List of top Quantitative Aptitude Questions asked in NPAT

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: \[ \frac{\sin \theta(1 + \tan \theta) + \cos \theta (1 + \cot \theta)}{\csc \theta - \sin \theta} \cdot \frac{\sec \theta}{\cos \theta (\tan \theta + \cot \theta)} = ? \]
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?
Calculate the variance of: 2, 4, 5, 6, 8, 17.
The scores of a batsman in 10 different test matches were 42, 38, 48, 70, 46, 63, 55, 34, 54, and 44. What is the mean deviation about the median of these scores?
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 \( k \)?
Let \( x \) be the median of the data: 23, 17, 19, 11, 7, 3, 13, 2, 5, 29. Let \( y \) be the median of the same data set obtained by replacing 2 by 21 and 13 by 31. What is the value of \( |x - y| \)?
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:
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:
The sum of the first \( n \) terms of a geometric progression is 255, the \( k \)-th term is 128, and the common ratio is 2. The value of \( k \) satisfies the equation:
The sum of the roots of the equation \( |x - 7|^2 + 2|x| - 7| = 24 \) is:
When 5 is subtracted from each of given \( n \) numbers, the sum of numbers so obtained is 210. When 8 is subtracted from each of the given \( n \) numbers, then the sum of numbers so obtained is 156. What is the mean of the given \( n \) numbers?
The ratio of the sum of the first \( n \) terms to the sum of the first \( s \) terms of an arithmetic progression is \( r^2 : s^2 \). What is the ratio of its 8th term to the 23rd term of this same progression?
If \( a + b + c = 2 \), \( a^2 + b^2 + c^2 = 36 \), then the value of \( a^3 + b^3 + c^3 - 3abc \) is:
The graphs of the equations \( 2x + 3y = a \) and \( x + 2y = b \) intersect at a point \( P(\alpha, \beta) \). What is the value of \( (3\alpha + 2\beta) \)?
If the equations \( x^2 + px + 12 = 0 \), \( x^2 + qx + 15 = 0 \), and \( x^2 + (p+q)x + 36 = 0 \) have a common positive root, then what is the value of \( (2p - q) \)?
If \( a_1, a_2, a_3, \dots \) is an arithmetic progression with the common difference of 1 and \( a_2 + a_4 + a_6 + \dots + a_{98} = 93 \), then \( \sum_{i=1}^{98} a_i \) is equal to \( k \). The sum of the digits of \( k \) is:
A person borrowed a certain sum on compound interest and agreed to return it in two years in two equal annual instalments. If the rate of interest is 10% p.a. and each annual instalment is ₹4,840, then the interest paid by him was: