List of top Mathematics Questions asked in KEAM

The determinant of the matrix\(\begin{vmatrix}      1 & 4 & 8\\      1 & 9 & 27\\      1 & 16 & 64  \end{vmatrix}\)  is?
The position vectors of two points P and Q are given by \(OP=2a-b\) and \(OQ=a+3b\) ,respectively.If a point R divides the line joining P and Q internally in the ratio \(1:2\) ,then the position vector of the point R is ?
\(\lim_{x\to0}\dfrac{ln(1+(ln5)x)}{5^{x}}-1\)
Let the Standard deviation of \(x_1,x_2\) and \(x_3\) be \(9\) .Then ,the variance of \(3x_1+4,\)  \(3x_2+4 \) and \(3x_3+4\) is 
Let, the coefficient of variation of two datasets be \(50 \) and \(75\) ,respectively and the corresponding variances be \(25\) and \(36\),respectively.Also let \(x_1\) and \(x_2\) denote the corresponding sample means. Then \(x_1+x_2\) is ?
The direction cosines of the vector \(a=-2i+j-k\) are ?

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

Let \(a=i+j+2k\) and \(b=i-2j+3k\) be two vectors. Then the unit vector in the direction of \(a-b\) is

The value of \(\tan^{-1}(√3)-\sec^{-1}(\dfrac{2}{√3})\) is ?
\(\lim_{x\to0} e^{x}-\dfrac{1}{3}×(1-e^{2x})\)\(=\)?
Let x be a real number and a be any non-zero vector such \(|(4-x)a|<|3a|\).Then which of the following options is correct?

The projection of the vector \(a=2i-3j+4k \)on the vector \(b=i+2j+2k\) is ?

\(∫\dfrac{1}{cosx(sinx+2cosx)} dx=\)
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 

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