List of top Mathematics Questions asked in KEAM

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 plane passing through the points(2,1,0), (5,0,1)and (4,1,1)intersects the x axis at
The angle between the lines, whose direction cosines are proportional to 4,√3-1,-√3-1 and 4,-√3-1,√3-1, is
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?
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 ?
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 ?
The value of \(cos^{-1}(cos(\dfrac{7\pi}{4}))\) 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 

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

A box contains 10 coupons, labelled as 1,2,.....10.Three coupons are drawn at random and without  X1,X2 and X3 denote the numbers on the coupons. Then the probability that max{X1,X2,X3}<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 ?
For a real number t ,the equation \((1+t)x^2 + (t-1)y^2 + t^2 - 1 = 0\) represents a hyperbola provided 
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 ?

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