List of top Questions asked in KEAM

If $x^{3}+2xy+\frac{1}{3}y^{3}=\frac{11}{3}$ then $\frac{dy}{dx}$ at $(2,-1)$ is

$\lim_{x\to0}\frac{x^{100}\sin 7x}{(\sin x)^{101}}$ is equal to

The general solution of $\frac{dy}{dx}=\frac{2x-y}{x+2y}$ is given by

Let \(f(x)=\begin{cases}cx^{2}+2x,&\text{if } x<2\\2x+4,&\text{if } x\ge2\end{cases}\). If the function \(f\) is continuous on \((-\infty,\infty)\), then the value of \(c\) is equal to

$\lim_{x\to4}\frac{\sqrt{x^{2}+9}-5}{x-4}$ is equal to

$\lim_{x\to3}\frac{e^{x-3}-x+1}{x^{2}-\log(x-2)}$ is equal to

Let the probability distribution of a random variable X be given by the following table: {cccccc} X & -1 & 0 & 1 & 2 & 3
$p(X)$ & a & 2a & 3a & 4a & 5a
Then the expectation of X is

Let \(f(x)=\begin{cases}1-5x,&\text{if } x<-2\\x^{2}-2x,&\text{if } -2\le x\le1\\-1+2x,&\text{if } x>1\end{cases}\). Then the value of \(f(-1)\) is equal to

Three different numbers are chosen at random from the set $\{1,2,3,4,5\}$ and arranged in increasing order. The probability that the resulting sequence is an A.P. is

Two dice are rolled. If each die has six faces which are numbered 2, 3, 5, 7, 11, 13, then the probability that sum of the numbers on the top faces being a prime number is

In an examination, 20% of the students scored 70 marks, 40% scored 80 marks, 30% scored 90 marks and the rest scored 100 marks. Then the mean score of the students is

If A and B are mutually exclusive events such that $p(A)=0.5$ and $p(A\cup B)=0.75$ then $P(B)$ is equal to

A jar contains 7 black balls, 6 yellow balls, 4 green balls and 3 red balls. All of them are of same size and weight. If a ball is drawn at random, then the probability of the ball being red is

The Cartesian equation of the line passing through the points $(1,-1,2)$ and $(7, 0, 5)$ is

The point at which the line $\frac{x-2}{1}=\frac{y-4}{-5}=\frac{z+3}{4}$ intersects the xy-plane is

The angle between the planes $x+y+z=1$ and $x-2y+3z=1$ is

The sum of the intercepts made by the plane $\vec{r}\cdot(3\hat{i}+\hat{j}+2\hat{k})=18$ on the co-ordinate axes is

The equation of the plane passing through the intersection of the planes $x+2y-z=3$ and $x+y-3z=5$ and passing through the point $(1,-1,0)$ is

The average marks of 30 students in a class was 80. After two students left out of the class, the average marks of the remaining students was 82. Then the average marks of the two left out students is

If $|\vec{a}|=2$, $|\vec{b}|=3$ and $\vec{a}\cdot\vec{b}=4$, then $|\vec{a}-\vec{b}|$ is equal to

Which one of the following points lies on the straight line $\frac{x-1}{2}=\frac{y+1}{4}=\frac{z-2}{-2}$?

If $\vec{a}=2\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{b}=2\hat{i}-\hat{j}+\hat{k}$, then the value of $(\vec{a}+\vec{b})\cdot(\vec{a}-\vec{b})$ is equal to

Let $\vec{a}=\hat{i}+2\hat{j}-3\hat{k}$ and $\vec{b}=\lambda\hat{j}+3\hat{k}$. If the projection of $\vec{a}$ on $\vec{b}$ is equal to the projection of $\vec{b}$ on $\vec{a}$, then the values of $\lambda$ are

The distance of the point $(4,2,3)$ from the plane $\vec{r}\cdot(6\hat{i}+2\hat{j}-9\hat{k})=46$ is

A plane passes through the point $(0,1,1)$ and has normal vector $\hat{i}+\hat{j}+\hat{k}$. Its equation is