List of top Mathematics Questions asked in KEAM

The value of \( \lim_{x \to 1} \frac{x^2 + 2x - 3}{x - 1} \) is:
The value of \( \lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} \) is:
The probability that at least one of \( A \) or \( B \) occurs is 0.6. If \( A \) and \( B \) occur simultaneously with probability 0.2, then \( P(A') + P(B') \) is:
If \( A \) and \( B \) are two independent events such that \( P(A) = 0.4 \) and \( P(A \cup B) = 0.7 \), then \( P(B) \) is equal to:
If the mean of five observations \( x, 2x+5, 13, 2x-7, \) and 9 is 22, then the value of \( x \) is:
If \( x_1, i=2, 3, \ldots, n \) are \( n \) observations such that \( \sum_{i=1}^{n} x_i^2 = 550 \), mean \( \bar{x} = 5 \) and variance is zero, then the number of observations is equal to:
If \( \vec{a} \) and \( \vec{b} \) are non-collinear unit vectors and \( |\vec{a} + \vec{b}|^2 = 3 \), then \( (3\vec{a} + 2\vec{b}) \cdot (3\vec{a} - \vec{b}) \) is equal to:
A vector of magnitude 6 and perpendicular to \( \vec{a} = 2i + 2j + k \) and \( \vec{b} = i - 2j + 2k \), is:
If \( \vec{a} = 2\vec i + 4\vec j + 7\vec k \) and \( \vec {b} = 4\vec i + 7\vec j + 2\vec k \), then the angle between \( \vec{a} + \vec{b} \) and \( \vec{a} - \vec{b} \) is equal to:
Equation of the line parallel to the line \( \frac{x-2}{2} = \frac{y-2}{3} = \frac{z-1}{-2} \) and passing through the point \( (3, 2, -1) \) is:
The direction ratios of the line joining the points \( (2, 3, 4) \) and \( (-1, 4, -3) \) is:
A line makes angles \( \alpha, \beta, \gamma \) with \( x, y \), and \( z \)-axes respectively. Then the value of \( \sin^2\alpha + \sin^2\beta - \cos^2\gamma \) is:
If the parametric form of the circle is \( x = 3\cos\theta + 3 \) and \( y = 3\sin\theta \), then the Cartesian form of the equation of the circle is:
The eccentricity of an ellipse is \( \frac{1}{3} \) and its center is at the origin. If one of the directrices is \( x = 9 \), then the equation of the ellipse is:
The radius of the circle \( x^2 + y^2 - 2x - 4y - 4 = 0 \) is:
If the point \( (2, k) \) lies on the circle \( (x - 2)^2 + (y + 1)^2 = 4 \), then the value of \( k \) is:
If the sum of distances of a point from the origin and the line \( x = 3 \) is 8, then its locus is:
The equation of the straight line, intersecting the coordinate axes \( x \) and \( y \) are respectively 1 and 2, is:
The area of the triangle formed by the coordinate axes and a line whose perpendicular from the origin makes an angle of 45° with the x-axis is 50 square units. Then the equation of the line is:
The equation of the straight line passing through the point \( (1, 1) \) and perpendicular to the line \( x + y = 5 \) is:
The length of perpendicular from the origin to the line \( \frac{x}{5} - \frac{y}{12} = 1 \) is:
If \( P(-3, 4) \) and \( Q(3, 1) \) are points on a straight line, then the slope of the straight line perpendicular to PQ is:
If \( \sin x = \frac{3}{5} \), then the value of \( \sec x + \tan x \) is equal to:
sin\(^{-1} \left( \sin \left( \frac{5\pi}{6} \right) \right) \) is equal to:
tan\(^{-1} 2 - \) tan\(^{-1} \frac{1}{3}\) is equal to: