List of top Mathematics Questions asked in KCET

The number of solutions of the equation $z^2+\bar{z}=0$, where $z \in C$ are

The characteristic equation of a matrix $A$ is $\lambda^3 - 5\lambda^2 - 3\lambda + 2 = 0$ then $| adj (A) |$ is equal to

The maximum value of $xe^{ -x}$ is

If $\cos \alpha + 2 \cos \beta + 3 \cos \gamma = 0,\sin \alpha + 2 \sin \beta + 3 \sin \gamma = 0 $ and $ \alpha + \beta + \gamma = \pi, $ then $ \sin 3\alpha + 8 \sin 3\beta + 27 \sin 3\gamma$ =

If $a , b$ and $c$ are three non-coplanar vectors and $p , q$ and $r$ are vectors defined by $p =\frac{ b \times c }{[ a b c ]}, q =\frac{ c \times a }{[ a b c ]}$ and $r =\frac{ a \times b }{[ a b c ]}$, then the value of $( a + b ) \cdot p +( b + c ) \cdot q +( c + a ) \cdot r$ is equal to

If $\alpha $ and $\beta$ are different complex numbers with $ | \beta | = 1$, then $\frac {\beta-\alpha}{1-\overline {\alpha} \beta}$ is equal to

$2 \cos^{-1} x = \sin^{-1} ({2x \sqrt {1-x^2)}}$ is valid for all values of $x$ satisfying

If $ \log_2 (9 ^{x-1} + 7) - \log_2 (3^{x-1 } + 1) = 2 $ then $x$ values are

If $\frac {3x+1}{(x-1)(x+3)} =\frac {A}{x-1} + \frac {B} {x+3} \sin^{-1} \frac {A}{B}$ = is equal to

Length of the subtangent at $ (x_1, y_1)$ on $x^n y^m = a^{m+n}, m, n > 0,$ is

If the conjugate of $(x + iy) (1 - 2i)$ is $1 + i,$ then

If $(\vec{a} \times \vec{b})^2+(\vec{a}.\vec{b})^2=144$ and $|\vec{a}|$ then $ |\vec{b}|$=

If $\alpha ,\beta,\gamma$ are the roots of the equation $x^3+4x+2=0$ then $\alpha^3+\beta^3+\gamma^3$

The value of $^{10}C_1+^{10}C_2+^{10}C_3+....+^{10}C_9 $ is

The digit in the unit's place of $7^{171} +(177)!$ is

$G = \left\{\begin{bmatrix} x&x \\[0.3em] x & x \end{bmatrix} , x \text{ is a nonzero real number} \right\}$ is a group with respect to matrix multiplication. In this group, the inverse of $\begin{bmatrix} \frac{1}{3} &\frac{1}{3} \\[0.3em] \frac{1}{3} & \frac{1}{3} \end{bmatrix}$ is

$\begin{vmatrix} {Sin \alpha}&{ \cos\alpha} &Sin ({\alpha+ \delta })\\ {Sin \beta}&{ Cos \beta}& Sin ({\beta+\delta}) \\ {Sin \gamma}&{ Cos \gamma}&Sin ({\gamma+\delta})\\ \end{vmatrix} $ is equal to

Suppose $ P(2,\,y,\,z) $ lies on the line through $ A(3,-1,4) $ and $ B(-4,2,1) $ . Then, the value of z is equal to

In $n$ is an odd positive integer and $(1+x +x^2 +x^3)^n =\displaystyle\sum_{r=0}^{3n} a_rx^r$ then $a_0 -a_1+a_2-a_3 +\dots -a_{3n}$ is equal to

Angles of elevation of the top of a tower from three points (collinear) $A, B$ and $ C$ on a road leading to the foot of the tower are $30^\circ$, $45^\circ$ and $60^\circ$ respectively. The ratio of $AB$ to $BC$ is

The derivative of $tan ^{-1}[\frac{Sin x}{1+ Cos x}]$ with respect to $tan^{-1}[\frac{Cos x}{1+Sin x}]$ is

The value of $\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$ is

The sum of the first n terms $ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$ $\dots$ is

If $\alpha , \beta ,\gamma$ are the roots of $x^3-2x+1=0$, then the value of $(\sum \frac {1} {\alpha +\beta -\gamma}$) is

If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is