List of top Mathematics Questions

The vertices of a triangle are \( (4, 6), (2, -2) \), and \( (0, 2) \). Then the coordinates of its centroid must be:

The L.C.M. of \( 12x^2 y^3 z^2 \) and \( 18x^4 y^3 z^3 \) is:

Ravi can do \( \frac{3}{4} \) of a work in 12 days. In how many days Ravi can finish the \( \frac{1}{2} \) work?

The value of \( \frac{\cos 20^\circ \cos 70^\circ - \sin 20^\circ}{\sin 70^\circ} \) is:

If \( 5\sqrt{5} \times 5^3 \div 5^{-3/2} = 5^a \), then the value of \( a \) is:

The volume of a cuboid is \( x^3 - 7x + 6 \), then the longest side of the cuboid is:

The value of \( \sin \theta + \cos(90^\circ + \theta) + \sin(180^\circ - \theta) + \sin(180^\circ + \theta) \) is:

The value of \( \sqrt[3]{72.9} \) is:

\(\tan 3A - \tan 2A \cdot \tan A\) is equal to:

The perimeter of an equilateral triangle whose area is \( 4\sqrt{3} \, \text{cm}^2 \) is equal to:

Let $f : \mathbb{R} \to \mathbb{R}$ be given by $f(x) = \tan x$. Then $f^{-1}(1)$ is:

Let $a$, $b$, $c$, and $d$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a + k, b + k, c + k, d + k$ is:

$\int_{1}^{5} \left(|x - 3| + |1 - x|\right) \, dx =$

The function $f(x) = |\cos x|$ is:

Two finite sets have m and a elements respectively. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and a respectively are:

If $y = 2x^{3x}$, then $\frac{dy}{dx}$ at $x = 1$ is:

If \(f(x) = \begin{bmatrix} \cos x & x &1 \\ 2 \sin x & x & 2x \\ \sin x & x & x \end{bmatrix}\). Then \(\lim_{x \to 0} \frac{f(x)}{x^2}\) is:

If A.M. and G.M. of roots of a quadratic equation are $5$ and $4$ respectively, then the quadratic equation is:

If $A$ is a square matrix such that $A^2 = A$, then $(I + A)^3$ is equal to:

$\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} \, dx =$

A random variable $X$ has the following probability distribution: \[ \begin{array}{|c|c|c|c|} \hline X & 0 & 1 & 2 \\ \hline P(X) & \frac{25}{36} & k & \frac{1}{36} \\ \hline \end{array} \] If the mean of the random variable $X$ is $\frac{1}{3}$, then the variance is:

If $A = \begin{bmatrix} x & 1 \\ 1 & x \end{bmatrix}$ and $B = \begin{bmatrix} x & 1 & 1 \\ 1 & x & 1 \\ 1 & 1 & x \end{bmatrix}$, then $\frac{dB}{dx}$ is:

The plane containing the point $(3, 2, 0)$ and the line $\frac{x - 3}{1} = \frac{y - 6}{5} = \frac{z - 4}{4}$ is

Let $f : \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^2 + 1$. Then the pre-images of $17$ and $-3$ respectively are: