List of top Quantitative Aptitude Questions

A coin is biased so that the probability of obtaining a head is 0.25. Another coin is biased so that the probability of obtaining a tail is 0.4. If both the coins are tossed together, the probability of obtaining at least one head is:
From a point on a bridge across a river, the angles of depressions of the banks on opposite sides of the river are \(30^\circ\) and \(60^\circ\), respectively. If the height of the bridge from the banks is \( h \) metres and the width of the river is \( k \) metres, then \( h : k \) is equal to:
The expression \( \frac{(1 + \tan \theta) \cos \theta}{\sin \theta \tan \theta (1 - \tan \theta) + \sin \theta \sec^2 \theta} \) is equal to:
The expression \( \frac{\sec^6 \theta - \tan^6 \theta - 3 \sec^2 \theta \tan^2 \theta}{1 + 2 \sin^2 \theta - \sin^4 \theta + \cos^4 \theta} \) is equal to:
The marks obtained by seven students in a test are: 36, 46, 70, 60, 20, 18, 30. What is the mean deviation of the data from the mean?
The graphs of \(2x - y = 1\) and \(3x - 2y = -1\) intersect at a point \(P\), which lies on the graph of the equation:
When 8 is added to each of the given 'n' numbers, the sum of the resulting numbers is 207. When 5 is subtracted from each of the given 'n' numbers, the sum of the resulting numbers is 77. What is the mean of the given 'n' numbers?
Which of the following statements is true about the solutions of the equation \(\lvert x^2 - 5x \rvert = 6\)?
The ratio of the sum of the first \(m\) terms to the sum of the first \(n\) terms of an arithmetic progression is \(m^2 : n^2\). What is the ratio of its 17th term to the 29th term?
The sum of the first three terms of an infinite geometric progression, with common ratio less than one, is 56. If 1, 7 and 21 are subtracted from its first, second and third term, respectively, then these three terms are in the arithmetic progression. The common ratio of the progression is:
Let \[ x = \sqrt{-4\sqrt{2} + 17 (-\sqrt{2})^2 + 2}. \] If \( x = a + b \sqrt{2} \), then what is the value of \( (a - b) \)?
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?
Which of the following functions satisfies these two criteria: \( f(0) = 0 \) and \( f(x+1) = 2f(x) + 1 \)?
If \( f(x) = \frac{1}{x^2 + 1} \), \( 0<x<1 \), then \( f^{-1} \left( \frac{1}{4} \right) + f^{-1} \left( \frac{3}{4} \right) \)= : ?
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 \( (a - b + c) \)?
Given \( f(x) = \frac{4x + 1}{4} \) and \( g(x) = \sqrt{x^3} \), then \( (g \circ f^{-1}) \left( \frac{3}{8} \right) = \)?
The value of \( \frac{(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta)}{\tan^2 \theta + \cot^2 \theta - \sec^2 \theta \csc^2 \theta} \) is:
If \( 3 \sin^2 x + 10 \cos x - 6 = 0, 0^\circ<\theta<90^\circ \), then the value of \( \sec x + \csc x + \cot x \) is:
If \( \sec \theta = a + \frac{1}{4a}, 0^\circ<\theta<90^\circ \), then \( \csc \theta + \cot \theta = \):
Simplify the expression: \[ \frac{\sin \theta(1 + \tan \theta) + \cos \theta (1 + \cot \theta)}{\csc \theta - \sin \theta} \cdot \frac{\sec \theta}{\cos \theta (\tan \theta + \cot \theta)} = ? \]
The mean of the following distribution is 23.8 .

\[ \begin{array}{|c|c|c|c|c|c|} \hline \textbf{Class} & 0\text{–}10 & 10\text{–}20 & 20\text{–}30 & 30\text{–}40 & 40\text{–}50 \\ \hline \textbf{Frequency} & 7 & 5 & 3 & 4 & k \\ \hline \end{array} \]

What is the value of \( k \)?
If the standard deviation of the series \( x_1, x_2, \dots, x_n \) is \( \sigma \), then the standard deviation of the series \( \frac{6x_1 - 7}{3}, \frac{6x_2 - 7}{3}, \dots, \frac{6x_n - 7}{3} \) is:
A die is constructed so that when it is thrown, each of the three even numbers 2, 4 and 6 is twice as likely to come up as each of the odd outcomes 1, 3 and 5. What is the probability that 4 comes up when the die is thrown once?
X and Y are the two points that are 135 m apart on the ground on either side of a pole and in the same line. The angles of elevation of a bird sitting on the top of the pole from X and Y are 30° and 60° respectively. The distance of Y from the foot of the pole (in m) is: