List of top Mathematics Questions asked in KCET

The derivative of $\cos^{-1} (2x^2 - 1)$ w.r.t $\cos^{-1} x$ is

If $\, {{^n C}_{12}}$ =$\, {{^n C}_8}$ then $n$ is equal to

If $tan^{-1} \,x + tan^{-1} \,y = \frac{4\pi}{5}$, then $cot^{-1}\, x + cot^{-1} \,y$ is equal to

The total number of terms in the expansion of ${(x+a)^{47} - (x-a)^{47}}$ after simplification is

The point on the curve $y^2 = x$ where the tangent makes an angle of $\pi /4$ with X-axis is

The eccentricity of the ellipse $\frac{x^2}{36} + \frac{y^2}{16} = 1$ is

The value of $cos^2 \, 45^{\circ} - sin^2 \, 15^{\circ}$ is

Two events $A$ and $B$ will be independent if

The differential coefficient of $\log_{10} x$ with respect to $\log_{x} 10$ is

If $\sin^{-1} \, x + \sin^{-1} \,y= \frac{\pi}{2}$ , then $x^2$ is equal to

The equation of the normal to the curve $y(1 + x^2) = 2 - x$ where the tangent crosses $x-axis$ is

$\displaystyle\lim_{x \to 0} \frac{xe^x - \sin \, x}{x}$ is equal to

The two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 = 2$

The general solution of $\cot\, \theta + \tan\, \theta = 2$ is

Two cards are drawn at random from a pack of $52$ cards. The probability of these two being "Aces" is

Two dice are thrown simultaneously, the probability of obtaining a total score of $5$ is

The simplified form of $\tan^{-1}$ $\left(\frac{x}{y}\right)$ $- \tan^{-1}$ $\left(\frac{x-y}{x+y}\right)$ is equal to

The simplified form of $i^{n} + i^{n +1} + i^{n +2} + i^{n +3}$ is

The sum of $1^{st}$ $n$ terms of the series $\frac{1^{2}}{1}+\frac{1^{2}+2^{2}}{1+2}+\frac{1^{2}+2^{2}+3^{2}}{1+2+3} + ...$

The slope of the tangent to the curve $ { x = t^2 + 3t -8 , y = 2t^2 - 2t - 5}$ at the point $(2, -1)$ is

If $x y z$ are not equal and $\neq$ 0, $\neq$ 1 the value of $\begin{vmatrix} \log x& \log y& \log z\\ \log 2x& \log 2y& \log 2z\\ \log 3x& \log 3y& \log 3z\end{vmatrix}$ is equal to

The solution for the differential equation ${ \frac{dy}{y} +\frac{ dx}{x} = 0 }$ is

The maximum value of $\left( \frac{1}{x} \right)^x$ is

If $A= \frac {1} { \pi}\begin{bmatrix} \sin^{-1} (\pi x) & \tan^{-1} (\frac {x}{\pi}) \\[0.3em] \sin^{-1}\frac {x}{\pi}& \cot^{-1}(\pi x) \end{bmatrix}$ , $B= \frac {1} { \pi}\begin{bmatrix} -\cos^{-1} (\pi x) & \tan^{-1} (\frac {x}{\pi}) \\[0.3em] \sin^{-1}(\frac {x}{\pi})& -\tan^{-1}(\pi x) \end{bmatrix}$ then $A - B$ is equal to

The length of latus rectum o f the parabola $4y^2 + 3x + 3y + 1 = 0$ is