Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
If 25 persons can complete a work in 140 days, then how many persons will be required to complete the same work in 70 days?
70
50
40
80
Correct answer
70
The value of \(\left(2 \cos ^2 \theta-1\right)\left[\frac{1+\tan \theta}{1-\tan \theta}+\frac{1-\tan \theta}{1+\tan \theta}\right]\) is:
2
0
\(\frac{\sqrt{3}}{2}\)
1
Correct answer
2
ΔABC and ΔDEF are two triangles such that ΔABC ≅ ΔFDE. If AB = 5 cm, ∠B = 40° and ∠A = 80°, then which of the following options is true?
DF = 5 cm, ∠E = 60°
DE = 5 cm, ∠F = 60°
DE = 5 cm, ∠D = 60°
DE = 5 cm, ∠E = 60°
Correct answer
DF = 5 cm, ∠E = 60°
The ratio of the number of boys and girls in a school is 3 ∶ 4 respectively. If the number of boys is increased by 10% and the number of girls is increased by 15%, then what will be the new ratio of the number of boys to the number of girls?
\(\frac{33}{45}\)
\(\frac{35}{46}\)
\(\frac{33}{46}\)
\(\frac{46}{33}\)
Correct answer
\(\frac{33}{45}\)
Four numbers are in the ratio 1 ∶ 2 ∶ 3 ∶ 5. Two times their sum is 44. Find the ratio in the numbers obtained by subtracting 3 from the cube of each number.
2 ∶ 31 ∶ 204 ∶ 999
3 ∶ 13 ∶ 208 ∶ 992
11 ∶ 67 ∶ 219 ∶ 1003
5 ∶ 61 ∶ 213 ∶ 997
Correct answer
2 ∶ 31 ∶ 204 ∶ 999
If x4 + x-4 = 47, x > 0, then what is the value of \(x+\frac{1}{x}-2 \)?
1
0
5
3
Correct answer
1
The given graph shows the number(in hundreds) of trees axed in four cities during the period 2016-2020.
Find the year in which the least number of trees are axed.
2016
2020
2019
2017
Correct answer
2016
Solve the following.
\(\frac{24 \div \frac{3}{8} \text { of }(8+2 \times \overline{7-3})+\left[\frac{2}{11} \div \frac{4}{55}-\left{\frac{5}{8}+\frac{6}{16}\right}\right]}{32 \div \overline{15-7}+75 \div(6+15 \div 3+4)}\)
\(\frac{23}{27}\)
\(\frac{9}{2}\)
\(\frac{11}{18}\)
\(\frac{15}{19}\)
Correct answer
\(\frac{23}{27}\)
A field is in the shape of a rectangle of length 90 m and breadth 75 m. In one corner of the field, a pit, which is 18 m long 15 m broad and 6 m deep, has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. Find the rise in the level of the field?
27 cm
25 cm
28 cm
24 cm
Correct answer
27 cm
Simplify the following.
813/4 + [(20 ÷ 5 of 3 × 6) + {(8 ÷ 24 of 3) × 4} - 10 ÷ 5] - \(\left(\frac{1}{32}\right)^{-(2/5)} \).
\( 24 \frac{1}{4}\)
\(21 \frac{1}{9}\)
\(27 \frac{4}{5}\)
\(29 \frac{4}{9}\)
Correct answer
\( 24 \frac{1}{4}\)
If \(x^4+\frac{1}{x^4}=1154\), where x > 0, then what is the value of \(x^3+\frac{1}{x^3} ?\)
205
214
185
198
Correct answer
205
The value of (1018)2 - 1019 × 1017 + 1015 × 1012 - 1016 × 1011 is:
1
4
3
5
Correct answer
1
Two trains - A and B - having the lengths 195 m and 165 m, respectively, are running in the same direction on parallel lines. If the speed of A and B be 77 km/h and 85 km/h, respectively, what will be the time (in seconds) taken by them to cross each other?
162
164
160
166
Correct answer
162
If \(x=\frac{2 \sin \theta}{(1+\cos \theta+\sin \theta)}\), then the value of \(\frac{1-\cos \theta+\sin \theta}{(1+\sin \theta)}\) is:
\(\frac{x}{(1+x)}\)
X
\(\frac{1}{\mathrm{x}}\)
\(\frac{(1+x)}{x}\)
Correct answer
\(\frac{x}{(1+x)}\)
The ratio between the height and radius of the base of a cylinder is 7 ∶ 5. If its volume is 14836.5 cm3, then find its total surface area (take π = 3.14).
3391.2 cm2
5391.2 cm2
5491.2 cm2
5393.2 cm2
Correct answer
3391.2 cm2
On a certain sum, the difference between compound interest and simple interest at 10% per annum for 2 years is Rs. 250. The sum is ______.
Rs. 25,450
Rs. 26,550
Rs. 25,000
Rs. 26,000
Correct answer
Rs. 25,450
Marks scored by a student in different subjects are given in the table below
| Subjects | Marks obtained out of 100 |
|---|---|
| English | 55 |
| Hindi | 90 |
| Mathematics | 75 |
| Science | 80 |
| Foreign language | 90 |
Five marks are to be deducted from each subject due to shortage of attendance. The net average of the mean, median and mode of the marks obtained is ____.
79.33
77.67
82.66
73
Correct answer
79.33
16 sec2 A - 16 tan2 A = _______.
9
0
16
1
Correct answer
9
In the given figure, the length of arc AB is equal to twice the length of radius r of the circle. Find the area of sector OAB in terms of the radius r.
3r
2r
πr2
r2
Correct answer
3r
If p ∶ q = 4 ∶ 5, q ∶ r = 3 ∶ 4 and r ∶ s = 2 ∶ 5, then p ∶ s is:
2 ∶ 5
6 ∶ 25
5 ∶ 2
25 ∶ 6
Correct answer
2 ∶ 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.