List of top Mathematics Questions asked in KEAM

Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that \( \min(a, b, c) = 6 \) 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:

Let \( f(x) = \begin{cases} 3x + 6, & \text{if } x \ge c \\ x^{2} - 3x - 1, & \text{if } x<c \end{cases} \), where \( x \in \mathbb{R} \) and \( c \) is a constant. The values of \( c \) for which \( f \) is continuous on \( \mathbb{R} \) are:

If \(x + 13y = 40\) is normal to the curve \(y = 5x^{2} + \alpha x + \beta\) at the point (1,3), then the value of \(\alpha\beta\) is equal to:

\( \int \left(\tan^{2}(2x) - \cot^{2}(2x)\right)\,dx \)

If \( -1 + 7i \), \( -1 + xi \) and \( 3 + 3i \) are the three vertices of an isosceles triangle which is right angled at \( -1 + xi \), then the value of \( x \) is equal to

Evaluate the integral: \( \int \frac{1}{x^3} \sqrt{1 - \frac{1}{x^2}} \text{dx} = \)

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

Consider the following statements :
(i) For every positive real number $x$, $x - 10$ is positive.
(ii) Let $n$ be a natural number. If $n^2$ is even, then $n$ is even.
(iii) If a natural number is odd, then its square is also odd.
Then

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

Find the equation of the curve \( (x, y) \) if \( \cos^{-1}(x-2) = \sin^{-1}(y+1) \).

The distance between the foci of the ellipse \(\frac{(x + 2)^{2{9} + \frac{(y - 1)^{2}}{4} = 1\) is}

The circle passing through the point (1, -2) and touching the x-axis at (3,0) also passes through the point

The axis of the parabola \(x^{2} + 6x + 4y + 5 = 0\) is

The value of \(k\), if the circles \(2x^{2} + 2y^{2} - 4x + 6y = 3\) and \(x^{2} + y^{2} + kx + y = 0\) cut orthogonally is

The value of the integral \(\int_{0}^{\pi} \frac{\cos x}{1 + \sin^{2} x} \, dx\) is

If $x^{22}$ is in the $(r + 1)^{\text{th}}$ term of the binomial expansion of $(3x^3 - x^2)^9$, then the value of $r$ is equal to

A set contains 9 elements. Then the number of subsets of the set which contains at most 4 elements is:

The foci of a hyperbola are (8,3) and (0,3) and eccentricity is $4/3$. Then the length of the transverse axis is:

The end-points of a diameter of a circle are (−1,4) and (5,4). Then the equation of the circle is

The equation of perpendicular bisector of the line segment joining the points (10, 0) and (0, -4) is

If $a y = x + b$ is the equation of the line passing through the points (-5, -2) and (4, 7), then the value of $2a + b$ is equal to:

Given \( a_1 + a_2 + a_3 + a_4 = 960 \) and \( a_4 - 8a = a_1 \), find \( a_1 \).

(3, −4) and (4, −a) lie on line. Find a?