List of top Questions asked in KEAM

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
Let \(x\) denote the mean of the observations \(1,3,5,a,9\) and \(y\) denote the mean of the observations \(2,4,b,6,8\) where \(a,b>0\) .If \(x=y\) ,the value of \(2(a-b)\) is ?
If the median of the observations \(4,6,7,x,x+2,12,12,13\) arranged in an increasing order is 9,then the variance of these observations is 
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 
Which of the following is the correct formulation of the linear programming problem ?
In a linear programming problem ,the restrictions under which the objective function is to be optimized are called as?
Consider the Linear Programming Problem:
Minimize 3x1+4x2 +2x3
subject to
x1+x2+x3≤6
x1+2x2+x3≤10
x1,x2,x3≥0.
Then, the number of basic solutions are
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 ______.
Suppose there are 5 alike dogs, 6 alike monkeys and 7 alike horses. The number of ways of selecting one or more animals from these is
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 \(S\)

If f(z)=zn+an-1zn-1 +......+a1zn+a0 ∈ R[z] is a polynomial in z with no root over R,then deg(f)is
If \(x+iy=\dfrac{1}{(1+cosθ)+isinθ}\),then the value of \(x^2+1\) is ?
Suppose \(A=\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{bmatrix}\) is an adjoint of the matrix \(\begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 3 & 4\end{bmatrix}\). Then the value of \(\frac{a_!+b_2+c_3}{b_1a_2}\) is

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

The determinant of the matrix\(\begin{vmatrix}      1 & 4 & 8\\      1 & 9 & 27\\      1 & 16 & 64  \end{vmatrix}\)  is?
The contrapositive of the statement "If the number is not divisible by 3, then it is not divisible by 15" is
Let A be (2n+1)×(2n+1) matrix with integer entries and positive determinant,where n∈N.If AAT = I = ATA, then which of the following statements always holds?
\(\int^{1}_{0}\frac{2e^x}{1+e^{2x}}dx=\)
The sides of a right-angled triangle ae in an arithmetic progression. If the area of the triangle is 54, then the length of the longest side is
Let \(a_1,a_2,a_3,..\). be an increasing sequence of natural numbers, which are in an arithmetic progression with common difference d. Suppose \(a_1+a_2+a_3=27\) and \(a_1^2+a_2^2+a_3^2=275\). Then the value of \(a_1,d\) are 

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 

The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is 

Let \(f(x)=\dfrac{x-1}{x+1}\) ,Let \(S ={x∈R \text{ Iff } -1(x)=x \text{  does not hold} }\).The cardinality of S 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