List of top Mathematics Questions

If \( A = \begin{bmatrix} 2 & 3 \\ 1 & k \end{bmatrix} \) is a singular matrix, then the quadratic equation having the roots \( k \) and \( \frac{1}{k} \) is:
If \( \theta \) is an acute angle, \( \cosh x = K \) and \( \sinh x = \tan \theta \), then \( \sin \theta = \dots \)
The sum of the series \( \frac{1}{1.5} + \frac{1}{5.9} + \frac{1}{9.13} + \cdots \) up to \( n \) terms is:
If \( \omega \) is the cube root of unity, then: \[ \frac{a + b\omega + c\omega^2}{c + a\omega + b\omega^2} = \frac{a + b\omega + c\omega^2}{b + c\omega + a\omega^2} \]
The radius of the circle which cuts the circles \( x^2 + y^2 - 4x - 4y + 7 = 0 \), \( x^2 + y^2 + 4x + 6 = 0 \), and \( x^2 + y^2 + 4x + 4y + 5 = 0 \) orthogonally is:
The range of the real valued function \( f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15} \) is:
If \( (a, b) \) is the midpoint of the chord \( 2x - y + 3 = 0 \) of the circle \( x^2 + y^2 + 6x - 4y + 4 = 0 \), then \( 2a + 3b = \):
If a direct common tangent is drawn to the circles \( x^2 + y^2 - 6x + 4y + 9 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \) that touches the circles at points \( A \) and \( B \), then \( AB = \):
If $$ \lim\limits_{x \to \infty} \frac{\left(\sqrt{2x+1} + \sqrt{2x-1}\right) + \left(\sqrt{2x+1} - \sqrt{2x-1}\right) P x^4 - 16} {(x+\sqrt{x^2 - 2}) + (x - \sqrt{x^2 - 2})} = 1, $$ then P = ? 
The complex conjugate of \( (4 - 3i)(2 + 3i)(1 + 4i) \) is:
If all chords of the curve \( 2x^2 - y^2 + 3x + 2y = 0 \), which subtend a right angle at the origin, always pass through the point \( (a, \beta) \), then \( (a, \beta) = \):
If \( (3 + i) \) is a root of \( x^2 + ax + b = 0 \), then \( a = {?} \)
If \( f(x) = x^x \), then the interval in which \( f(x) \) decreases is:
The area of the region under the curve \( y = |\sin x - \cos x| \) in the interval \( 0 \leq x \leq \frac{\pi}{2} \), above the x-axis, is (in square units):
The domain of the real-valued function \( f(x) = \log_2 \log_3 \log_5 (x^2 - 5x + 11) \) is:
If \[ \int \frac{1}{1 - \cos x} \, dx = \tan \left( \frac{x}{4} + \beta \right) + c, \] then one of the values of \( \frac{\pi}{4} - \beta \) is:
If a number is drawn at random from the set \( \{1, 3, 5, 7, \dots, 59\} \), then the probability that it lies in the interval in which the function \( f(x) = x^3 - 16x^2 + 20x - 5 \) is strictly decreasing is:
Which one of the following is false?
If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority is:
The algebraic equation of degree 4 whose roots are the translates of the roots of the equation \( x^4 + 5x^3 + 6x^2 + 7x + 9 = 0 \) by \( -1 \) is:
Let \( \alpha \in \mathbb{R} \). If the line \( (a + 1)x + \alpha y + \alpha = 1 \) passes through a fixed point \( (h, k) \) for all \( a \), then \( h^2 + k^2 = \):
7 coins are tossed simultaneously and the number of heads turned up is denoted by the random variable \( X \). If \( \mu \) is the mean and \( \sigma^2 \) is the variance of \( X \), then \( \frac{\mu^2}{P(X = 3)} \) is:
If \( y = \frac{ax + \beta}{\gamma x + \delta} \), then \( 2y_1 y_3 = \) ?
In a triangle ABC, if \( BC = 5 \), \( CA = 6 \), \( AB = 7 \), then the length of the median drawn from \( B \) onto \( AC \) is:
Let \( A \) be a \( 4 \times 4 \) matrix and \( P \) be its adjoint matrix. If \( |P| = \left| \frac{A}{2} \right| \), then \( |A^{-1}| = ? \)