List of top Mathematics Questions asked in KCET

The value of $\int \frac{e^{6 \log x} -e^{5 \log x}}{e^{4 \log x} - e^{3 \log x}} dx$ is equal to
The value of the $\sin \; 1^{\circ} + \sin \; 2^{\circ} +......+ \sin 359^{\circ}$ is equal to
If $\vec{a}$ and $\vec{b}$ are unit vectors then what is the angle between $\vec{a}$ and $\vec{b}$ for $\sqrt{3} \, \vec{a} - \vec{b}$ to be unit vector ?
The value of $\tan \frac{\pi}{8}$ is equal to
The value of $\sin^{-1}\left ( \cos\, \frac { 53 \pi}{5}\right)$ is
If the straight lines $2x + 3y - 3 = 0$ and $x + ky + 7 = 0$ are perpendicular, then the value of $k$ is
If $a = 3, b = 4, c = 5$ each one of $a ,b$ & $c$ is perpendicular to the sum of the remaining then $| a + b + c | $ is equal to
The value of $ \tan( 1^\circ) +\, tan(89^\circ)$ is
If $\alpha$ and $\beta$ are the roots of $x^2 - ax + b^2 = 0$, then $\alpha^2 + \beta^2$ is equal to
A box contains $6$ red marbles numbers from $1$ through $6$ and $4$ white marbles $12$ through $15$. Find the probability that a marble drawn 'at random' is white and odd numbered.
Write the set builder form $A = {-1, 1}$
A bag contains $(2 n+1)$ coins. It is known that $n$ of these coins have a head on both sides, whereas the remaining $(n+1)$ coins are fair. $A$ coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $31 / 42$, then $n$ is equal to
Evaluate $\left|\begin{array}{ll}\cos 15 & \sin 15 \\ \sin 75 & \cos 75\end{array}\right|$
A balloon which always remains spherical is being inflated by pumping in $10$ cubic centimeters of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15$ cms.
Slope of Normal to the curve $y=x^2 - \frac {1}{x^2}$ at $(-1,0)$ is
Equation of line passing through the point $(2, 3, 1) $and parallel to the line of intersection of the plane $x- 2y - z + 5 = 0$ and $x + y + 3z = 6$ is
Area bounded by $y = x^3, y = 8$ and $x = 0 $ is
If $ f(x) = 2-2x^2,$ find $\frac {f(3,8)-f(4)} {3.8-4} $,
The solution set of the inequation $\frac {x^2+6x-7}{|x+4|}<0$ is
The value of $\sin ^{-1} (\frac {2 \sqrt {2}}{3})+\sin^{-1} (\frac {1}{3}) $ is equal to
The order of differential equation of all circles of given radius $'a'$ is _____
If $x$ is real, then the minimum value of $x^2 - 8x+17 $ is
The middle term of expansion of $(\frac {10}{x}+\frac {x}{10})^{10}$ is
The function $f(x) = [x]$, where $[x]$ denotes greatest integer function is continuous at
If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than $5$ is