List of top Mathematics Questions asked in KEAM

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 \(A=\begin{bmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{bmatrix}\) 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

Let \(f:R→R\) be a function defined by
\(f(x) =   \begin{cases}     3e^x       & \quad \text {if}\  {x<0}\\     x^2+3x+3  & \quad \text {if}\  0≤x<1   \\ x^2-3x-3 & \quad \text {if} \ x≥1\end{cases}\)

Let α and β be such that α+β=π. If \(\cos\alpha=\frac{1}{\sqrt2}\), then the value of cot (β-α) is

If f(z)=zⁿ+a_n-1z^n-1 +......+a₁zⁿ+a₀ ∈ R[z] is a polynomial in z with no root over R,then deg(f)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 [.]denote the greatest integer function and f(x)=[x]+[2-x],-1≤x≤4.Then

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 \(\int^{2}_{0}f(x)dx=\)

If α+β+γ=2π, then the value of \(\cot\frac{\alpha}{2}\cot\frac{\beta}{2}+\cot\frac{\alpha}{2}\cot\frac{\gamma}{2}+\cot\frac{\beta}{2}\cot\frac{\gamma}{2}\) is

Let p,q and r be real numbers such that \(|r|\gt\sqrt{p^2+q^2}\).Then the equation \(p\cos\theta+q\sin\theta=r\) has

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 E^c denote the complement of an event E.Then P((A∩B)^c∪C^c) is

Let the probability distribution of random variable X be

X	-2	-1	1	2	3
P(X=x)	k	2k	2k	k	3k

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 AA^T = I = A^TA, then which of the following statements always holds?