Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
The largest six-digit number that is divisible by 198. If the digits are rearranged, the number will be divisible by:
3
6
2
7
Correct answer
3
A hemispherical bowl of internal radius 6 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 2 cm and height 4 cm. How many bottles will be needed to empty the bowl?
32
37
38
36
Correct answer
32
Simplify \(\frac{\cos ^4 θ-\sin ^4 θ}{\sin ^2 θ}\)
1 - tan2 θ
tan2 θ - 1
cot2 θ - 1
1 - cot2 θ
Correct answer
1 - tan2 θ
AB is the common tangent to both circles as shown in the given figure. What is the distance between the centres of the circles?
20 cm
15 cm
10 cm
30 cm
Correct answer
20 cm
If a = 9.6, b = 4.44 and c = 5.16, then the value of a3 - b3 - c3 - 3abc is:
0
-1
2
1
Correct answer
0
What is the LCM of a3b - ab3, a3b2 - a2b3, ab(a - b)?
a2b2(a2 + b2)
a2b2(a2 - b2)
a2b3(a2 + b2)
a3b2(a2 - b2)
Correct answer
a2b2(a2 + b2)
The value of \(6 \frac{8}{15} \div \frac{7}{9}\) of \(\left(1 \frac{1}{10}+5 \frac{1}{5}\right)+\frac{2}{5} \div 7 \frac{1}{5}~~\) is:
\(\frac{25}{16}\)
\(\frac{5}{14}\)
\(\frac{25}{18}\)
\( \frac{5}{18}\)
Correct answer
\(\frac{25}{16}\)
What is the value of 12 - 8 ÷ 2 - {16 of (-2) + (3 × 5 - 4)}?
29
45
1
0
Correct answer
29
By selling 24 items, a shopkeeper gains the selling price of 4 items. His gain percentage is:
\(16 \frac{1}{3} %\)
20%
\(33 \frac{1}{3} %\)
\(16 \frac{2}{3} %\)
Correct answer
\(16 \frac{1}{3} %\)
The average age of 10 students and their class teacher is 17 years. If the age of the class teacher is excluded, the average age of the 10 students is reduced by 2 years. What is the age of the class teacher?
38 years
36 years
37 years
35 years
Correct answer
38 years
The weight of a person was entered incorrectly as 83 kg instead of 63 kg. As a result, the average weight of a group of people increased by 500 gm. What is the total number of people in the group?
44
48
40
50
Correct answer
44
The circle graph given here shows the spending of a country on various sports during a year. Study the graph carefully to answer the question.
Percentage of money spent on various sports for one year.
If the total amount spent during the year was ₹1,20,00,000, then how much was spent on Basket Ball?
₹25,00,000
₹10,00,000
₹40,00,000
₹30,00,000
Correct answer
₹25,00,000
The total number of teachers in different subjects and the respective percentage of females among them in a school are given in the following table. Study the table and answer the following question.
| Subject | Total number of teachers | Percentage of females |
|---|---|---|
| Hindi | 50 | 80 |
| English | 40 | 90 |
| Mathematics | 60 | 35 |
| Science | 55 | 40 |
| Commerce | 30 | 50 |
| Social Science | 40 | 75 |
In which subject are the maximum number of teachers males?
Mathematics
Hindi
Commerce
English
Correct answer
Mathematics
Find the value of a in the following equation. (Given a < 10.)
\(\frac{(187 \div 17 \times \mathrm{a}-3 \times 3)}{\left(8^2-9 \times 7+\mathrm{a}^2\right)}=1~\)
2
1
4
3
Correct answer
2
If \(a+\frac{1}{a}=P^2\), then find \(a^2+\frac{1}{a^2}\)
P2 - 2
P2 + 2
P4 - 2
P4 + 2
Correct answer
P2 - 2
In the given figure, DE || BC. If AD = 5 cm, DB = 10 cm, and AE = 8 cm, then AC is:
24 cm
32 cm
8 cm
16 cm
Correct answer
24 cm
Arrange the given ratios in descending order
15 ∶ 7, 5 ∶ 11 and 21 ∶ 77.
21 ∶ 77 > 5 ∶ 11 > 15 ∶ 7
15 ∶ 7 > 5 ∶ 11 > 21 ∶ 77
15 ∶ 7 > 21 ∶ 77 > 5 ∶ 11
5 ∶ 11 > 15 ∶ 7 > 21 ∶ 77
Correct answer
21 ∶ 77 > 5 ∶ 11 > 15 ∶ 7
A gives B a head-start of 10 seconds in a 1500 m race and both finish the race at the same time. What is the time taken by A (in minutes) to finish the race if speed of B is 6 m/s?
3
4
8
5
Correct answer
3
The following pie chart shows the distribution of income from different taxes. Study the chart and answer the question.
If the income from the market tax in a year is ₹260 crore, then the total income from other sources is : (in ₹ crore)
540
560
740
760
Correct answer
540
A shopkeeper increases the selling price of an article by 15%. After increasing the selling price, he noticed that the profit percentage changed from 5% to 15%. The percentage increase in the cost price is:
20%
10%
15%
5%
Correct answer
20%
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.