List of top Mathematics Questions asked in KEAM

Let f(x)=√x+5 for 1≤x≤9. Then the value of c whose existence is guaranteed by the Mean Value Theorem is
If \(f(x) =   \begin{cases}  e^x, & \text{if}\ x\leq1 \\  mx+6, & \text{if}\ x\gt1 \end{cases}\) be differentiable at x=1. Then the value of m is
If the tangent line to the graph of a function f at the point x=3 has x-intercept \(\frac{5}{2}\) and y-intercept-10, then f'(3) is equal to
\(\lim\limits_{t\rightarrow0}\frac{tan^2(\frac{\pi}{3}+t)-3}{t}\) is equal to
If \(f(x)=(x^3+sin\pi x)^5\), then \(f'(1)\) is equal to
\(\lim\limits_{t\rightarrow0}\frac{x}{\sqrt{9-x}-3}\) is equal to
\(\lim\limits_{t\rightarrow-3}\frac{x^2+16x+39}{2x^2+7x+3}\) is equal to
Let \(f(x)=6\sqrt{x^5}^3\). If \(f'(x)=ax^p\), where a and p are constants, then the value of p is equal to
\(\lim\limits_{t\rightarrow0}\frac{\sin2t}{8t^2+4t}\) is equal to
Let y=(tanx)sinx for \(0\lt x\lt\frac{\pi}{2}\). If \(\frac{dy}{dx}=(\tan x)^{\sin x}((\cos x)\log(\tan x)+g(x))\), then g(x)=
If \(f(x) =   \begin{cases}  3x+2, & \text{if}\ x\lt-2 \\  x^2-3x-1, & \text{if}\ x\geq-2 \end{cases}\). Then \(\lim\limits_{x\rightarrow2^-}f(x)\) and \(\lim\limits_{x\rightarrow2^+}f(x)\) are respectively
Assume that n distinct values x1,x2,...,xn occur with frequencies \(f_1,f_2....,f_n\). respectively, If \(\bar{x}=7\) and \(\displaystyle\sum^{8}_{i=1}f_ix_i=315\), then \(\displaystyle\sum^{8}_{i=1}f_i=\)
If A and B are two events such that P(A) = 0.2, P(B) = 0.55 and P(A∩B)=0.1, then P(B∩Ac) is equal to
If X is a random variable with E(X) = 6 and V(X) = 3, then E(X2) is equal to
Two dice are rolled. If A is the event that sum of the numbers is 4 and B is the event that at least one of the dice shows a 3, then P(A|B) is equal to
If \(f(x) =   \begin{cases}  2x & \text{for}\ x\lt1 \\  5a-x & \text{for}\ x\geq1 \end{cases}\) is continuous on \(\R\), then the value of a is equal to
Let \(f(x)=\frac{4x+3}{x+2}\), Then the value of \(f^{-1}(-2)\) is equal to
The variance of the data \(x_1,x_2,...,x_{30}\) with \(\displaystyle\sum^{50}_{i=1}x_i=650\) and \(\displaystyle\sum^{50}_{i=1}x_i^2=10000\) is
A bag contains 5 yellow, 3 green, 2 blue and 7 white balls. If 4 balls are chosen at random, then the probability that none of them are white is
The Cartesian equation of the line passing through (7, 5, 3) and perpendicular to the plane 3x + 2y + z = 6 is
If the liner \(\overrightarrow{r}=2\hat{i}+\hat{j}+t(3\hat{i}+\hat{j}-2\hat{k})\) is parallel to the plane 2x+4y+az=8, then the value of a is equal to
The angle between the lines \(\overrightarrow{r}=\hat{i}+4\hat{k}+\lambda(2\hat{i}+\hat{j}-\hat{k})\) and \(\overrightarrow{r}=2\hat{i}-\hat{j}+3\hat{k}+\mu(3\hat{i}+\hat{k})\) is
The vector equation of the line joining the points (2, 1, 3) and (-2, 4, 1) is
The acute angle between the planes 2x-y-3z=7and x+2y+2z=0 is
An urn contains 25 marbles which are numbered from 1 to 25 and a marble is chosen at random two times with replacement. Then the probability that both times the marble has the same number is