List of top Mathematics Questions asked in KCET

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

In the group $G= \{0, 1,2, 3,4, 5\}$ under addition modulo $6,(2 +_6 3^{-1} +_6 4)^{-1}$=

The smallest positive integral value of $'n'$ such that $\left[\frac {1+\sin \frac {\pi}{8}+\,i\,\cos \frac {\pi}{8}}{1+\sin \frac {\pi}{8}-\,i\,\cos \frac {\pi}{8}} \right]^n$ is purely imaginary is, $n$ =

If$\vec{a}.\vec{b}\, = \,- |\vec{a}| \, |\vec{b}|$ then the angle between $\vec{a}$ and $ \vec{b}$ is

If the volume of the parallelopiped with $ \vec{a},\vec{b} $ and $ \vec{c}$ as coterminous edges is $40 \,cubic$ units, then the volume of the parallelopiped having $ \vec{b}+\vec{c} , \vec{c}+ \vec{a} $ and $ \vec{a}+ \vec{b}$ as coterminous edges in cubic units is

If $\begin{vmatrix} {1+\sin^2}&{\cos^2 \theta } &{4\sin 2\theta}\\ {\sin^2}&{1+\cos^2}& {4\sin2\theta} \\ {\sin^2\theta}&{\cos^2\theta}&{4\sin2\theta-1}\\ \end{vmatrix} =0 $ and $ 0< \theta

The foot of the perpendicular from the point $(2, 4)$ upon $x + y = 4$ is

On the set of all natural numbers $N$, which one of the following $*$ is a binary operation ?

Which one of the following is not true ?

The maximum value of $\frac{Log \, x}{x} $ in $(2, \infty)$ is

If $Log_{10}7=0.8451$ then the position of the first significant figure of $7^{-20}$ is