List of top Questions asked in KEAM

Let \(f(x) =   \begin{cases}     3x+6,       & if\ x\geq c \\       x^2-3x-1,       & if\ x\lt c   \end{cases}\), where x∈R and c is a constant. The values of c for which f is continuous on R are
\(\displaystyle\lim_{t\rightarrow0}\frac{sin(t^2)}{tsin(5t)} \ is\ equal\ to\)
\(\displaystyle\lim_{x\rightarrow0}\frac{\log(1+x)+1-e^x}{4x^2-9x} \ is\ equal\ to\)
\(\displaystyle\lim_{t\rightarrow0}(\frac{(2t-3)(1-2)}{t}-\frac{3(t+2)}{t})\ is\ equal\ to\)
In a box there are four marbles and each of them is marked with distinct number from the set {1, 2, 5, 10}. If one marble is randomly selected four times with replacement and the number on it noted, then the probability that the sum of numbers equals 18 is
There are 4 red, 3 blue and 3 yellow marbles in an urn. If three marbles are drawn simultaneously, then the probability that the number of yellow marbles will be less than 2 is equal to
The coefficient of variation (C.V.) and the mean of a distribution are respectively 75 and 44. Then the standard deviation of the distribution is
A fair coin is tossed twice. Given that the first toss resulted in head, then the probability that the second toss also, would result in head is
There are 37 men and 33 women at a party. If a prize is given to one person chosen at random, then the probability that the prize goes to a woman is
If A and B are two events such that P(A)=0.5, P(B)=0.4 and P(A\(\cap\)B)=0.2, then P(A|(A\(\cup\)B)) is equal to
Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that min(a, b, c) =6 is
The angle between the planes x=√3 and z = √2 is equal to
The distance from the point (2, 2, 2) to the plane 2x-y+3z = 5 is equal to
If \(\theta\) is angle between the lines \(\frac{x}{1}=\frac{y+1}{2}=\frac{z-1}{3}\) and \(\frac{x+1}{3}=\frac{y}{2}=\frac{z}{1}\), then \(\cos\theta=\)
The equation of the plane through the point (1, 5, 3) and having a normal vector \(\hat n=2\hat i-2\hat j-\hat k\) is
If the points (1, 0, 0), (0, 3, 0) and (0, 0, 2) lie on a plane, then the unit normal vector \(\hat n\) to the plane is
The equation of the line through the point (1, 1, 1) and parallel to the line joining the points (-2, 2, 0) and (-1, 1, 1) is
The equation of the plane passing through the point (-1,-2,-3) and perpendicular to the x-axis is
If \(|\bar u|=3,|\bar v|=2\ and\ |\bar u\times \bar v|=3\), then the angle between \(\bar u\ and\ \bar v\) is equal to
If \(\bar{a}=2\hat{i}+3\hat{j}-4\hat{k}\) and \(\bar{b}=\hat{i}+3\hat{j}+2\hat{k}\), then a unit vector in the direction of \(\bar a +\bar b\) is
If \(\bar a\ and\ \bar b\) are position vectors of the points (a, 3, 0) and (1, 0, 0) respectively and if the angle between the vectors \(\bar a\ and\ \bar b\ is\ \frac{\pi}{4}\), then the value of a is equal to
If \(\bar{a}=\hat{i}-3\hat{j}+3\hat{k}\) and \(\bar{b}=2\hat{i}+\hat{j}-3\hat{k}\), then the value of \((\bar a\times\bar b)\cdot\bar b\) is equal to
If \(|\bar a|=10\ and\ |\bar b|=5\), then the value of \((\bar a+2\bar b)\cdot(\bar a-2\bar b)\) is equal to
If \(|\bar{a}|=\sqrt{14},|\bar{b}|=\sqrt{10},|\bar{a}-\bar{b}|=\sqrt{24}\ and\ \theta\) is angle between \(\bar{a}\ and\ \bar{b}\), then \(\cos\theta=\)
Let \(\bar{a}=\hat{i}+2\hat{j}-3\hat{k}\) and \(\bar{a}+\bar{b}=4\hat{i}-2\hat{j}+\lambda\hat{k}\). If \(\bar{a}\cdot\bar{b}=4\), then the value of \(\lambda\) is equal to