List of top Questions asked in AP EAMCET

When the origin is shifted to \( (h, k) \) by translation of axes, the transformed equation of \( x^2 + 2x + 2y - 7 = 0 \) does not contain \( x \) and constant terms. Then \( (2h + k) = \):
Let \( A, B, C, D, \) and \( E \) be \( n \times n \) matrices, each with non-zero determinant. If \( ABCDE = I \), then \( C^{-1} \) is:
If \( (1,3) \) is the midpoint of a chord of the circle \( x^2 + y^2 - 4x - 8y + 16 = 0 \), then the area of the triangle formed by that chord with the coordinate axes is:
A pair of lines drawn through the origin forms a right-angled isosceles triangle with right angle at the origin with the line \( 2x + 3y = 6 \). The area (in square units) of the triangle thus formed is:
Numerically greatest term in the expansion of \( (5 + 3x)^6 \), when \( x = 1 \), is:
If the locus of the mid points of the chords of the circle \(x^2 + y^2 = 25\) that subtend a right angle at the origin is given by \( \frac{x^2}{a^2} + \frac{y^2}{a^2} = 1\), then \(|a| =\)
A person is known to speak false once out of 4 times. If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is
Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]
Evaluate: \[ \tan^{-1} 2 + \tan^{-1} 3 \]
If \( X \sim B(5, p) \) is a binomial variate such that \( p(X = 3) = p(X = 4) \), then \( P(|X - 3|<2) = \dots \)
The number of different permutations that can be formed by taking 4 letters at a time from the letters of the word "REPETITION" is:
The area (in square units) of the smaller region lying above the X-axis and bounded between the circle \[ x^2 + y^2 = 2ax \] and the parabola \[ y^2 = ax \]
The system \( x + 2y + 3z = 4, \, 4x + 5y + 3z = 5, \, 3x + 4y + 3z = \lambda \) is consistent and \( 3\lambda = n + 100 \), then \( n = ? \)
Evaluate the integral: \[ \int_{0}^{1} \sqrt{\frac{2 + x}{2 - x}} \, dx \]
Evaluate \( \int (\log x)^m x^n dx \).
If \( \alpha, \beta \) are the roots of the equation \( x^2 - 6x - 2 = 0 \), \( \alpha > \beta \), and \( a_n = \alpha^n - \beta^n, n \geq 1 \), then the value of \( \frac{a_{10} - 2 a_8}{2 a_9} \) is:
If \[ y = (x - 1)(x + 2)(x^2 + 5)(x^4 + 8), \] then \[ \lim\limits_{x \to -1} \left( \frac{dy}{dx} \right) = ? \]
If the roots of the quadratic equation \( x^2 - 35x + c = 0 \) are in the ratio 2:3 and \( c = 6K \), then \( K \) is:
If \( n \geq 2 \) is a natural number and \( 0<\theta<\frac{\pi}{2} \), then \[ \int \frac{(\cos^n \theta - \cos \theta)^{1/n}}{\cos^{n+1} \theta} \sin \theta \, d\theta = \]
The algebraic equation of degree 4 whose roots are the translates of the roots of the equation \( x^4 + 5x^3 + 6x^2 + 7x + 9 = 0 \) by \( -1 \) is:
A line \( L \) passes through \( (1,2,-3) \) and \( (3,3,-1) \), and a plane \( \pi \) passes through \( (2,1,-2), (-2,-3,6), (0,2,-1) \). If \( \theta \) is the angle between \( L \) and \( \pi \), then \( 27 \cos^2 \theta = \) ?
A test containing 3 objective type of questions is conducted in a class. Each question has 4 options and only one option is the correct answer. No two students of the class have answered identically and no student has written all correct answers. If every student has attempted all the questions, then the maximum possible number of students who have written the test is:
If \[ \frac{1}{(3x+1)(x-2)} = \frac{A}{3x+1} + \frac{B}{x-2} \quad {and} \quad \frac{x+1}{(3x+1)(x-2)} = \frac{C}{3x+1} + \frac{D}{x-2}, \] then \[ \frac{1}{(3x+1)(x-2)} = \frac{A}{3x+1} + \frac{B}{x-2}, { find } A + 3B = 0, A:C = 1:3, B:D = 2:3. \]
The angle between the planes \( \vec{r} \cdot (12\hat{i} + 4\hat{j} - 3\hat{k}) = 5 \) and \( \vec{r} \cdot (5\hat{i} + 3\hat{j} + 4\hat{k}) = 7 \) is:
The independent term in the expansion of \( (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 \) is: