List of top Mathematics Questions asked in KCET

The general solution of the differential equation $\frac {dy}{dx}+\frac {y}{x}=3x$ is

If the function $f(x)$ defined by $\frac {x^{100}}{100}+\frac {x^{99}}{100}+\dots \frac {x^2}{100}+x+1$ then $f'(0)$ is equal to

Given $0 \leq x \leq \frac {1}{2}$ then the value of $\tan \left[\sin^{-1}\left\{\frac{x}{\sqrt {2}}+\frac {\sqrt {1-x^2}} {\sqrt {2}}\right\}-\sin^{-1}x\right]$ is

If $a, b$ and $c$ are in A.P., then the value of $\begin{vmatrix} {x+2}&{x+3} &{x+a}\\ {x+4}&{x+5}& {x+b} \\ {x+6}&{x+7} &{x+c}\\ \end{vmatrix}$ is

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$, if each number starts with $67$ and no digit appears more than once ?

Area of the region bounded by two parabolas $y\, =\, x^2$ and $x \,= \, y^2 $ is

The area of the parallelogram whose adjacent sides are $\hat{i}+ \hat {k} $ and $2\hat {i}+\hat {j}+\hat {k}$ is

The order and degree of the differential equation $y=x\frac{dy}{dx}+\frac{2}{\frac{dy}{dx}}$ is

The value of $\sin (2\, \sin^{-1}\, 0.8)$ is equal to

The value of the integral $\int_\limits{-\pi/4}^{\pi/4} \log (\sec \theta-\tan \theta) d \theta$ is

A stone is dropped into a quiet lake and waves move in circles at the speed of $5\, cm/sec$. At that instant, when the radius of circular wave is $8 \,cm$, how fast is the enclosed area increasing ?

If $A$ is $3 \times 4$ matrix and $B$ is a matrix such that $A'B$ and $BA'$ are both defined. Then $B$ is of the type

The angle between two diagonals of a cube is

In a triangle $ABC, a[b \,cos \,C - c\, cos\, B]$ =

The symmetric part of the matrix $A =\begin{bmatrix} {1}&{2} &{4}\\ {6}&{8}& {2} \\ {2}&{-2}&{7}\\ \end{bmatrix} $ is

The value of $[( a - b )( b - c )( c - a )]$ is equal to

If the line $6x - 7y + 8 + \lambda (3x - y + 5) = 0$ is parallel to y-axis, then $\lambda$ is equal to

The number of real circles cutting orthogonally the circle $x^2 + y^2 + 2x - 2y + 7 = 0$ is

If $\sin x- \sin y = \frac {1}{2}$ and $\cos x- \cos y = 1$, then $ \tan(x + y) $ is equal to

If the determinant of the adjoint of a (real) matrix of order $3$ is $25$, then the determinant of the inverse of the matrix is

If the area of the auxiliary circle of the ellipse $\frac {x^2}{a^2}+\frac {y^2}{b^2}=1 (a >\, b)$ is twice the area of the ellipse, then the eccentricity of the ellipse is

The range of the function $f(x)= \sin [x],-\frac {\pi}{4} < x < \frac {\pi}{4}$ where $[x]$ denotes the greatest integer $\leq x$, is ________

If $a$ is a vector perpendicular to both $b$ and $c$, then

The angle between the lines $\sin^2 \alpha \cdot y^2 - 2xy \cdot \cos^2 \alpha + (\cos^2 \alpha - 1)x^2 = 0$, is

The equation of the tangent to the parabola $y^2 = 4x$ inclined at an angle of $\frac{\pi}{4}$ to the $+ve$ direction of $x$-axis is