List of top Mathematics Questions asked in KCET

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
$log (\sin \,1^\circ ) \times \log(\sin\, 2^\circ) \times \log(\sin \,3^\circ)\dots log (sin \,179^{\circ})$
If $\frac {(x+1)^2}{x^3+x}=\frac {A}{x}+\frac {Bx+C}{x^2+1}$, then $\sin^{-1} \,A + \tan ^{-1} \,B + sec ^{-1} \,C$ is equal to
If the value of $C_0 + 2 \cdot C_1 + 3 \cdot C_2 + \dots+ (n+1) \cdot C_n=576$ ,then n is equal to
The minimum area of the triangle formed by the variable line $3 \, \cos\,\theta \cdot x + 4 \,\sin \,\theta \cdot y = 12$ and the co-ordinate axes is
The inverse of the proposition $(p \wedge \sim q)\rightarrow r$ is
Solution of $e^\frac {dy}{dx} = x$ when $x = 1$ and $y = 0$ is
If one of the slopes of the pair of lines $ax^2 + 2hxy + by^2 = 0$ is $n$ times the other then
The last digit of number $7^{886}$ is
The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle is
$p \rightarrow \sim q$ can also be written as
The length of the sub-tangent, ordinate and the sub-normal are in
$\frac {\sin 70^\circ\, +\cos 40^\circ} {\cos 70^\circ + \sin 40^\circ}$=
The least and the greatest distances of the point $(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ are
If the straight line $3x + 4y = k$ touches the circle $x^2 + y^2 = 16x$, then the value of $k$ is
The equations of the two tangents from $(-5, - 4)$ to the circle $x^2 + y^2 + 4x + 6y + 8 = 0$ are