List of top Mathematics Questions asked in KEAM

If \(x+iy=\dfrac{1}{(1+cosθ)+isinθ}\),then the value of \(x^2+1\) is ?
The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}\)  is

Suppose a line parallel to \(ax+by=0\) (where \(b≠0\))intersects\( 5x-y+4=0\) and \(3x+4y-4=0\) ,respectively at P and Q. If the midpoint of PQ is \((1,5)\),then the value of \(\dfrac{a}{b}\) is

Suppose P is the point on the line joining  \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?
If \(θ1,θ2, θ3\) are the angles made by a line with the positive directions of the \( x,y,z\) axes, then the value of \(cos^{2}θ_1 +cos^{2}θ_2+cos^{2}θ_3\) is
If the \(XZ\)-plane divides the straight line joining the points \((2,4,7)\) and \((3,-5,8)\)  in the ratio \(α:1\),then the value of \(α\) is ? 
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an
The equation of the circle that can be inscribed in the square formed by \(x^2-8x+12=0\) and \(y^2-14y+45=0\) is ?

If a straight line in XY plane is passes through \((-a,-b),(a,b),(k,k),(a^2,a^3)\) for some real number \(a,b\) and \(k\),where \(a≠0\),then which of the following option is correct?

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 ? 

If \(A =[5a-b 32]\) and A.adjA=AA^T,then which of the following statements is true

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 ?
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:
A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome 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 
An urn contains 8 black marbles and 4 white marbles. Two marbles are chosen at random and without replacement. Then the probability that both marbles are black 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
The end points of the major axis of an ellipse are (2, 4) and (2,-8). If the distance between foci of this ellipse is 4, then the equation of the ellipse is
If \(y=e^{3\log(2x+1)}\), then \(\frac{dy}{dx}=\)
If α and β are two acute angles of a right triangle, then (sinα+sinβ)2+(cosα+cosβ)2=
The equation of the circle touching the x-axis at (5, 0) and the line y = 10 is