List of top Mathematics Questions asked in KCET

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
A vector perpendicular to the plane containing the points $A (1, -1, 2), B (2, 0, -1), C (0,2,1)$ is
The solution of $Tan^{-1}x+ 2cot^{-1}x=\frac {2\pi}{3}$ is
$Sin^2 \; 17.5^{\circ} + Sin^2 \; 72.5^{\circ}$ is equal to
The value of $\int e^x(x^5+5x^4+1).dx $ is
The value of $\int \frac{x^2+1}{x^2-1}dx$ is

The orthocentre of the triangle with vertices $O(0, 0), A(0,3/2)$ and $B(-5, 0)$ is

If $\frac {x^2}{36}-\frac{y^2} {k^2} = 1$ is a hyperbola, then which of the following statements can be true ?
If a and b are vectors such that $|a+b|=|a-b|$ then the angle between a and b is
The value of the integral $\int\limits_0^{\pi/2}$($Sin^{100} x-Cos^{100}x)dx$ is
If $3x + y + k = 0$ is a tangent to the circle $x^2+y^2=10$ the values of k are,
If $sin \, 3 \,\theta\, = \, Sin \, \theta$ , how many solutions exist such that $-2 \pi
If $\vec {a}= {2\hat{i}}+3\hat{j}-\hat k,\vec b = \hat i+2 \hat j-5 \hat k ,\vec{ c} =3 \hat i+ 5\hat j-\hat k,$ then a vector perpendicular to $\vec{a}$ and in the plane containing $\vec {b}$ and $\vec {c}$ is
OA and BO are two vectors of magnitudes 5 and 6 respectively. If $\angle B O A=60^{\circ}$, then $0 A \cdot O B$ is equal to
If $A = \begin{bmatrix} {1}&{-2} &{2}\\ {0}&{2}& {-3} \\ {3}&{-2}&{4}\\ \end{bmatrix} $,then $A . adj(A)$ is equal to
$x^2 + y^2 -6x-6y + 4 = 0, x^2 + y^2 - 2x - 4y + 3 - 0 , x^2 + y^2 + 2k x + 2y +1 = 0$. If the Radical centre of the above three circles exists, then which of the following cannot be the value of $k$ ?