List of top Mathematics Questions asked in AP EAMCET

Evaluate the integral: \[ \int_{0}^{1} \sqrt{\frac{2 + x}{2 - x}} \, dx \]
Evaluate the integral: \[ \int \sin^4 x \cos^4 x \, dx. \]
Evaluate the integral: \[ \int e^{4x^2 + 8x -4} (x+1) \cos(3x^2 + 6x -4) \, dx.= \]
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):
The semi-vertical angle of a right circular cone is \( 45^\circ \). If the radius of the base of the cone is measured as 14 cm with an error of \( \left(\frac{\sqrt{2}-1}{11} \right) \) cm, then the approximate error in measuring its total surface area is (in sq. cm).
If \[ f(x) = 5 \cos^3 x - 3 \sin^3 x \quad \text{and} \quad g(x) = 4 \sin^3 x + \cos^2 x, \] then the derivative of \( f(x) \) with respect to \( g(x) \) is:
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:
Parametric equations of the circle \( 2x^2 + 2y^2 = 9 \) are:
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:
Based on the following statements, choose the correct option: Statement-I: The variance of the first \( n \) even natural numbers is \[ \frac{n^2 - 1}{4} \] Statement-II: The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112.
In a triangle ABC, if \( a = 13, b = 14, c = 15 \), then \( r_1 = \)
Evaluate: \[ \tan \alpha + 2 \tan 2\alpha + 4 \tan 4\alpha + 8 \cot 8\alpha. =\]
The values of \( x \) in \( (-\pi, \pi) \) which satisfy the equation \( \cos x + \cos 2x + \cos 3x + \cdots = 4^3 \) are:
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:
Consider the system of linear equations: \[ x + 2y + z = -3, \] \[ 3x + 3y - 2z = -1, \] \[ 2x + 7y + 7z = -4. \] Determine the nature of its solutions.