List of top Mathematics Questions asked in KCET

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

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

If $\vec{a} $ and $\vec{b}$ are unit vectors and $|\vec{a} + \vec{b}|=1$ then $|\vec{a} -\vec{b}|$ is equal to

The angles $A, B$ and $C$ of a triangle $ABC$ are in A.P. If $b : c =\sqrt {3} : \sqrt {2}$ then the angle $A$ is

$R $ is a relation on $N$ given by $R =\{(x, y ) | 4x +3y = 20\}$. Which of the following belongs to $R$ ?

The number of solutions for the equation $Sin\, 2x + Cos \; 4x = 2$ is

The remainder when $3^{100} \times 2^{500}$ is divided by $5$ is

If $\vec{a}\cdot\hat {i}= \vec{a} \cdot(\hat {i}+\hat {j})= \vec{a}\cdot (\hat {i}+\hat {j}+\hat {k})=1$ then $\vec{a}$=

The perimeter of a certain sector of a circle is equal to the length of the arc of the semicircle. Then the angle at the centre of the sector in radians is

The tangents drawn at the extremeties of a focal chord of the parabola $y^2 = 16 x$

The point $(5, - 7)$ lies outside the circle

The equation to the normal to the hyperbola $\frac {x^2}{16}- \frac {y^2}{9}=1$ at $(-4,0)$ is

If the circles $x ^2 + y ^2 =9$ and $x^2 + y^ 2 + 2\alpha x + 2y +1 = 0$ touch each other internally, then $\alpha$ =

The projection of $\vec{a}=3\hat{i}-\hat{j}+5\hat {k} $ on $\vec{b}=2 \hat {i}+3 \hat j+\hat k$ is

The ten's digit in $1! + 4!+ 7! + 10!+12! + 13! + 15! +16! + 17!$ is divisible by

The characteristic roots of the matrix $\begin{bmatrix} {1}&{0} &{0}\\ {2}&{3}& {0} \\ {4}&{5}&{6}\\ \end{bmatrix} $ are