List of top Mathematics Questions asked in KEAM

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) is 

Suppose P is the point on the line joining  \((-9,4,5)\) and \((11,0,-1)\) that lies closest to the origin O. Then \(|OP|^2\) equals to?
Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is 
If the coefficients of \((5r+4)th\) term and \((r-1)th\) term in the expansion of \((1+x)^{25}\) are equal, then \(r\) is 
Let \(k\) be a real number such that \(\sin \dfrac{3π}{14} \cos \dfrac{3π}{14} = k \cos \dfrac{π}{14}\).Then the value of \(4k\) 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

A biased die is rolled such that the probability of getting k dots,1≤k≤6, on the upper face of the die is proportional to k. Then the probability that five dots appear on the upper face of the die is 
\(\text{The value of    } cosec20°tan60°-sec20° \text{is }\)
The area of the region in the first quadrant which is above the parabola \(y = x^2\) and enclosed by the circle \(x^2 +y^2 = 2 \) and the y-axis is
The area of the region in the first quadrant enclosed by the curves\( y=√x,y=-x+6 \)and the x-axis is 

For \(i=1,2,3,4\), suppose the points\((\cosθi,\secθi)\) lie on the boundary of a circle,where \(θi∈[0,\frac{π}{6})\) are distinct. Then \(\cosθ_1\ \cosθ_2\ \cosθ_3\ \cosθ_4\)  equals

For any \(n≥0\) the value of \(\sum_{r=0}^n \dfrac{(4r+3).(nC_r)^2}{(2n+3)}\) is 
For a real number t ,the equation \((1+t)x^2 + (t-1)y^2 + t^2 - 1 = 0\) represents a hyperbola provided 
The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an

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 

Let f(x)=πcosx+x2.The value of c∈(0,π) where f attains its local maximum/minumum is
If (2,-6),(5,2) and (-2,2) constitute the vertices of a triangle then the the line joining the origin and its orthocentre is
Let A and B be two independent events such that the odds in favour of A and B are \(1:1 \) and \(3:2\) respectively .Then the probability that only one of the two occurs is 
\(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
A six faced fair die is rolled for a large number of times. Then, the mean value of the outcome is 
If \( α,β,γ\) are the cube roots of \(-2\) ,then the value of \(xα+yβ+zγ/xβ+yγ+zα\) is (\(x,y,z\) are variables)
Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is 
Let the probability distribution of random variable X be
X-2-1123
P(X=x)k2k2kk3k

Then, the value of E(X2) is
\(∫\dfrac{1}{cosx(sinx+2cosx)} dx=\)
Let \(f:\R\rightarrow\R\) be defined by
\(f(x) =   \begin{cases} x & \text{if}\ x\leq1 \\  -x+2 & \text{if}\ x\gt1\end{cases}\)
Then \(\int^{2}_{0}f(x)dx=\)