List of top Mathematics Questions

The value of $\tan^{-1} 1 + \tan^{-1} 2 + \tan^{-1} 3$ is:}

The equation of a circle whose Centre is $(-3, 2)$ and area is $176$ units is:

The conjugate of $(1+i)^3$ is:

If $z_1 = 4i^{40} - 5i^{35} + 6i^{17} + 2$ and $z_2 = -1 + i$, then $|z_1 + z_2| =$

The equation of a circle whose Centre is (2, -1) and which passes through the point (3, 6) is

The value of $\cos 6^\circ \sin 24^\circ \cos 72^\circ$ is:

If $\cos \theta = \frac{1}{2}(a + \frac{1}{a})$, then $4 \cos^3 \theta - 3 \cos \theta =$

If $\tan \theta + \sec \theta = \sqrt{3}$ then the principal value of $\theta$ in $[0, 2\pi]$ is

The expression $\frac{\tan x - 1 + \sec x}{\tan x - \sec x + 1}$ is equal to:}

The value of $\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ$ is:

If $\frac{x}{(x-1)^{2}(x+2)}=\frac{A}{(x-1)^{2}}+\frac{B}{9(x-1)}+\frac{C}{(x+2)}$ then $A+B=$

If $2 \sin^{-1} x = \sin^{-1} k$ then $k =$

If $\sin^{-1} \frac{5}{x} + \sin^{-1} \frac{12}{x} = \frac{\pi}{2}$ then $x =$

The number of solutions of the equation $\sin 2x - \cos 2x = 2 - \sin 2x$ lying in the interval $[0, \pi]$ is

If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$, then $A+B =$

Which of the following systems has non-trivial solution?

If $\begin{bmatrix}x+y & 2 \\ 1& x-y\end{bmatrix}=\begin{bmatrix}4& 2 \\ 1& 2\end{bmatrix}$, then the values of $x$ and $y$ are:}

If $\frac{x+4}{(x+2)^{2}(x+3)}=\frac{A}{(x+2)^{2}}+\frac{B}{(x+2)}+\frac{C}{(x+3)}$ then $A+B+C=$

If $\begin{vmatrix}2x& 5 \\ 8 & x\end{vmatrix}=\begin{vmatrix}6 &-2 \\ 7& 3\end{vmatrix}$ then the value of $x$ is

If $A$ is a square matrix of order 3 and $|A|=5$, then the value of $|2A^{T}|$ is

In the matrix $A=\begin{bmatrix}1& 2& 3 \\ 4& 5 & 6 \\ 7& 4 & 9\end{bmatrix}$, the minor $M_{23}$ of the $a_{23}$ is

Position vector of \( P \) and \( Q \) are \( \hat{i} + 3\hat{j} - 7\hat{k} \) and \( 5\hat{i} - 2\hat{j} + 4\hat{k} \) respectively. Then the cosine of the angle between \( \overrightarrow{PQ} \) and the y-axis is

Shortest distance between the lines \( \vec{r} = (8 + 3\lambda)\hat{i} - (9 + 16\lambda)\hat{j} + (10 + 7\lambda)\hat{k} \) and \( \vec{r} = 15\hat{i} + 29\hat{j} + 5\hat{k} + \mu(3\hat{i} + 8\hat{j} - 5\hat{k}) \) is

Evaluate the limit \[ \lim_{x \to 1} \frac{(\sqrt{x-1})(2x-3)}{2x^2 + x - 3} \]

Domain of the function \[ f(x) = \sqrt{\sin^{-1}(2x) + \frac{\pi}{6}} \text{ for real values of } x \]