List of top Mathematics Questions asked in KCET

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

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

The coaxal system of circles given by $x^{2} + y^{2} + 2gx + c = 0$ for $c < 0$ represents.

The equation of the director circle of the hyperbola $\frac {x^{2}} {16}-\frac{y^{2}} {4}=1$ is given by .............

The value of $k$ so that $x^{2} + y^{2} + kx + 4y + 2 = 0 $ and $2(x^{2}+y^{2})- 4x - 3y + k = 0$ cut orthogonally is

If $Sin^{-1} \frac {x}{5}+Cosec^{-1} \frac {5}{4}=\frac {\pi}{2}$ then $x=$

The set of all integral multiples of $5$ is a subgroup of

Which of the following is not a proposition.

The distance of the point $'\theta'$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ from a focus is

The distance of a focus of the ellipse $9x^2+16y^2 =144$ from an end of the minor axis is

$\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{1}{7}+\tan^{-1}\frac{1}{18}+.........+\tan^{-1}\left(\frac{1}{n^2+n+1}\right)+....to\infty$ is equal to

If $p \Rightarrow (q \vee r)$ is false, then the truth values of $p, q, r$ are respectively