Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
The ratio of the speed of a boat to that of the current water is 35 : 8. The boat goes along with the current in 5 hours 10 minutes. What will be the time taken by the boat to come back?
5 hours 15 minutes 58 seconds
9 hours 30 minutes 49 seconds
6 hours 45 minutes 10 seconds
8 hours 13 minutes 48 seconds
Correct answer
5 hours 15 minutes 58 seconds
The side PR of a ΔPQR is extended to S such that QR = RS. If ∠PRQ = 86°, then find the value of ∠PSQ.
43°
86°
54°
94°
Correct answer
43°
If 12 people can print 540 identical books in 10 days, then how many more people will be required to print 720 such books in 8 days?
8
6
12
4
Correct answer
8
The following bar graph shows the production of cement (in lakh tonnes) of four companies-W, X, Y, and Z-over the years.
The production of cement by company X in 2020 and production of cement by company Z in 2022 together is what percentage of the production by company W in 2021?
275
180
250
220
Correct answer
275
In an election, 95% of the total voters cast their votes. In this election, there were only two candidates A and B. The winner A, by obtaining 75% of the total votes, defeated his contestant B by 5500 votes. Find the total number of voters in the election.
12,000
11,000
13,000
10,000
Correct answer
12,000
If \(\cos A=\frac{4}{5}\), then find the value of (8 + sin A)(3 - tan A).
\(\frac{373}{20}\)
\(\frac{387}{20}\)
\(\frac{381}{20}\)
\(\frac{367}{20}\)
Correct answer
\(\frac{373}{20}\)
A man borrowed Rs. 29,000 for 3 years and Rs. 45,000 for 5 years at the same rate of simple interest. If he paid a total interest of Rs. 62,400, then what was the rate of interest?
18%
20%
27%
25%
Correct answer
18%
A shopkeeper offers a 10% discount on dairy products and still manages to make a 20% profit. What is the actual cost (in Rs.) to the shopkeeper of a dairy product marked Rs. 420?
325
340
350
315
Correct answer
325
Find the mean from the following table (rounded off to two decimal places).
| Score | Frequencies |
|---|---|
| 15 | 2 |
| 18 | 3 |
| 21 | 4 |
| 22 | 1 |
| 19 | 5 |
| 23 | 1 |
| 24 | 2 |
17.56
20.82
18.44
19.78
Correct answer
17.56
A dishonest dealer claims to sell his products at 24% loss on the cost price but uses 100 g weight instead of 200 g weight. His profit percentage is:
55%
52%
40%
48%
Correct answer
55%
If 2a + 2b + c = 0, then find the value of \(\frac{4 a^2+4 b^2+4 c^2}{5 c^2-8 a b}\).
-1
1
\(-2 \sqrt{3}\)
\(2 \sqrt{3}\)
Correct answer
-1
A man travels some distance from his house to the exhibition ground by an auto at a speed of 30 km/h and returns by a cab at a speed of 50 km/h. What is his average speed (in km/h)?
37.5
40
28
38
Correct answer
37.5
The value of \(\frac{61+\frac{2}{5} \times 75 \div 6-\left(3 \times 6 \div \frac{1}{3}\right) \times \frac{1}{6}}{5+\frac{2}{3} \times(58-37)}\) is:
3
11
19
57
Correct answer
3
Study the given table and answer the question that follows.
The table shows the production of five different types of cars by a company from 1989 to 1994.
| Year → Type ↓ | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | Total |
|---|---|---|---|---|---|---|---|
| P | 8 | 20 | 16 | 17 | 21 | 6 | 88 |
| Q | 16 | 10 | 14 | 12 | 12 | 14 | 78 |
| R | 21 | 17 | 16 | 15 | 13 | 8 | 90 |
| S | 4 | 6 | 10 | 16 | 20 | 31 | 87 |
| T | 25 | 18 | 19 | 30 | 14 | 27 | 133 |
| Total | 74 | 71 | 75 | 90 | 80 | 86 | 476 |
In which year was the production of cars of all types taken together approximately equal to the average of the total production during the period?
1993
1990
1992
1991
Correct answer
1993
Simplify the given expression.
\(55 \frac{1}{3} \div\left[3 \frac{1}{5}+\left{2 \frac{1}{2}-\left(2 \frac{1}{3}+\frac{3}{5}\right)\right}\right]\)
25
15
20
35
Correct answer
25
An alloy contains the metals A, B and C in the ratio 2 ∶ 3 ∶ 1 and another contains the metals B, C and D in the ratio 5 ∶ 4 ∶ 3. If equal weights of both alloys are mixed together to form a third alloy, then how much part of the metal B is in new alloy?
\(\frac{1}{8}\)
\(\frac{1}{6}\)
\(\frac{3}{24}\)
\(\frac{11}{24}\)
Correct answer
\(\frac{1}{8}\)
A shopkeeper sold 3 wristwatches for ₹2,800 each. If he has sold the watches with 40%, 25% and 12% profit, respectively, then find his overall profit percentage (correct to 2 decimal places).
0.2455
0.2475
0.2419
0.2463
Correct answer
0.2455
A student goes to his school by cycle. The distance from his house to school is 5 km and he covers this distance in 1 hour. While going he stops twice for 5 minutes each. Find his average speed (in km/h).
5.5
6
6.5
4.5
Correct answer
5.5
Two rectangular sheets of paper, each 60 cm × 36 cm, are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is:
5 ∶ 6
5 ∶ 3
8 ∶ 3
7 ∶ 4
Correct answer
5 ∶ 6
What is the value of \(\frac{[(\sin x+\sin y)(\sin y-\sin x)]}{[(\cos x+\cos y)(\cos y-\cos x)]}\) ?
-1
0
2
1
Correct answer
-1
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.