List of top Questions asked in KEAM

Let f(x) = x2 logx, x > 0. Then the minimum value of f is
The derivative of a function f is given by \(f'(x)=\frac{x-5}{\sqrt{x^2+4}}\). Then the interval in which f is increasing, is
Let f(x)=√x+5 for 1≤x≤9. Then the value of c whose existence is guaranteed by the Mean Value Theorem is
The slope of tangent line to the curve 4x2+2xy+y2=12 at the point (1, 2) 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 \(f(x) =   \begin{cases}  e^x, & \text{if}\ x\leq1 \\  mx+6, & \text{if}\ x\gt1 \end{cases}\) be differentiable at x=1. Then the value of m is
If h(x)=4x3-5x+7 is the derivative of f(x), then \(\lim\limits_{t\rightarrow0}\frac{f(1+t)-f(1)}{t}\) is equal to
If \(f(x)=(x^3+sin\pi x)^5\), then \(f'(1)\) 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)=
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
\(\lim\limits_{t\rightarrow-3}\frac{x^2+16x+39}{2x^2+7x+3}\) is equal to
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
\(\lim\limits_{t\rightarrow0}\frac{x}{\sqrt{9-x}-3}\) is equal to
\(\lim\limits_{t\rightarrow0}\frac{\sin2t}{8t^2+4t}\) 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
If X is a random variable with E(X) = 6 and V(X) = 3, then E(X2) 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
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 \(\displaystyle\sum^{8}_{i=1}f_i=\)
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 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
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
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 vector equation of the line joining the points (2, 1, 3) and (-2, 4, 1) is