List of top Mathematics Questions asked in KCET

The value of $\begin{vmatrix} x+y&y+z & z+ x \\[0.3em] x & y & z \\[0.3em] x-y & y-z & z-x \end{vmatrix}$ = is equal to :

If $Sin (x + y)+Cos(x + y) = Log (x + y),$ then $\frac {d^2y}{dx^2}$=

If $a, b$ and $c \in N$ which one of the following is not true ?

The digit in the units place in the number $7^{289}$ is

In the group $ (Q^+ ,\star )$ of positive rational numbers w.r.t. the binary operation $\star$ defined by $a^{\star} b=\frac {ab}{3} , \forall a,b \in Q^{+}$ the solution of the equation $5 ^{\star} x=4^{-1}$ in $Q^+$ is

In the group $G. = \{1, 3,7,9 \}$ under multiplication modulo $10$, the inverse of $3$ is

The identity element in the group $M = \left\{ \begin{bmatrix} x & x \\ x & x\\ \end{bmatrix} | x \ \in \ R, x \neq 0 \right\}$ with respect to matrix multiplication is

The converse of the contrapositive of $p \to \sim q$ is

The solutions of the equation $\begin{vmatrix} {x}&{2} &{-1}\\ {2}&{5}& {x} \\ {-1}&{z}&{x}\\ \end{vmatrix} =0$ are

If $A=\begin{bmatrix} {3}&{5}\\ {2}&{0}\\ \end{bmatrix} $ and $B$ = $\begin{bmatrix} {1}&{17}\\ {0}&{-10}\\ \end{bmatrix} $then $|AB|$ is equal to

The contrapositive of "If two triangles are identical, then these are similar" is

The inverse of the matrix $\begin{bmatrix} {5}&{-2}\\ {3}&{1}\\ \end{bmatrix}$ is is

The projection of the vector $2\hat{i}+\hat{j}-3\hat{k}$ on the vector $\hat{i}-2\hat{j}-\hat{k}$ is

If $\omega$ is a complex cube-root of unity then, $\begin{vmatrix} {1}&{\omega} &{\omega^2}\\ {\omega}&{\omega^2}& {1} \\ {\omega^2}&{1}&{\omega}\\ \end{vmatrix} $ is equal to

A unit vector perpendicular to the plane containing the vectors $\hat {i}-\hat {j}+\hat{k} $ and $ -\hat{i}+\hat {j}+\hat{k}$ is

The contrapositive of the inverse of $p \to \sim q$ is

The value of $Cos (270^\circ +\theta )Cos (90^\circ - \theta ) - Sin (270^\circ - \theta )Cos \theta$ is

If $(0, 6)$ and $(0, 3)$ are respectively the vertex and focus of a parabola then its equation is

If the foci of the ellipse $ \frac {x^{2}} {{16}}$+$ \frac {y^{2} }{{b}^2} $=1 and hyperbola $\frac {x^{2}} {144} - \frac {y^{2}}{81}=\frac {1}{25}$ coincide then the value of $b^2$ is

If $w= \frac {-1+\sqrt {3i}}{2} $ then $(3+w+3w^2)^4 $

If $Cos^{-1} p + Cos ^{-1} q + Cos ^{-1} r = \pi $ then $p^{2} + q^{2} +r^{2} +2pqr=$

The differential coefficient of $f (Sin \,x)$ w.r.t. $x$ where $f (x) = \log\, x$ is

The smallest positive integer $n$ for which $(1+i)^{2n} = (1-i)^{2n}$ is

If $0 \leq x \leq \pi$ and +$81^{sin^2x}+81^{Cos^2x}=30$ then $x=$

The radius of the circle passing through the point $(6, 2)$ and two of whose diameters are $x + y = 6$ and $x + 2y = 4$ is