List of top Mathematics Questions asked in KEAM

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 

Suppose a and b are lengths of major and minor axes of an ellipse that passes through the points (4,3) and (-1,4). If the major axis of the ellipse lies along the x-axis , then the value of \(\frac{1}{a^2}+\frac{16}{b^2}\) is

For the circle \(C=x^2+y^2-6x+2y=0\),which of the following is incorrect:

The equation of the circle that can be inscribed in the square formed by \(x^2-8x+12=0\) and \(y^2-14y+45=0\) is ?

Suppose the line mx-y+ 5m-4=0 meets the lines x+3y+2=0, 2x+3y+4=0 and x-y-5=0 at the points R. S and T, respectively. If R, S and T are at distances r1, r2 and r3, respectively, from (-5,-4) and \((\frac{15}{r_1})^2+(\frac{10}{r_2})^2=(\frac{6}{r_3})^2\) then the value of m 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 ?

The line perpendicular to \(4x-5y+1=0\) and passing through the point of intersection of the straight line \(x+2y-10=0\) and \(2x+y+5=0\) is ?

The inequality \(\frac{2x-1}{3}\geq\frac{3x-2}{4}-\frac{(2-x)}{5}\) holds for x belonging to

Let f(x)=cosx for \(0\leq x \leq\frac{\pi}{3}\). Then the value of c which satisfies the conclusion of the Mean Value Theorem for the function f on \([0,\frac{\pi}{3}]\) is equal to

If n^th term of a series is n+(-1)^n-1, n = 1,2,3,..., then the sum of first 40 terms of the series is

If A=[2 0 6] and \(B=\begin{bmatrix} 3&\ \ 5\\7&-2\\6&\ \ 6 \end{bmatrix}\), then AB=

The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is

In a box there are four marbles and each of them is marked with distinct number from the set {1, 2, 5, 10}. If one marble is randomly selected four times with replacement and the number on it noted, then the probability that the sum of numbers equals 18 is

If ¹¹P_r=7920 and ¹¹C_r = 330, then the value of r is equal to

Let ⊙ be a binary operation on Q - {0} defined by a⊙b=\(\frac{a}{b}\). Then 1⊙(2⊙(3⊙4)) is equal to

Let A = {x∈Z: -1 ≤ x < 4} and let B = {x ∈ Z:0 < \(\frac{x}{2}\) ≤ 3}. Then A∩B is equal to

The three vertices of a triangle are (0, 0), (3, 1) and (1, 3). If this triangle is inscribed in a circle, then the equation of the circle is

If z₁ and z₂ are two different complex numbers with |z₂|=1, then \(|\frac{1-\bar{z_1}z_2}{z_1-z_2}|\)is equal to

The equation of the circle touching the x-axis at (5, 0) and the line y = 10 is

If \(z=\frac{(3+i)(7-i)^2}{3-i}\), then the value of |z| is equal to