List of top Mathematics Questions asked in AP EAPCET

\( \int 3^{-\log_3 x^2} dx = \)
If two angles \( \alpha, \beta \) are such that \( 0<\alpha, \beta<\frac{\pi}{4} \), \( \sqrt{1 + \cos 2\alpha} = \frac{3}{\sqrt{5}} \) and \( \frac{\sqrt{1 - \cos 2\beta}}{\sqrt{1 + \cos 2\beta}} = \frac{1}{7} \), then \( (2\alpha + \beta) = \)
In \( \triangle ABC \), if \( (\sin A + \sin B)(\sin A - \sin B) = \sin C(\sin B + \sin C) \), then \( \angle A = \)
If \( C_j \) stands for \( \binom{n}{j} \), then: \[ \frac{C_1}{C_0} + 2 \times \frac{C_2}{C_1} + 3 \times \frac{C_3}{C_2} + ... + n \times \frac{C_n}{C_{n-1}} \]
If \( f(x) = \sqrt{x} + \sin x \), then all the points of the set \( \left( x, f(x) \right)/f'(x) = 0 \) lie on:
If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting a tail on both the coins is:

If a straight line is equally inclined at an angle $ \theta $ with all the three coordinate axes, then $ \tan \theta =$

If \[ \lim_{x \to 2} \frac{1 + \sqrt{1 + 4\log_2 x}}{2 + (2x + \sin^2 x + 2\cos x)(2x - 4)} = m, \] then \( m(m - 1) = \):
If the chord of contact of the point \( P(1, 1) \) with respect to the circle \( S = x^2 + y^2 + 4x + 6y - 3 = 0 \) meet the circle \( S = 0 \) at A and B, then the area of \( \triangle PAB \) is:
If \[ \int \frac{\sin^2 \alpha - \sin^2 x}{\cos x - \cos \alpha} \, dx = f(x) + Ax + B, \, B \in \mathbb{R}, \text{ then} \] \[ \frac{\sin^2 \alpha - \sin^2 x}{\cos x - \cos \alpha} \, dx = f(x) + Ax + B, \, B \in \mathbb{R} \]
The mean of 5 observations is 4.4 and their variance is 8.24. If three of those observations are 1, 2, and 6, then the other two observations are:
The greatest integer \( r \) such that \( 30^r \) divides \( 30! \) is:
A and B are mutually exclusive events of a random experiment and \( P(B^c) \ne 1 \), then \[ P(A | B^c) = ? \]
If \( f(n) = n!(31-n)! \), where \( n \in \{ 0, 1, 2, \dots, 31 \} \), then the minimum value of \( f(n) \) is:
Let the equation \[ ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0 \] represent a point circle (not at the origin). Then which one of the following conditions must hold?
Let a focal chord \( 12x + 5y - 27 = 0 \) of the parabola \( y^2 = kx \) intersect the parabola at points \( P \) and \( P' \). If \( S \) is the focus of the parabola, then \( 9(SP + SP') \) = ?
If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is not in the first quadrant, then \( 15 \sin 2\theta - 20 \cos 2\theta - 7 \tan 2\theta \) is:
A ray of light incident along a line meets another line $7x - y + 1 = 0$ at the point $(0,1)$ and is then reflected along the line $y + 2x = 1$. Then the equation of the line of inciden is
If \( 2\sinh x = \cosh x \), then \( x = \)
The locus of the poles of the tangents to the circle \( x^2 + y^2 - 2x + 2y - 2 = 0 \) with respect to the circle \( x^2 + y^2 = 4 \) is
In \( \triangle ABC \), \( (\cot A + \cot B)(\cot B + \cot C)(\cot C + \cot A) = \)
If \( \lim_{x \to \infty} y(x) = \frac{\pi}{2} \), then the solution of \( x^3 \sin y \frac{dy}{dx} = 2 \) is \( \cos y = \)
For a positive real number \( \lambda \), if the vector \( \vec{a} = \lambda \vec{i} - 5\vec{j} + 6\vec{k} \) satisfies the equation \[ \left[ \vec{i} \times (\vec{a} \times \vec{i}) + \vec{j} \times (\vec{a} \times \vec{j}) + \vec{k} \times (\vec{a} \times \vec{k}) \right]^2 = 440, \] then \( \lambda = \)
From a collection of eight cards numbered 1 to 8, if two cards are drawn at random, one after the other with replacement, then the probability that the product of numbers that appear on the cards is a perfect square is:
If the numerically greatest term in the expansion of \( (2 - 3x)^9 \) when \( x = 1 \) is \( P_1^q P_2^r P_3^s P_4^t \) (where \( P_1 < P_2 < P_3 < P_4 \) are the first four prime numbers), then \( \alpha + \beta + \gamma + \delta = \):