Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
In an equilateral ∆PQR, S is point on the side QR such that QR = 3QS. If PQ = 9 cm, then what will be the length (in cm) of PS?
\(\sqrt{60}\)
\(\sqrt{63}\)
\(\sqrt{62}\)
\(\sqrt{61}\)
Correct answer
\(\sqrt{60}\)
If \(a-\frac{1}{a}=4\), then the value of \(a+\frac{1}{a}\) is:
5√5
4√5
2√5
3√5
Correct answer
5√5
The following table shows the data of 10th grade students of Portland High school.
| Boys | Girls | |
|---|---|---|
| Enrolled in Science | 25 | 20 |
| Not enrolled in Science | 20 | 30 |
What is the approximate percentage of the 10th grade boys of Portland High school who are NOT enrolled in Science?
22.22%
55.55%
33.33%
44.44%
Correct answer
22.22%
Which of the following ratios is the greatest?
2 ∶ 5
7 ∶ 10
5 ∶ 6
1 ∶ 3
Correct answer
2 ∶ 5
Robert takes twice as much time as Tom and thrice as much time as George to complete a work. If working together, they can complete it in 23 hours, then find the time that Tom will take to complete the work.
46 hours
69 hours
11 hours
39 hours
Correct answer
46 hours
A sum amounts to Rs. 7,656 in 4 years and to Rs. 8,120 in 5 years at a certain simple interest rate per cent per annum. The rate of interest is:
4%
3%
7%
8%
Correct answer
4%
What will be the least number which when doubled will be exactly divisible by 12, 14, 16 and 18?
636
428
504
226
Correct answer
636
Find the value of \(\frac{\sin ^2 39^{\circ}+\sin ^2\left(90^{\circ}-39^{\circ}\right)}{\cos ^2 35^{\circ}+\cos ^2\left(90^{\circ}-35^{\circ}\right)}\) + 3 tan 25° tan 65° :
2
4
3
1
Correct answer
2
Study the given table chart carefully and answer the question that follows.
The given table represents the number of employees in five different organisations, i.e., A, B, C, D and in 2019, 2020, 2021 and 2022.
| Organisation | Years | |||
|---|---|---|---|---|
| 2019 | 2020 | 2021 | 2022 | |
| A | 4000 | 7800 | 2600 | 5200 |
| B | 3800 | 9200 | 9100 | 7300 |
| C | 4500 | 5500 | 7800 | 3250 |
| D | 7000 | 3800 | 8000 | 4650 |
| E | 6600 | 6200 | 7600 | 2880 |
The ratio of the number of employees in 2019 in organisations D and E taken together to that in 2021 in the same organisations is:
9 ∶ 14
39 ∶ 34
14 ∶ 9
34 ∶ 39
Correct answer
9 ∶ 14
A family earns Rs. 75,000, out of which 10% is saved. 30% of the remaining expenditure is incurred on education, while Rs. 30,375 is spent on health and the remaining amount is spent on food. What is the percentage of food expenditure to the total income?
32.5%
22.5%
20%
21.5%
Correct answer
32.5%
In a survey, 200 respondents were asked whether they owned a vehicle or not. Their responses are tabulated below. What percentage of respondents do NOT own a car?
| Men | Women | ||
|---|---|---|---|
| Own Vehicle | Scooter | 30 | 20 |
| Car | 25 | 10 | |
| Both | 15 | 5 | |
| Do not own vehicle | 50 | 45 |
68.5%
75%
65%
72.5%
Correct answer
68.5%
The following table shows the marks obtained out of 100 , by 5 students in subjects.
| Students | Hindi | English | Maths | Science | Social |
|---|---|---|---|---|---|
| Ravi | 78 | 84 | 88 | 75 | 79 |
| Abhishek | 84 | 86 | 78 | 89 | 80 |
| Ayush | 88 | 80 | 90 | 82 | 85 |
| Rohit | 72 | 85 | 88 | 89 | 78 |
| Aryan | 86 | 88 | 77 | 79 | 89 |
What are the total marks scored by Ayush in all the subjects?
435
465
445
425
Correct answer
435
Arbind has 650 kg of wheat. A part of which he sells at 9% profit and the rest at 19% profit to get 15% profit on the whole. What is the quantity (in kg) of wheat sold by Arbind at 9% profit?
260
195
455
390
Correct answer
260
Two circles touch each other externally at C. AB is a direct common tangent to the two circles, A and B are points of contact and ∠CAB = 55°. Then ∠ACB is:
35°
90°
55°
45°
Correct answer
35°
By selling a table for Rs. 1,596, Aarav loses 24%. At what price (in Rs.) should he sell it to gain 24%?
3196
3024
1979
2604
Correct answer
3196
A train of length 180 m takes 40 seconds to cross a tunnel of length 500 m. What is the speed of the train, in km/h?
71.2
61.2
80.5
52.5
Correct answer
71.2
What is the LCM of 0.15, 0.18 and 0.45?
0.9
0.09
0.81
0.6
Correct answer
0.9
The curved surface area of a solid cylinder of height 15 cm is 660 cm2. What is the volume (in cm3) of the cylinder? (Тakе π = \(\frac{22}{7}\))
2060
2540
2310
3210
Correct answer
2060
Study the given pie-chart and answer the question that follows.
The pie-chart shows the sale of different fruits in a shop in a day.
If a total of 1200 kg of fruits were sold in a day, find the difference between sales of grapes and oranges (in kg).
60
55
65
45
Correct answer
60
Find the LCM of 20, 30, 45 and 65.
2000
2340
2240
180
Correct answer
2000
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.