List of practice Questions

There are 980 students in a school, of which 50% play cricket, 30% play basketball and 40% play football. If 60 students play cricket and basketball, 48 students play basketball and football, 180 students play cricket and football, and 35 students play all the three games, then how many students play none of the games?
When 3 is subtracted from each of the given 'n' numbers, then the sum of the numbers so obtained is 84. When 8 is added to each of the given 'n' numbers, then the sum of the resulting numbers is 216. The mean of the given 'n' numbers is:

The mean of five observations is 4.4 and their variance is 8.24. If three of the five observations are 1, 4 and 9, then the product of other two observations is:

The mean deviation about the mean of the dataset \( \{22, 24, 30, 27, 29, 31, 25, 28, 41, 43, 30\} \) is:
The ratio of the number of boys and the girls in a group is 5 : 8. If 4 more girls join the group and 5 boys leave the group, then the ratio of the number of boys to the number of girls becomes 1 : 2. Originally, what was the difference between the number of boys and girls in the group?
A person borrows a sum of ₹10,920 at 10% p.a. compounded interest and promises to pay it back in two equal annual instalments. The interest to be paid by him under this instalment scheme is:
Two persons A and B start moving at the same time towards each other from points x and y, respectively. After crossing each other, A and B now take \( 4\frac{1}{6} \) hours and 6 hours, respectively, to reach their respective destinations. If the speed of A is 72 km/h, then the speed (in km/h) of B is:
Let A = \(\{2, 3, 4, 8, 10\}\), B = \(\{3, 4, 5, 10, 12\}\), and C = \(\{4, 5, 6, 12, 14\}\) be the three sets. If $D = ((A \cup B) \cap (A \cup C)) - (B \cap C)$, then the number of elements in D is:
The number of elements in sets X and Y are $p$ and $q$ respectively. The total number of subsets of X is 112 more than that of Y. What is the value of $(2p - 3q)$?
Let $A = \{2, 4, 6, 9\}$ and $B = \{4, 6, 18, 27, 81\}$. If $C = \{(x, y) \mid x \in A, y \in B$ such that $x$ is a factor of $y$ and $x<y\}$, then $n(C)$ is:
The value of \( \frac{0.35 \times 0.7}{0.63 \times 3.6} + 0.27 (0.83 + 0.16) \) is:
The sum of the first 10 terms of the series \( \frac{7}{3} + \frac{7}{5} + \frac{1}{5} + \frac{1}{9} + \cdots = \frac{a}{b} \), where HCF(a,b) = 1. What is the value of \( |a - b| \)?
Let \( x = -4\sqrt{2} + \sqrt{17(-\sqrt{2})^2 + 2} \). If \( \frac{1}{x} = a + b\sqrt{2} \), then what is the value of \( (a - b) \)?
In a year, out of 160 games to be played, a cricket team wants to win 80% of them. Out of 90 games already played, the success rate is \( 66\frac{2}{3} %\). What should be the success rate for the remaining games in order to reach the target?
A shopkeeper has two varieties of rice A and B. By selling A at ₹75 per kg, he loses 20%; and by selling B at ₹90 per kg, he gains 25%. If he mixes A and B in the ratio 4 : 5 and sells the mixture at ₹110.25 per kg, then his profit percentage is:
Shikha sells an article for ₹253, after giving 12% discount on its marked price. Had she not given any discount, she would have earned a profit of 25% on the cost price. What is the cost price of the article?
If \( 3\sin^2 x + 10\cos x - 6 = 0 \), \( 0^\circ<x<90^\circ \), then the value of \( \sec x + \cosec x + \cot x \) is:
If \( \sec \theta = a + \frac{1}{4a^2} \), \( 0^\circ<\theta<90^\circ \), then \( \csc \theta + \cot \theta = \):
Evaluate: \[ \frac{\sin \theta (1 + \tan \theta) + \cos \theta (1 + \cot \theta)}{(\cos \theta - \sin \theta)(\sec \theta - \cos \theta)(\tan \theta + \cot \theta)} \]
The value of \( \left( \frac{5}{13} \cdot \frac{1}{14} + \frac{2}{25} \cdot \frac{3}{10} - \frac{7}{18} \cdot \frac{1}{35} \right) \div \left( \frac{3}{5} \cdot \frac{4}{21} \cdot \frac{2}{5} \right) \) lies between:
The income of A is \( \frac{3}{5} \) of B's income, and the expenditure of A is \( \frac{4}{5} \) of B's expenditure. If A's income is \( \frac{9}{10} \) of B's expenditure, then the ratio of savings of A and B is:
If \( \frac{46}{159} = \frac{1}{x} + \frac{1}{y + \frac{1}{z}} \), where \( x, y, z \) are positive integers, then the value of \( (2x + 3y - 4z) \) is:
Let \( A = \{1,2,5,6\}, B = \{1,2,3\} \) and \( C = (A \times B) \cap (B \times A) \). Which of the following is INCORRECT?
If \( f(2x) = \frac{2}{2 + x} \) for all \( x>0 \), and \( 5f(x) = 8 \), then what is the value of \( x \)?
Let \( f(x) = \frac{3x - 5}{2x + 1} \). If \( f^{-1}(x) = \frac{-x + a}{bx + c} \), then what is the value of \( (a - b + c) \)?