List of top Questions asked in KEAM- 2023

An urn contains 8 black marbles and 4 white marbles. Two marbles are chosen at random and without replacement. Then the probability that both marbles are black is 

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

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 \(X\) be a random variable following Binomial distribution B in(\(n.p\)),where n is the number of independent Bernoulli trials and \(p\) is the probability of success. If \(E(X)=1\) and \(Var(X)=\dfrac{4}{5}\) ,then the values of \(n\) and \(p\) are

A coin is tossed thrice. The probability of getting a head on the second toss given that a tail has occurred in at least two tosses is 

There are two cash counters A and B for placing orders in a college canteen. Let \(EA\) be the event that there is a queue at counter A and \(EB\) denotes the event that there is a queue at counter B. If \(P(EA)=0.45\) ,\(P(EB)=0.55\) and \(P(EA∩EB)=0.25\),then the probability that there is no queue at both the counters is:

Consider two independent events \(E\) and \(F\) such that\( P(E)=1/4,P(E∪F)=2/5\) and \(P(F)=a\).Then,the value of \(a\) 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 ?

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 

Which of the following is the correct formulation of the linear programming problem ?

Consider the following Linear Programming Problem(LPP):Maximize \(z=60x_1+50x_2\) subject to \(x_1+2x_2≤40 3x_1+2x_2≤60 x_1,x_2≥0\).Then, the ______.

Suppose there are 5 alike dogs, 6 alike monkeys and 7 alike horses. The number of ways of selecting one or more animals from these is

The number of ways in which we can distribute n identical balls in k boxes 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 \(x+iy=\dfrac{1}{(1+cosθ)+isinθ}\),then the value of \(x^2+1\) 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

The determinant of the matrix\(\begin{vmatrix}      1 & 4 & 8\\      1 & 9 & 27\\      1 & 16 & 64  \end{vmatrix}\)  is?

The contrapositive of the statement "If the number is not divisible by 3, then it is not divisible by 15" is

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?

The sides of a right-angled triangle ae in an arithmetic progression. If the area of the triangle is 54, then the length of the longest side 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