List of top Mathematics Questions

$\frac{\cos 15^\circ \cos^2 22\frac{1}{2}^\circ - \sin 75^\circ \sin^2 52\frac{1}{2}^\circ}{\cos^2 15^\circ - \cos^2 75^\circ} =$

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

If $C_0, C_1, C_2, \dots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then $\sum_{r=1}^{n} \frac{r C_r}{C_{r-1}} =$

The equation having the multiple root of the equation $x^4 + 4x^3 - 16x - 16 = 0$ as its root is

Numerically greatest term in the expansion of $(2x-3y)^n$ when $x=\frac{7}{5}, y=\frac{3}{7}$ and $n=13$ is

Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is

Number of all possible ways of distributing eight identical apples among three persons is

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x^4 - 4x^3 + 3x^2 + 2x - 2 = 0$ such that $\alpha$ and $\beta$ are integers and $\gamma, \delta$ are irrational numbers, then $\alpha + 2\beta + \gamma^2 + \delta^2 =$

If both roots of the equation $x^2 - 5ax + 6a = 0$ exceed 1, then the range of 'a' is

The set of all values of $\theta$ such that $\frac{1-i\cos\theta}{1+2i\sin\theta}$ is purely imaginary is

If the equations $x^2 + px + 2 = 0$ and $x^2 + x + 2p = 0$ have a common root then the sum of the roots of the equation $x^2 + 2px + 8 = 0$ is

If $\alpha$ is a root of the equation $x^2-x+1=0$ then $(\alpha + \frac{1}{\alpha}) + (\alpha^2 + \frac{1}{\alpha^2}) + (\alpha^3 + \frac{1}{\alpha^3}) + \dots$ to 12 terms =

If $\cos\alpha+\cos\beta+\cos\gamma = 0 = \sin\alpha+\sin\beta+\sin\gamma$, then $\sin 2\alpha + \sin 2\beta + \sin 2\gamma =$

The sum of all the roots of the equation $\begin{vmatrix} x & -3 & 2 \\ -1 & -2 & x-1 \\ 1 & x-2 & 3 \end{vmatrix} = 0$ is

If the system of simultaneous linear equations $x+\lambda y-2z=1$, $x-y+\lambda z=2$ and $x-2y+3z=3$ is inconsistent for $\lambda = \lambda_1$ and $\lambda_2$, then $\lambda_1 + \lambda_2 =$

If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$, then Adj(Adj(Adj A)) =

One of the values of $\sqrt{24-70i} + \sqrt{-24+70i}$ is

The system of linear equations $(\sin\theta)x+y-2z=0$, $2x-y+(\cos\theta)z = 0$ and $-3x+(\sec\theta)y+3z=0$, where $\theta \neq (2n+1)\frac{\pi}{2}$, has non-trivial solution for

If $\frac{1}{2.7} + \frac{1}{7.12} + \frac{1}{12.17} + \dots$ to 10 terms = k, then k =

If the domain of the real valued function $f(x) = \frac{1}{\sqrt{\log_{\frac{1}{3}}\left(\frac{x-1}{2-x}\right)}}$ is $(a,b)$, then $2b =$

If $D \subset \mathbb{R}$ and $f : D \to \mathbb{R}$ defined by $f(x) = \frac{x^2+x+a}{x^2-x+a}$ is a surjection then '$a$' lies in the interval

The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word INCONVENIENCE is:

The general solution of the differential equation $\left( x \sin \frac{y}{x} \right) \frac{dy}{dx} = y \sin \frac{y}{x} - x$ is
Identify the correct option from the following: