List of top Mathematics Questions

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

Find the length of the chord whose midpoint is \( \left( \frac{3}{2}, 0 \right) \) of the ellipse \[ \frac{x^2}{2} + \frac{y^2}{4} = 1. \]
If \( \vec{A} = 2\hat{i} + 3\hat{j} \) and \( \vec{B} = 4\hat{i} - \hat{j} \), then the dot product \( \vec{A} \cdot \vec{B} \) is:
The limit of \( \lim_{x \to 0} \frac{\sin x}{x} \) is:
The perpendicular distance of the line \( \frac{x - 1}{2} = \frac{y + 2}{-1} = \frac{z + 3}{2} \) from the point \( P(2, -10, 1) \) is:
The value of \[ \int_{e^2}^{e^4} \frac{1}{x} \left( \frac{e^{\left( (\log_e x)^2 +1 \right)^{-1}}}{e^{\left( (\log_e x)^2 +1 \right)^{-1}} + e^{\left( (6-\log_e x)^2 +1 \right)^{-1}}} \right) dx \] is:
The derivative of $e^{2x}\sin x$ with respect to $x$ is
If vector $\vec{a} = 2\hat{i} + m\hat{j} + \hat{k}$ and vector $\vec{b} = \hat{i} - 2\hat{j} + 3\hat{k}$ are perpendicular to each other, then the value of $m$ is
From a pack of 52 cards, two cards are drawn at random. What is the probability that both are Kings?
The number of ways in which the letters of the word ``APPLE'' can be arranged is
If $A$ is a symmetric matrix, then the transpose of $A'$ is equal to
The slope of the tangent to the curve $y = 3x^4 - 4x$ at $x = 4$ is
In a Geometric Progression (G.P.), if the third term is 4, then the product of the first 5 terms is
The integration of $\log x$ with respect to $x$ is
If the function $f(x) = x^3 - 3x^2 + 6$ is defined on the interval $[0,4]$, the maximum value is
What is the value of $i^{99}$ (where $i$ is the imaginary unit)?
The value of $\tan 75^\circ - \cot 75^\circ$ is equal to
If set $A$ has 3 elements and set $B$ has 4 elements, then the number of injective mappings from $A$ to $B$ is
Two dice are tossed. The probability that the total score is a prime number is
The value of the limit as $x$ approaches $0$ for $\frac{\sin(5x){x}$ is}
If A is a square matrix of order 3 such that the determinant $|A| = 5$, what is the value of the determinant $|2A|$?
A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let \( r \) be the radius of a circle that has centre at the point \( (2, 5) \) and intersects the circle C at exactly two points. If the set of all possible values of \( r \) is the interval \( (\alpha, \beta) \), then \( 3\beta - 2\alpha \) is equal to:
If the system of equations \[ 2x - y + z = 4, \] \[ 5x + \lambda y + 3z = 12, \] \[ 100x - 47y + \mu z = 212, \] has infinitely many solutions, then \( \mu - 2\lambda \) is equal to:
The sum of all values of \( \theta \in [0, 2\pi] \) satisfying \( 2\sin^2\theta = \cos 2\theta \) and \( 2\cos^2\theta = 3\sin\theta \) is:
Let \( \alpha_1 \) and \( \beta_1 \) be the distinct roots of \( 2x^2 + (\cos\theta)x - 1 = 0, \ \theta \in (0, 2\pi) \). If \( m \) and \( M \) are the minimum and the maximum values of \( \alpha_1 + \beta_1 \), then \( 16(M + m) \) equals: