List of top Mathematics Questions asked in KEAM

\(∫\dfrac{1}{cosx(sinx+2cosx)} dx=\)
\(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
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 

For four observations X,X2,X3,X4, it is given that ,\(∑x_i^{2}=656\) and  \(∑x_i=32\). Then, the variance of these four observations is ?

The mean deviation about the median for the data \(3,5,9,3,8,10,7\) is ?
The value of λ for which the vectors \(2i-3j+4k\) and \(-4i+λj-8k\) are collinear is 
\(∫^1_0\dfrac{x}{x^2-4}dx=?\)
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 

If \(y=x^{e^x}+x^{e} for x>0\),the  \( \dfrac{dy}{dx}\) is equal to ?
Let \(f(x)=αsin^23x\) .If  \(f ′(\dfrac{π}{12})\) = \(−3\),then the value of \(α \) 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 ?
Consider the following Linear Programming Problem(LPP):Maximize \(z=60x_1+50x_2\) subject to \(x_1+2x_2≤40 3x_1+2x_2≤60 x_1,x_2≥0\).Then, the ______.
The number of ways in which we can distribute n identical balls in k boxes is 

Let \(S=\){\(n∈NIn^3+3n^2+5n+3\) is not divisible by \(3\)}.Then, which of the following statements is true about \(S\)