List of top Questions asked in AP EAMCET

An alkyl halide \( C_3H_7Cl \), on reaction with a reagent X, gave the major product Y (\( C_4H_7N \)). Y on hydrolysis released a gas, which turns red litmus to blue. What are X and Y?
If a real valued function \( f: [a, \infty) \to [b, \infty) \) is defined by \( f(x) = 2x^2 - 3x + 5 \) and is a bijection, then find the value of \( 3a + 2b \):
The domain of the real valued function \( f(x) = \frac{1}{\sqrt{log_{0.5}(2x-3)}} + \sqrt{4 - 9x^2} \) is:

Evaluate the following determinant: \( \begin{vmatrix} 1 & 1 & 1 \\ a^2 & {b^2} & {c^2} \\ {a^3} & {b^3} & {c^3} \\ \end{vmatrix} \)

If \( A = \begin{pmatrix} 1 & 2 \\ -2 & -5 \end{pmatrix} \) and \( \alpha^2 + \beta A = 21 \) for some \( \alpha, \beta \in \mathbb{R} \), then find \( \alpha + \beta \):
The system of equations \( x + 2y + 3z = 6 \), \( x + 3y + 5z = 9 \), \( 2x + 5y + az = 12 \) has no solution when \( a = \):
If a complex number \( z \) is such that \( \frac{z-2i}{z-2} \) and the locus of \( z \) is a closed curve, then the area of the region bounded by that closed curve and lying in the first quadrant is:
The real part of \( \frac{\left( \cos a + i \sin a \right)^6}{\left( \sin b + i \cos b \right)^8} \) is:
If \( \alpha, \beta, \gamma \) are roots of the equation \( x^3 + ax^2 + bx + c = 0 \), then \( \alpha^{-1} + \beta^{-1} + \gamma^{-1} \) is:
If set \( A \) contains 8 elements, then the number of subsets of \( A \) which contain at least 6 elements is:
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 sum of the series \( 1 - \frac{2}{3} + \frac{2.4}{3.6} - \frac{2.4.6}{3.6.9} + \cdots \infty \) is:
If \( \frac{1}{x^4 + 1} = \frac{Ax + B}{x^2 + \sqrt{2}x + 1} + \frac{Cx + D}{x^2 - \sqrt{2}x + 1} \), then \( BD - AC = \):
The smallest positive value (in degrees) of \( \theta \) for which \( \tan(\theta + 100^\circ) = \tan(\theta + 50^\circ) \tan(\theta - 50^\circ) \) is valid, is:
Statement (S1): \( \sin 55^\circ + \sin 53^\circ - \sin 19^\circ - \sin 17^\circ = \cos 2^\circ \)
Statement (S2): The range of \( \frac{1}{3 - \cos 2x} \) is \( \left[ \frac{1}{4}, \frac{1}{2} \right] \) Which one of the following is correct?
The general solution of \( 2 \cos^2 x - 2 \tan x + 1 = 0 \) is:

The value of \( \cosh \left( \sin^{-1} \left( \sqrt{8} \right) + \cosh^{-1} 5 \right) \) is:

In \(\Delta ABC\) if \(B = 90^\circ\) then \(2(r + R) = \)
In a triangle ABC, if \( r_1 = 2r_2 = 3r_3 \), then \(\sin A\): \(\sin B\): \(\sin C\) = Options:

If \( L, M, N \) are the midpoints of the sides PQ, QR, and RP of triangle \( \Delta PQR \), then \( \overline{QM} + \overline{LN} + \overline{ML} + \overline{RN} - \overline{MN} - \overline{QL} = \):

In a triangle ABC, if \( (a-b)(s-c) = (b-c)(s-a) \), then \( r_1 + r_3 = \):
Let \( \vec{a} \times \vec{b} = 7\hat{i} - 5\hat{j} - 4\hat{k} \) and \( \vec{a} = \hat{i} + 3\hat{j} - 2\hat{k} \), if the length of projection of \( \vec{b} \) on \( \vec{a} \) is \( \frac{8}{\sqrt{14}} \), then \( |\vec{b}| \) is:
Let ABC be an equilateral triangle of side \(a\). M and N are two points on the sides AB and AC respectively such that \(AN = K \cdot AC\) and \(AB = 3 \cdot AM\). If the vectors \(BN\) and \(CM\) are perpendicular, then \(K = \) ?

Let a and b be two non-collinear vectors of unit modulus. If u = a − (a · b)b and v = a × b, then ∥v∥ = ?

Find the shortest distance between the skew lines $\vec{r} = (-\hat{i} - 2\hat{j} - 3\hat{k}) + t(3\hat{i} - 2\hat{j} - 2\hat{k})$ and $\vec{r} = (7\hat{i} + 4\hat{k}) + s(\hat{i} - 2\hat{j} + 2\hat{k})$.