List of top Mathematics Questions asked in KEAM

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 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

Given the points \(A(6,-7,0),B(16,-19,-4),C(0,3,-6)\) and \(D(2,-5,10)\),the point of intersection of the lines \(AB\) and \(CD\) is 

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

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 \(\int^{2}_{0}f(x)dx=\)

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

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

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

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

An electric bulb manufacturing company manufactures three types of electric bulbs A, B and C. In a room containing these three types of electric bulbs, it is known that 6% of type A electric bulbs are defective, 4% of type B electric bulbs are defective and 2% of type C electric bulbs are defective. An electric bulb is selected at random from a lot containing 50 type A electric bulbs,30 type B electric bulbs and 20 type C electric bulbs. The selected electric bulb is found to be defective. Then the probability that the selected electric bulb was type A 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?