List of top Mathematics Questions asked in KEAM

The value of \(λ\) for which the vectors \(i+j-k\)and \(λi+3j+k\) are perpendicular is ?

Let A be an invertible matrix of size 4x4 with complex entries. If the determinant of adj(A) is 5,then the number of possible value of determinant of A is

\(∫^1_0\dfrac{x}{x^2-4}dx=?\)

The mean deviation about the median for the data \(3,5,9,3,8,10,7\) is ?

In a linear programming problem ,the restrictions under which the objective function is to be optimized are called as?

A point moves in such a way that it remains equidistant from each of the lines \(3x±2y= 5\). Then the path along which the point moves is?

For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is

Let a,b be two real numbers between \(3\) and \(81 \)such that the resulting sequence \(3,a,b,81\) is in a geometric progression. The value of \(a+b\) is

Let \(f:R→R\) be defined by \(f(x)=\){\(2x+3,x≤5 3x+α,x>5\) .Then the value of \(α\) so that f is continuous on \(R\) is

The equation of the line passing through origin which is parallel to the tangent of the curve \(y=\dfrac{x-2}{x-3}\) at \(x=4\) is

Let \( f(x)=(1-1/x)2,x>0\). Then

Let \(f(x)\)={-\(5,x≤0 x-5,x>0\) and \(g(x)=If(x)+2f(IxI)\).Then \(g(-2)\) will be

Let, \(a=i-j+2k\). Then the vector in the direction of a with magnitude \(5\) units is ?

Let \(X\) be a random variable following Binomial distribution B in(\(n.p\)),where n is the number of independent Bernoulli trials and \(p\) is the probability of success. If \(E(X)=1\) and \(Var(X)=\dfrac{4}{5}\) ,then the values of \(n\) and \(p\) are

Consider two independent events \(E\) and \(F\) such that\( P(E)=1/4,P(E∪F)=2/5\) and \(P(F)=a\).Then,the value of \(a\) is

Which of the following is the correct formulation of the linear programming problem ?

The number of ways in which we can distribute n identical balls in k boxes is

If \(x+iy=\dfrac{1}{(1+cosθ)+isinθ}\),then the value of \(x^2+1\) 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 ?