Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A shopkeeper offers 3 schemes of discounts to his customers. Which of the following schemes will fetch the minimum discount percentage?
A)Two successive discounts of 24% and 27%.
B) Buy 5 get three free.
C) Buy 6 and get 10.
B
A
C
Both 1 and 3
Correct answer
B
A can do a work in 20 days and B in 30 days. If they work on it together for 2 days, then what is the fraction of the work that is left?
\(\frac{5}{8}\)
\(\frac{3}{5}\)
\(\frac{5}{7}\)
\(\frac{5}{6}\)
Correct answer
\(\frac{5}{8}\)
If tan(t) + cot(t) = 2, then one of the values of the expression \(\frac{1}{\sin (t)+\cos (t)}\) is _________.
\(\frac{\sqrt{3}}{2}\)
\(\frac{2}{\sqrt{3}}\)
\(\frac{1}{\sqrt{2}}\)
\(\sqrt{3}\)
Correct answer
\(\frac{\sqrt{3}}{2}\)
What is the total surface area of a cone whose radius is \(\frac{r}{4}\) and slant height is 4l ?
4πr(l + r)
\(\pi r\left(l+\frac{r}{4}\right)\)
\(\pi r\left(l+\frac{r}{16}\right)\)
8πr(l + r)
Correct answer
4πr(l + r)
Simplify:
\(\left(1+\tan ^2 A\right)+\left(1+\frac{1}{\tan ^2 A}\right) \)
\(\frac{1}{\cot ^2 A-\tan ^4 A}\)
\(\frac{1}{\sin ^2 A-\sin ^4 A}\)
\(\frac{1}{\sin ^2 A-\cos ^4 A}\)
\(\frac{1}{\cos ^2 A-\sin ^4 A}\)
Correct answer
\(\frac{1}{\cot ^2 A-\tan ^4 A}\)
Simplify the following expression.
\(3 \frac{1}{5}\) of \(2 \frac{3}{4} \div \frac{11}{3}\) + \((2 \frac{1}{5} \div 1 \frac{2}{5} \text { of } 1 \frac{3}{7}-2 \frac{1}{3}) \)
\( 2 \frac{1}{6}\)
\(4 \frac{1}{6} \)
\(1 \frac{1}{6}\)
\(3 \frac{1}{6}\)
Correct answer
\( 2 \frac{1}{6}\)
Study the given bar-graph and answer the question that follows.
The bar-graph gives the sales and profit (both in Rs. cr.) of company Z across four years.
What was the approximate percentage profit margin on revenue of company Z in 2016?
70%
54.64%
41.18%
60%
Correct answer
70%
The value of \(3 \frac{2}{3} \div 2 \frac{1}{5} \times \frac{1}{4} \times\left(1+\frac{3}{1-\frac{2}{5}}\right)\) is:
\(2 \frac{1}{4} \)
\(1 \frac{3}{4}\)
\(3 \frac{1}{2} \)
\(2 \frac{1}{2}\)
Correct answer
\(2 \frac{1}{4} \)
In ∆ABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is:
2 : 1
1 : 3
1 : 2
3 : 1
Correct answer
2 : 1
Find the single discount rate percentage equivalent to the successive discounts of 10%, 20% and 20%.
40%
42.4%
50%
54.6%
Correct answer
40%
The chord length of a chord made on an arc of a circle is equal to the radius of the circle. The length of the arc is _______ (in units), if the radius of the circle is 21 units.
(Take \(\pi=\frac{22}{7}\))
21
24
22
20
Correct answer
21
The sum of two numbers x and y (where x is greater than y) is equal to four times of their difference. Find the value of \(\frac{5 x y}{3\left(x^2-y^2\right)}\).
\(\frac{25}{16}\)
16
\(2 \frac{3}{16}\)
25
Correct answer
\(\frac{25}{16}\)
Find the value of 24 ÷ (3 – 8 × 3 + 27) + 3.
\(\frac{3}{2}\)
7
\(\frac{1}{2}\)
\(\frac{6}{5}\)
Correct answer
\(\frac{3}{2}\)
Simplify the given expression.
25 ÷ 5 × 7 of (5 + 7) - 13(6 × 4)
108
138
126
112
Correct answer
108
A thief running at 7 km/h is chased by a policeman whose speed is 12 km/h. If the thief is 280 m ahead of the policeman, then the time required for the policeman to catch the thief will be:
\(3 \frac{1}{25}\) minutes
\(3 \frac{9}{25}\) minutes
\(4 \frac{9}{25}\) minutes
\(3 \frac{2}{25}\) minutes
Correct answer
\(3 \frac{1}{25}\) minutes
From an external point A, tangents AP and AQ are drawn to a circle with centre O. If ∠APQ = 40°, then find ∠POQ.
60°
100°
110°
80°
Correct answer
60°
A hemispherical bowl is 88 cm round the brim. Assuming it to be full, how many persons may be served from it in hemispherical glasses, 7 cm in diameter at the top? (Where π =(22)/(7))
68
64
74
70
Correct answer
68
The base of a parallelogram is twice its height. If the area of the parallelogram is 338 cm2, then find its height (in cm).
11
13
14
12
Correct answer
11
A 12 litre solution of acid and water contains 30% acid. How much water (in litres) must be added to get a solution having 20% acid?
3
6
5
4
Correct answer
3
The following table shows the classification of 100 students based on the marks obtained by them in Maths and Science in an examination.
| Subjects | Marks out of 100 | ||||
|---|---|---|---|---|---|
| 80 and above | 60 and above | 40 and above | 20 and above | 0 and above | |
| Maths | 12 | 35 | 80 | 94 | 100 |
| Science | 16 | 43 | 76 | 88 | 100 |
| Average (Aggregate) | 14 | 39 | 78 | 91 | 100 |
What is the difference between the number of students who passed with 60 as cut-off marks in Science and those who passed with 60 as cut-off marks in aggregate?
5
3
6
4
Correct answer
5
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.