List of top Mathematics Questions asked in KEAM

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 
Let \(f(x)=αsin^23x\) .If  \(f ′(\dfrac{π}{12})\) = \(−3\),then the value of \(α \) is
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
If\( \dfrac{1+sinx}{1-sinx}=\dfrac{(1+siny)^3}{(1-siny)^3}\) for some real values \(x\) and \(y\) ,then \(\dfrac{sinx}{siny}\)=

For any real number \(x\), the least value of \(4cosx-3sinx+5\) is ?

\(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
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 S={\(a,b,c\)} be the sample space with the associated probabilities satisfying \(P(a)=2P(b)\) and \(P(b)=2P(c).\)Then the value of \(P(a)\) is 

For four observations X,X2,X3,X4, it is given that ,\(∑x_i^{2}=656\) and  \(∑x_i=32\). Then, the variance of these four observations is ?

If the median of the observations \(4,6,7,x,x+2,12,12,13\) arranged in an increasing order is 9,then the variance of these observations 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 ?
For a real number t ,the equation \((1+t)x^2 + (t-1)y^2 + t^2 - 1 = 0\) represents a hyperbola provided 
The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are
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 
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 ______.

Let \(f:R→R\) be a function defined by \(f(x)=x^2+9\).The range of \(f \) 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
The domain of the real valued function \(f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}\)  is
\(∫xlog(1+x^2)dx=\)?
The area of the region in the first quadrant enclosed by the curves\( y=√x,y=-x+6 \)and the x-axis is 

The minimum of \(f(x)=\sqrt{(10-x^2)}\) in the interval \([-3,2]\) is

Let f(x)=πcosx+x2.The value of c∈(0,π) where f attains its local maximum/minumum is
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
If, \(x∈(0,π)\) satisfies the equation \(6^{1+sinx+sin^2x....}=36\) ,then the value of \(x\) is_____.
If the two sides AB and AC of a triangle are along \(4x-3y-17 = 0\) and  \(3x+4y-19= 0\), then the equation of the bisector of the angle between AB and AC is ?