List of top Questions asked in AP EAPCET

The number of solutions of the equation $\sqrt{3x^2 + x + 5} = x - 3$ is
If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1 + x)^n$, then find \[ \frac{P_{n+1}}{P_n}. \]
The equation \[ x^{\frac{3}{4}(\log_{x} x)^2 + \log_{x} x^{-\frac{5}{4}}} = \sqrt{2} \] has
From a point \( P(-4, 0) \), two tangents are drawn to the circle \( x^2+y^2-4x-6y-12=0 \) touching the circle at \( A \) and \( B \). If the equation of the circle passing through \( P, A, B \) is \( x^2+y^2+2gx+2fy+c=0 \), then \( (g,f) = \):
After the roots of the equation $6x^3 + 7x^2 - 4x - 2 = 0$ are diminished by $h$, if the transformed equation does not contain $x$ term, then the product of all possible values of $h$ is
An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3. The device gives an accurate result in 8 out of 10 such tests. If the device reports that an item tested is not defective, then the probability that it is actually defective is
If the probability distribution of a discrete random variable X is given by \( P(X=k) = \frac{2^{-k(3k+1)}{2^c} \), k = 0, 1, 2, ..., \( \infty \) then P(X \( \le \) c) = } (The expression seems to be \( \frac{2^{-k}(3k+1)}{K} \) where K is a constant, or \(2^c\) is part of the constant. Assuming \(2^c\) is the normalization constant \(K\).)
Let \(z_1 = 3 + 4i\) and \(z_2 = 1 - 2i\). Then the argument of \(\frac{z_1}{z_2}\) is:
If \( A \) and \( B \) are both \( 3 \times 3 \) matrices, then which of the following statements are true? \[ \begin{cases}
Lines \(L_1\) and \(L_2\) have slopes 2 and \(-\frac{1}{2}\) respectively. If both \(L_1\) and \(L_2\) are concurrent with the lines \(x - y + 2 = 0\) and \(2x + y + 3 = 0\), then the sum of the absolute values of the intercepts made by the lines \(L_1\) and \(L_2\) on the coordinate axes is?
If \( y = \tanh^{-1} \left( \dfrac{1 - x}{1 + x} \right) \), then \( \dfrac{dy}{dx} = \)
The general solution of the differential equation \(\frac{dy}{dx} = \frac{x + y + 1}{x - 3y + 5}\) is
If \( \alpha, \beta, \gamma \) are the roots of the equation \( x^3 + ax^2 + bx + c = 0 \), then \( (\alpha + \beta - 2\gamma)(\beta + \gamma - 2\alpha)(\gamma + \alpha - 2\beta) = \)
Let 'a' be a non-zero real number. If the equation whose roots are the squares of the roots of the cubic equation \( x^3 - ax^2 + ax - 1 = 0 \) is identical with this cubic equation, then 'a' =
The point in the \(xy\)-plane which is equidistant from the points \(A(2,0,3), B(0,3,2)\) and \(C(0,0,1)\) has the coordinates?
On a line with direction cosines l, m, n, \( A(x_1, y_1, z_1) \) is a fixed point. If \( B=(x_1+4kl, y_1+4km, z_1+4kn) \) and \( C=(x_1+kl, y_1+km, z_1+kn) \) (\(k>0\)) then the ratio in which the point B divides the line segment joining A and C is
In a \( \triangle ABC \), \( A - B = 120^\circ \), \( R = 8r \), then \[ \frac{1 + \cos C}{1 - \cos C} =\ ? \]
If \( z_1 \) and \( z_2 \) are two of the \( n^{th} \) roots of unity such that the line segment joining them subtends a right angle at the origin, then for a positive integer \( k \), \( n \) takes the form:
If \( \frac{1}{2} \sin^{-1} \left( \frac{3\sin 2\theta}{5+4\cos 2\theta} \right) = \tan^{-1 x \) then \( x = \)}
If $$ y = A t^2 + \frac{B}{t} \quad (A, B \text{ constants}) $$ is a general solution of the differential equation $$ f(t) y'' + g(t) y' + h(t) y = 0, $$ then find the relation between $ g(t), f(t), h(t) $.
If the line $$ 4x - 3y + 7 = 0 $$ touches the circle $$ x^2 + y^2 - 6x + 4y - 12 = 0 $$ at $ (\alpha, \beta) $, then find $ \alpha + 2\beta $.
If the straight line \[ 2x + 3y + 1 = 0 \] bisects the angle between two other straight lines, one of which is \[ 3x + 2y + 4 = 0, \] then the equation of the other straight line is:
In \(\triangle ABC\), if \(a = 2\), \(b = 3\), and \(\angle C = 60^\circ\), then the value of \(c^{2}\) is:
If \( (2k - 1)x^2 - 2(3k - 2)x + 4k>0 \) for every \( x \in \mathbb{R} \), then the sum of all possible integral values of \( k \) is:
Evaluate \[ \lim_{n \to \infty} \frac{1}{2n} \left( \sin \frac{\pi}{2n} + \sin \frac{\pi}{n} + \sin \frac{2\pi}{2n} + \dots \right) = ? \]