List of top Questions asked in KEAM

The value of \(cos^{-1}(cos(\dfrac{7\pi}{4}))\) 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 

If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=

If \(x\) is a real number such that \(tanx+cotx=2\),then \(x=\)?

The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are

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

If, \(x∈(0,π)\) satisfies the equation \(6^{1+sinx+sin^2x....}=36\) ,then the value of \(x\) 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 α and β be such that α+β=π. If \(\cos\alpha=\frac{1}{\sqrt2}\), then the value of cot (β-α) is

Let P(x)=cos²x+sin⁴x,for any x∈R.Then which of the following options is correct for all x?

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

The mean deviation about the median for the data \(3,5,9,3,8,10,7\) 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 

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, 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 ?

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: