List of top Questions asked in AP EAMCET- 2024

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 \( (2h + k) = \):
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:
Numerically greatest term in the expansion of \( (5 + 3x)^6 \), when \( x = 1 \), 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:
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 \(|a| =\)
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 \[ y = (x - 1)(x + 2)(x^2 + 5)(x^4 + 8), \] then \[ \lim\limits_{x \to -1} \left( \frac{dy}{dx} \right) = ? \]
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 \[ y^2 = ax \]
Evaluate: \[ \tan^{-1} 2 + \tan^{-1} 3 \]
Evaluate \( \int (\log x)^m x^n dx \).
Evaluate the integral: \[ I = \int_{-5\pi}^{5\pi} \left(1 - \cos 2x \right)^{\frac{5}{2}} dx. \]
The number of different permutations that can be formed by taking 4 letters at a time from the letters of the word "REPETITION" is:
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
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 \( \alpha, \beta \) 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:
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: \[ \int_{0}^{1} \sqrt{\frac{2 + x}{2 - x}} \, dx \]
If \( X \sim B(5, p) \) is a binomial variate such that \( p(X = 3) = p(X = 4) \), then \( P(|X - 3|<2) = \dots \)
If $$ \lim\limits_{x \to \infty} \frac{\left(\sqrt{2x+1} + \sqrt{2x-1}\right) + \left(\sqrt{2x+1} - \sqrt{2x-1}\right) P x^4 - 16} {(x+\sqrt{x^2 - 2}) + (x - \sqrt{x^2 - 2})} = 1, $$ then P = ? 
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:
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 \( 27 \cos^2 \theta = \) ?
The solution of the differential equation \[ x dy - y dx = \sqrt{x^2 + y^2} dx \] when \( y(\sqrt{3}) = 1 \) is:
In a class consisting of 40 boys and 30 girls, 30% of the boys and 40% of the girls are good at Mathematics. If a student selected at random from that class is found to be a girl, then the probability that she is not good at Mathematics is:
The independent term in the expansion of \( (1 + x + 2x^2) \left( \frac{3x^2}{2} - \frac{1}{3x} \right)^9 \) is:
Evaluate the integral \[ \int \frac{x^4 + 1}{x^6 + 1} dx. \]