List of top Mathematics Questions asked in AP EAMCET

If a man of height 1.8 m is walking away from the foot of a light pole of height 6 m with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph):
Evaluate the limit: \[ \lim\limits_{x \to \infty} \frac{[2x - 3]}{x}. \]
Evaluate the limit: \[ \lim\limits_{x \to 0} \frac{\cos 2x - \cos 3x}{\cos 4x - \cos 5x}.= \]
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the Y-axis and Z-axis respectively, then the angle between \( L \) and another line having direction ratios \( 1,1,1 \) is:
If the equation \( \frac{x^2}{7-k} - \frac{y^2}{5-k} = 1 \) represents a hyperbola, then:
The locus of the point of intersection of perpendicular tangents drawn to the circle \( x^2 + y^2 = 10 \) is:
The normal drawn at \( (1,1) \) to the circle \( x^2 + y^2 - 4x + 6y - 4 = 0 \) is:
If the reflection of a point \( A(2,3) \) in the X-axis is \( B \); the reflection of \( B \) in the line \( x + y = 0 \) is \( C \) and the reflection of \( C \) in \( x - y = 0 \) is \( D \), then the point of intersection of the lines \( CD, AB \) is:
If each of the coefficients \( a, b, c \) in the equation \( ax^2 + bx + c = 0 \) is determined by throwing a die, then the probability that the equation will have equal roots, is:
A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from the first bag and two balls from the second bag at random, the probability that out of the three, two are black and one is red, is:
A radar system can detect an enemy plane in one out of 10 consecutive scans. The probability that it cannot detect an enemy plane at least two times in four consecutive scans, is:
If \( \hat{i} - \hat{j} - \hat{k} \), \( \hat{i} + \hat{j} + \hat{k} \), \( \hat{i} + \hat{j} + 2\hat{k} \), and \( 2\hat{i} + \hat{j} \) are the vertices of a tetrahedron, then its volume is:
In a triangle ABC, if \( a = 13, b = 14, c = 15 \), then \( r_1 = \)
The values of \( x \) in \( (-\pi, \pi) \) which satisfy the equation \( \cos x + \cos 2x + \cos 3x + \cdots = 4^3 \) are:
Evaluate: \[ \tan \alpha + 2 \tan 2\alpha + 4 \tan 4\alpha + 8 \cot 8\alpha. =\]
The number of ways of arranging 9 men and 5 women around a circular table so that no two women come together are:
The quotient when \[ 3x^5 - 4x^4 + 5x^3 - 3x^2 + 6x - 8 \] is divided by \( x^2 + x - 3 \) is:
Let \( P(x_1, y_1, z_1) \) be the foot of the perpendicular drawn from the point \[ Q(2, -2, 1) \] to the plane \[ x - 2y + z = 1. \] If \( d \) is the perpendicular distance from the point \( Q \) to the plane and \[ I = x_1 + y_1 + z_1, \] then \( I + 3d^2 \) is:
The product of perpendiculars from the two foci of the ellipse \[ \frac{x^2}{9} + \frac{y^2}{25} = 1 \] on the tangent at any point on the ellipse is:
If the ordinates of points \( P \) and \( Q \) on the parabola \[ y^2 = 12x \] are in the ratio 1:2, then the locus of the point of intersection of the normals to the parabola at \( P \) and \( Q \) is:
An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is:

The coefficient of variation for the frequency distribution is: 

The shortest distance between the skew lines \( \vec{r} = (2\hat{i} - \hat{j}) + t(\hat{i} + 2\hat{k}) \) and \( \vec{r} = (-2\hat{i} + \hat{k}) + s(\hat{i} - \hat{j} - \hat{k}) \) is:
If \( \vec{a}, \vec{b}, \vec{c} \) are 3 vectors such that \( |\vec{a}| = 5, |\vec{b}| = 8, |\vec{c}| = 11 \) and \( \vec{a} + \vec{b} + \vec{c} = 0 \), then the angle between the vectors \( \vec{a} \) and \( \vec{b} \) is:
If \( \vec{i} - 2\vec{j} + 3\vec{k}, 2\vec{i} + 3\vec{j} - \vec{k}, -3\vec{i} - \vec{j} - 2\vec{k} \) are the position vectors of three points A, B, C respectively, then A, B, C: