than the number of boys, find the product of the number of boys and girls.
63
36
56
65
Correct answer
63
The speed of a boat when travelling downstream is 33 km/h, whereas when travelling upstream it is 27 km/h. What is the speed of the boat in still water?
30 km/h
60 km/h
12 km/h
6 km/h
Correct answer
30 km/h
The value of \(\frac{(275 \times 275 \times 275+725 \times 725 \times 725)}{(275 \times 275+725 \times 725-725 \times 275)}\) × \(\frac{(275 \times 275 \times 275-725 \times 725 \times 725)}{(275 \times 275+725 \times 725+725 \times 275)}\) is:
−45000
450000
45000
−450000
Correct answer
−45000
Study the given table and answer the question that follows.
The table shows the yearly production (in thousands) of scooters in five different factories (P, Q, R, S and T) from 1985 to 1989.
Yearly production (in thousands) of scooters in different factories.
| Factory | 1985 | 1986 | 1987 | 1988 | 1989 |
|---|---|---|---|---|---|
| P | 20 | 15 | 24 | 13 | 17 |
| Q | 16 | 23 | 41 | 20 | 15 |
| R | 14 | 21 | 30 | 16 | 12 |
| S | 25 | 17 | 15 | 12 | 22 |
| T | 40 | 32 | 39 | 41 | 35 |
| Total | 115 | 108 | 149 | 102 | 101 |
The ratio of the production of scooters by factory P to that by factory T in 1985 is:
3 ∶ 2
1 ∶ 2
2 ∶ 3
2 ∶ 1
Correct answer
3 ∶ 2
The value of (12 + 18) ÷ 2 − 11 + 16 × 4 − 28 + 13(−18 + 15) is:
3
0
1
2
Correct answer
3
A 234 m long train passes a person running at 9 km/h in the opposite direction, in 6 seconds. In how much time (in seconds) will it pass another person who is moving at 23.4 km/h, in the same direction?
7.8
7.2
8
8.4
Correct answer
7.8
If a + b + c = 13 and ab + bc + ca = 22, then the value of a3 + b3 + c3 - 3abc is ________.
1225
1625
1339
1911
Correct answer
1225
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.