List of top Mathematics Questions

If \( 0 \leq a, b \leq 3 \) and the equation \( x^2 + 4 + 3\cos(ax + b) = 2x \) has real solutions, then the value of \( (a + b) \) is:
Evaluate $ \lim_{x \to 2} \frac{x^2 - 4}{x - 2} $.
Find the shortest distance between the lines: \[ \frac{x+1}{2} = \frac{y-1}{1} = \frac{z-9}{-3} \] and \[ \frac{x-3}{2} = \frac{y+15}{-7} = \frac{z-9}{5}. \]
The general solution of the equation \[ 2\sin^2 \theta - \cos^2 \theta = \sin \theta \]
Let \(z_1 = 3 + 4i\) and \(z_2 = 1 - 2i\). Then the argument of \(\frac{z_1}{z_2}\) is:
The mean of 6 numbers is 15, and the standard deviation is 2. If each number is increased by 5, what is the new standard deviation?
The sum of the first 10 terms of an arithmetic progression is 145, and the first term is 1. Find the common difference.
If the arithmetic mean of the terms \(a, a + d, a + 2d, ..... a + (2n)d\) is 35 and the sum of the series is 735, then the value of \(n\) is:
If $ \sin \theta = \frac{3}{5} $ and $ \theta $ is in the first quadrant, find the value of $ \tan \theta $.
In \( \triangle ABC \), \( DE \parallel BC \), if \( AD = x + 1 \), \( DB = 3x - 1 \), \( AE = x \), and \( EC = 4x - 3 \), then the value of \( x \) is:
Let \( f(x) = 2x^3 - 3x \neq 4 \). Then the inverse function \( f^{-1}(x) \) is:
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:
If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:
If $a$ and $b$ are the roots of the equation $2x^2 + 5x + 30 = 0$, find the value of $a^2 + b^2$.
Find the distance between the points $ (2, 3) $ and $ (5, 7) $ in the Cartesian plane.
Consider an arithmetic progression where the sum of the first 5 terms is 85, and the sum of the next 5 terms is 235. Find the common difference of the AP.
Find the area of a triangle with vertices \( A(2, 3) \), \( B(5, 11) \), and \( C(8, 7) \).
If the roots of the equation \[ x^3 + p x^2 + q x + r = 0 \] are in arithmetic progression, then which of the following is always true?
A point P divides the line joining points $A(2, 3)$ and $B(10, 7)$ in the ratio 3:1 internally. What are the coordinates of point P?
A bag contains 4 red and 5 blue balls. One ball is drawn at random. What is the probability that it is red?