List of top Mathematics Questions asked in KEAM

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
A box contains 100 tickets numbered 00,01,02,....99 and a ticket is drawn at random. Let X denote the sum of the digits on that ticket and Y denote the product of those digits. Then the value of P(X=2IY=0) is
Let Ω={1,2,3,4,5}be the sample space with the events A={1,2,5},B={1,3,5} and c={2,3,5}.Let Ec denote the complement of an event E.Then P((A∩B)c∪Cc) is
Let the probability distribution of random variable X be
X-2-1123
P(X=x)k2k2kk3k

Then, the value of E(X2) is
The contrapositive of the statement "If the number is not divisible by 3, then it is not divisible by 15" is
The inequality \(\frac{2x-1}{3}\geq\frac{3x-2}{4}-\frac{(2-x)}{5}\) holds for x belonging to
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?
The angle between the lines, whose direction cosines are proportional to 4,√3-1,-√3-1 and 4,-√3-1,√3-1, is
The plane passing through the points(2,1,0), (5,0,1)and (4,1,1)intersects the x axis at
Suppose the line mx-y+ 5m-4=0 meets the lines x+3y+2=0, 2x+3y+4=0 and x-y-5=0 at the points R. S and T, respectively. If R, S and T are at distances r1, r2 and r3, respectively, from (-5,-4) and \((\frac{15}{r_1})^2+(\frac{10}{r_2})^2=(\frac{6}{r_3})^2\) then the value of m is
Suppose a and b are lengths of major and minor axes of an ellipse that passes through the points (4,3) and (-1,4). If the major axis of the ellipse lies along the x-axis , then the value of \(\frac{1}{a^2}+\frac{16}{b^2}\) is
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 ?
\(\lim_{x\to0}\dfrac{ln(1+(ln5)x)}{5^{x}}-1\)
The line of intersection of the planes \(3x-6y-2z-15=0\) and \(2x=y-2z-5=0\) 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 
The plane that is perpendicular to the planes \(x-y+2z-4=0\) and  \(2x-2y+z=0\) and passes through \( (1,-2,1)\) 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 ?

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

The value of \(\tan^{-1}(√3)-\sec^{-1}(\dfrac{2}{√3})\) is ?
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?
\(\lim_{x\to0} e^{x}-\dfrac{1}{3}×(1-e^{2x})\)\(=\)?

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