List of top Mathematics Questions asked in AP EAMCET

If the equation \( \frac{x^2}{7-k} - \frac{y^2}{5-k} = 1 \) represents a hyperbola, then:
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:
The length of the latus rectum of \( 16x^2 + 25y^2 = 400 \) is:
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:
Equation of the line touching both parabolas \( y^2 = 4x \) and \( x^2 = -32y \) is:
The equation of a line which makes an angle of \( 45^\circ \) with each of the pair of lines \[ xy - x - y + 1 = 0 \] is:
If the axes are rotated through an angle \( \alpha \), then the number of values of \( \alpha \) such that the transformed equation of \( x^2 + y^2 + 2x + 2y - 5 = 0 \) contains no linear terms is:
The locus of a variable point which forms a triangle of fixed area with two fixed points 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:
Let \( E_1 \) and \( E_2 \) be two independent events of a random experiment such that \[ P(E_1) = \frac{1}{2}, \quad P(E_1 \cup E_2) = \frac{2}{3}. \] Then match the items of List-I with the items of List-II:
two independent events
The correct match 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 and B throw a pair of dice alternately and they note the sum of the numbers appearing on the dice. A wins if he throws 6 before B throws 7, and B wins if he throws 7 before A throws 6. If A begins, the probability of his winning 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:
Let \( |\mathbf{a}| = 2, |\mathbf{b}| = 3 \) and the angle between \( \mathbf{a} \) and \( \mathbf{b} \) be \( \frac{\pi}{3} \). If a parallelogram is constructed with adjacent sides \( 2\mathbf{a} + 3\mathbf{b} \) and \( \mathbf{a} - \mathbf{b} \), then its shorter diagonal is of length:
The values of \( x \) for which the angle between the vectors \[ \mathbf{a} = x\hat{i} + 2\hat{j} + \hat{k}, \quad \mathbf{b} = -\hat{i} + 2\hat{j} + x\hat{k} \] is obtuse lie in the interval:
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 \( r_1 = \)
In a triangle ABC, if \( r : R = 1 : 3 : 7 \), then \( \sin(A + C) + \sin B = \)
Evaluate: \[ \tan \alpha + 2 \tan 2\alpha + 4 \tan 4\alpha + 8 \cot 8\alpha. =\]
Evaluate \[ \cot \left( \sum_{n=1}^{50} \tan^{-1} \left( \frac{1}{1 + n + n^2} \right) \right).= \]
cos 6° sin 24° cos 72° =