List of top Mathematics Questions asked in KCET

The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______

The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____

The area bounded by the curve $ y= \begin{cases} x^2,x<0 & \quad\\ x,x \geq 0 & \quad \\ \end{cases} $ and the line $y = 4$ is

The eccentric angle of the point $(2,\sqrt{3})$ lying on $\frac {x^2}{16}+\frac{y^2}{4}-1$ is _________

If $x\neq n \pi ,\, x \neq\,(2n+1)\frac {\pi}{2}.n\in Z, $ then $\frac {Sin^{-1}(Cos x) + Cos^{-1}(Sin x)}{Tan ^{-1}(Cot x)+ Cot^{-1}(Tan x)} $ =

In $\Delta ABC$, if $a =2, B = \tan ^{-1} \frac {1}{2}$ and $C = \tan ^{-1}\frac{1}{3}$, then $(A,b)$ =

The condition for the line $y = mx +c$ to be a normal to the parabola $y = 4ax$ is _______

The set of real values of x for which $ f(x) = \frac {x}{log\, x}$ increasing, is

$P$ is the point of contact of the tangent from the origin to the curve $y = log_ex$ The length of the perpendicular drawn from the origin to the normal at $P$ is ______

The length of the diameter of the circle which cuts three circles $x^2 + y^2 - x - y - 14 = 0;$ $x^2 + y^2 + 3x - 5y - 10 = 0 ;$ $x^2 + y^2 - 2x + 3y - 27 = 0$ orthogonally, is

If If $n =(2020)$, then $\frac {1}{\log_2n}+\frac {1}{\log_3n}+\frac {1}{\log_4n}+............+\frac {1}{\log_{2020} n}$

If$\vec{a}+2\vec{b}+3\vec{c}=\vec{0}$ then $\vec{a} \times \vec{b}+\vec{b} \times \,\vec{c}+\vec{c} \times \vec{a} $ =

If $A$ and $B$ are square matrices of the same order such that $(A + B) (A -B) = A^2-B^2$ then $(ABA^{-1} )^2=$

The negation of $p{\land}(q \to \sim r)$ is

If $'n '$ is a positive integer, then $n^3 + 2n$ is divisible by

On the set of integers $Z$. define $f: Z \to Z$ as $ f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ 0 & \quad \text{if } n \text{ is odd}\\ \end{cases} $ then $'f'$ is

The complex number $\frac {1+2i}{1-i}$ lies in

A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes $44\, metres$, when it has traced out $72^\circ$ at the centre, the length of the rope is

For the parabola $y^2 = 4x$, the point $P$ whose focal distance is $17$, is

The area bounded between the parabola $y^2= 4x$ and the line $y = 2x - 4$ is equal to

$\cot^{-1} (2.1^{2})+\cot^{-1} (2.2^{2})+\cot^{-1}(2.3^2)+$.........up to $\infty$=

The number of subgroups of the group $(Z_5, +_5)$is

If $A=\begin{bmatrix} {2}&{1} &{0}\\ {0}&{2}& {1} \\ {1}&{0}&{2}\\ \end{bmatrix}$ then $| adj A|$ =

If $\alpha$ and $\beta$ are the roots of $x^2 + x + 1 = 0$ then $\alpha^{16}+\beta^{16}$=

If one side of a triangle is double the other and the angles opposite to these sides differ by $60^\circ$, then the triangle is