List of top Mathematics Questions

If $a_1 ,b_1 ,c_1$ and $a_2 , b_2 ,c_2$ are the d.rs of two lines then $( a_1 a_2 + b_1 b_2 + c_1 c_2)^2 + \sum (b_1 c_2 - b_2 c_1)^2 =$

If $a_1,a_2,a_3,............$ is an A.P. such that $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225,$ then $a_1+a_2+a_3+.....+a_{23}+a_{24}$ is equal to

if A = $\begin{bmatrix}1&3\\ 3&4\end{bmatrix}$ and $A^2 - kA - 5I = 0$, then $k$ =

If A = {1, 2, 5} and B = {3, 4, 5, 9}, then $A \Delta B$ is equal to

if $A = \begin{bmatrix}1&-1\\ 2&-1\end{bmatrix} , B =\begin{bmatrix}x&1\\ y&-1\end{bmatrix}$ and $\left(A + B\right)^{2} =A^{2} + B^{2},$ then $x + y$ =

if $A \begin{bmatrix}1&2\\ 2&1\end{bmatrix}$and $f(x) = (1+x) (1 - x)$, then $f(A)$ is

If $A = \{1, 2, 3, 4, 5\}$, then the number of proper subsets of A is

If $ A=\begin{bmatrix}0&1\\ 0&0\end{bmatrix}$, I is the unit matrix of order 2 and a, b are arbitrary constants, then $(aI + bA)^2$ is equal to

If $A = \begin{bmatrix}0&-1\\ 1&0\end{bmatrix}$ then $A^{16}$ is equal to :

If $A = \begin{bmatrix}0&2&-3\\ -2&0&-1\\ 3&1&0\end{bmatrix}$ , then A is a

If $A = \begin{bmatrix}0&5\\ 0&0\end{bmatrix} $ and $f\left(X\right) =1+x+x^{2} +....+x^{16} $, then $f(A) = $

If $\frac{5z_2}{7z_1}$ is a purely imaginary number, then $\left|\frac{2z_1+3z_2}{2z_1-3z_2}\right|$ is equal to

If $\frac{5+9+13+.....n \, terms}{7+9+11+.......(n+1)terms}=\frac{17}{16}$ ,then n is equal to

If $4x + 3 < 6x + 7$, then $x\in$

If $\frac{3x - 4}{2} \ge \frac{x + 1}{4} - 1$, then $x\in$

If $\begin{bmatrix}3&1\\ 4&1\end{bmatrix} X = \begin{bmatrix}5&-1\\ 2&3\end{bmatrix} $ then X is equal to:

If $^{30}C_{r+2} = {^{30}C_{r-2}}$, then r equals :

If $\frac {2z_1} {3z_2} $ is a purely imaginary number, then $|\frac {z_1-z_2} {z_1+z_2}|$ is equal to

If $3\,\sin^{-1}\left(\frac{2x}{1+x^2}\right)-4\,\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right)+2\,tan^{-1}\left(\frac{2x}{1-x^2}\right)=\frac{\pi}{3}$, then $x$ is equal to

If $(2x^2 - x - 1)^5 = a_0 + a_1x + a_2x^2 + ... + a_{10}x^{10}$, then, $a_2 + a_4 + a_6 + a_8 + a_{10} =$

If $2x + 3y + 12 = 0$ and $x - y + 4\lambda$ = 0 are conjugate with respect to the parabola $y^2 = 8x,$ then $ \lambda$ is equal to

If $2 \alpha =-1-i \sqrt{3}$ and $2 \beta=-1+i \sqrt {3}$, then $5 \alpha^4+5 \beta^4 +7 \alpha ^{-1} \beta ^{-1}$ is equal to

If $1 + \sin\theta + \sin^2\, \theta + ............. $ $to \infty=4+2\sqrt{3},0

If ${^{10}C_{x}} = {^{10}C_{x + 4}}$, find the value of x.

If $1, log_{81} \left(3^x + 48\right)$ and $log_{9}\left(3^{x} - \frac{8}{3}\right) $ are in $A. P$., then $x$ is equal to