Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
The areas of two similar triangles ABC and PQR are 64cm2 and 144cm2, respectively. If the greatest side of the smaller ΔABC is 24 cm, then what is the greatest side of the bigger ΔPQR?
32 cm
24 cm
42 cm
36 cm
Correct answer
32 cm
A boat can travel 104 km downstream in 8 hours. If the speed of the stream is 2 km/h, then find in what time will it be able to cover 13 km upstream?
\(\rm 2\frac{2}{3} \ hours\)
\(\rm 1\frac{4}{9} \ hours\)
\(\rm 2\frac{1}{2} \ hours\)
\(\rm 1\frac{2}{3} \ hours\)
Correct answer
\(\rm 2\frac{2}{3} \ hours\)
A frustum of a right circular cone, whose height is 18 cm, large base radius is 25 cm, and small base radius is 20 cm, is melted to form a small sphere of diameter 2 cm. How many spheres will be formed?
6287
6862
4575
5857
Correct answer
6287
A grocer sells rice at 10% profit and uses weights which are 20% less than the market weight. The total gain earned by him is:
\(33\frac{1}{3}%\)
20%
40%
37.5%
Correct answer
\(33\frac{1}{3}%\)
The following table shows the number of candidates from different locations, who appeared and passed in a competitive examination over the years.
| Year | Rural | Semi-urban | State capitals | Metropolises | ||||
|---|---|---|---|---|---|---|---|---|
| App. | Passed | App. | Passed | App. | Passed | App. | Passed | |
| 1990 | 1652 | 208 | 7894 | 2513 | 5054 | 1468 | 9538 | 3214 |
| 1991 | 1839 | 317 | 8562 | 2933 | 7164 | 3248 | 10158 | 4018 |
| 1992 | 2153 | 932 | 8139 | 2468 | 8258 | 3159 | 9695 | 3038 |
| 1993 | 5032 | 1798 | 9432 | 3528 | 8529 | 3628 | 11247 | 5158 |
| 1994 | 4915 | 1658 | 9784 | 4015 | 9215 | 4311 | 12518 | 6328 |
| 1995 | 5628 | 2392 | 9969 | 4263 | 1725 | 4526 | 13624 | 6419 |
What approximate value was the percentage drop in the no. of semi-urban candidates, who appeared from 1991 to 1992?
15%
8%
5%
10%
Correct answer
15%
The value of (sin4 45°+ cos4 60°) + (tan4 45°+ cot4 45°) is:
\(\frac{37}{16}\)
\(\frac{33}{16}\)
\(\frac{35}{16}\)
\(\frac{39}{16}\)
Correct answer
\(\frac{37}{16}\)
The following pie chart shows the contribution (in Rs.) of some investors in the corpus fund of a company. If the total contribution by these investors is 100%, then what is the percentage contribution of Rakesh in the corpus fund?
17.30%
18.12%
17.95%
16.95%
Correct answer
17.30%
The monthly income of two persons is in the ratio 4 : 5 and their expenditures are in the ratio 7 : 9. If each saves Rs. 50 per month, then their monthly incomes are:
Rs. 900; Rs. 500
Rs. 400; Rs. 500
Rs. 700; Rs. 900
Rs. 400; Rs. 700
Correct answer
Rs. 900; Rs. 500
The number of factors of 196 which are divisible by 4 is:
228
4
57
3
Correct answer
228
PQ and RS are two parallel chords of a circle such that PQ is 48 cm and RS is 40 cm. If the chords are on the opposite sides of the centre and the distance between them is 22 cm, what is the radius (in cm) of the circle?
25
24
35
22
Correct answer
25
If three numbers are in the ratio of 1 : 3 : 7, and their LCM is 336, then their HCF is:
16
18
10
12
Correct answer
16
Two trains start from Delhi and Poona towards each other at 7 a.m. with speeds of 85 km/h and 67km/h, respectively. If they cross each other at 3.30 p.m., the distance between the stations is:
1245 km
1292 km
1283 km
1227 km
Correct answer
1245 km
72 ÷ 8 × [{(57 − 49) ÷ 2} + {(85 − 60) ÷ 5} – {(28 − 19) ÷ 3}] is equal to:
56
46
54
60
Correct answer
56
The following table represents the number of computers (numbers in thousands) manufactured by four companies from period 2014 to 2016. Study the table carefully and answer the following question.
| Years | A | B | C | D |
|---|---|---|---|---|
| 2014 | 1350 | 750 | 630 | 810 |
| 2015 | 570 | 520 | 1280 | 990 |
| 2016 | 420 | 1170 | 650 | 580 |
For the years 2014 to 2016, what is the difference (numbers in thousands) between the combined production of computers by Companies A and D and the production of computers by Companies B and C taken together?
460
280
370
310
Correct answer
460
A can do a piece of work in 10 days, while A and B together can complete it in \(2\frac{1}{2}\) days. How long will B alone take to complete the work?
\(\rm \frac{3}{10} \ days\)
\(\rm \frac{10}{3} \ days\)
3 days
4days
Correct answer
\(\rm \frac{3}{10} \ days\)
12 men or 20 boys can finish a work in 10 days. What part of the same work will be done by 4 men and 4 boys in 4 days?
\(\frac{49}{75}\)
\(\frac{16}{75}\)
\(\frac{26}{75}\)
\(\frac{59}{75}\)
Correct answer
\(\frac{49}{75}\)
How many of the following numbers are divisible by 156?
312, 620, 936, 1402, 1872, 3216, 7176, 8108.
5
3
4
2
Correct answer
5
The following table shows the percentage of population of three states below poverty line and the proportion of boys and girls.
| State | Percentage of population below poverty line | Proportion of boys and girls | |
|---|---|---|---|
| Below poverty line | Above poverty line | ||
| A | 25 | 3 ∶ 4 | 4 ∶ 3 |
| B | 60 | 2 ∶ 4 | 1 ∶ 2 |
| C | 15 | 4 ∶ 5 | 3 ∶ 1 |
If the total population of state B is 3000, then what is the number of girls below poverty line in state B?
1200
700
650
720
Correct answer
1200
The value of (1+ cot A – cosec A)(1 + tan A + sec A) – 1 is:
1
2
3
0
Correct answer
1
The sum of two numbers is 1224 and their HCF is 68. The number of co-prime pairs satisfying the above condition is:
3
4
6
2
Correct answer
3
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.