List of top Mathematics Questions asked in KEAM

The area of the region in the first quadrant which is above the parabola \(y = x^2\) and enclosed by the circle \(x^2 +y^2 = 2 \) and the y-axis is

Let \(a\) and \(b\) be perpendicular vectors such that \(IaI=√104\) and \(IbI=6\).Then the value of\( Ia-bI\) is ?

The value of \(\tan^{-1}(\dfrac{1}{2})+\tan^{-1}(\dfrac{2}{5})\) is ? 

A coin is tossed thrice. The probability of getting a head on the second toss given that a tail has occurred in at least two tosses is 

For the circle \(C=x^2+y^2-6x+2y=0\),which of the following is incorrect:

The line perpendicular to \(4x-5y+1=0\) and passing through the point of intersection of the straight line \(x+2y-10=0\) and \(2x+y+5=0\) is ?

A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome is 

There are two cash counters A and B for placing orders in a college canteen. Let \(EA\) be the event that there is a queue at counter A and \(EB\) denotes the event that there is a queue at counter B. If \(P(EA)=0.45\) ,\(P(EB)=0.55\) and \(P(EA∩EB)=0.25\),then the probability that there is no queue at both the counters is:

Let A and B be two independent events such that the odds in favour of A and B are \(1:1 \) and \(3:2\) respectively .Then the probability that only one of the two occurs is 

If n(A∪B)=97, n(A∩B) = 23 and n(A-B)=39, then n(B) is equal to

Let \(t_n=\frac{1}{n}\displaystyle\sum^{n}_{k=1}\left(\frac{k}{n} \right)^2\)for n=1,2,3…. Then t₁₀ is equal to

The value of \(\left[ \frac{5i}{(1-i)(2-i)(3-i)} \right]^{50}\)is equal to

The period of the function \(g(x)=5\cot(\frac{\pi}{3}x+\frac{\pi}{6})+2\) is equal to

If \(z=\frac{(3+i)(7-i)^2}{3-i}\), then the value of |z| is equal to

If \(x=\sqrt{10^{\cos^{-1}\theta}}\ and\ y=\sqrt{10^{\sin^{-1}\theta}}\), then \(\frac{dy}{dx}\) is equal to

If n^th term of a series is n+(-1)^n-1, n = 1,2,3,..., then the sum of first 40 terms of the series 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

\(\displaystyle\lim_{x\rightarrow-2}\frac{3x^2+ax-2}{x^2-x-6}\) is a finite number, then the value of a is equal to

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to

If z₁ and z₂ are two different complex numbers with |z₂|=1, then \(|\frac{1-\bar{z_1}z_2}{z_1-z_2}|\)is equal to

If the radius of the circle x²+y²+ax+by+3=0 is 2, then the point (a, b) lies on the circle

The equation of tangent to the circle (x-5)²+y² = 25 at (2, 4) is