List of top Mathematics Questions asked in KCET

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

The value of $\int \frac {1}{1+ Cos \; 8x}dx$ is

The number of positive divisors of $252$ is

The amplitude of $(1+i)^5$ is

$ABC$ is a triangle $G$ is the centroid $ D$ is the mid- point of $BC$. If $A - (2, 3) $ and $G = (7, 5)$, then the point $D$ is

If $A =\begin{bmatrix} {1}&{-1} &{1}\\ {2}&{1}& {-3} \\ {1}&{1}&{1}\\ \end{bmatrix} ,10B \begin{bmatrix} {4}&{2} &{2}\\ {-5}&{0}& {\alpha} \\ {1}&{-2}&{3}\\ \end{bmatrix} $ and $B$ is the inverse of $A$, then the value of $\alpha$ is

If the circles $x^2 + y^2 - 2x - 2y - 7 = 0$ and $x^2 + y^2 + 4x + 2y + k = 0$ cut orthogenally, then the length of the common chord of the circles is

The number of common tangents to the circles $x^2+y^2=4 $ and $ x^2+y^2-6x-8y-24=0 $ is

The conjugate of the complex number $ \frac {(1+i)^2}{1-i}$ is

The area enclosed by the pair of lines $xy = 0$ , the line $x - 4 = 0$ and $y + 5 = 0$ is

The ninth term of the expansion $\left(3x-\frac {1}{2x}\right)^8$ is