List of top Questions asked in AP EAPCET

If \( Q \) is the inverse point of the point \( P(2, 3) \) with respect to the circle \( x^2 + y^2 - 2x - 2y + 1 = 0 \), then the circle with \( PQ \) as diameter is
If a real valued function \( f \) is defined by \( f(x) = \frac{ax + \sqrt{a^2 - x^2}}{bx} \), then \( f \) is:
If \( \cos\theta \), \( \sin\theta \), and \( \cot\theta \) are in geometric progression, then: \[ \sin^9\theta + \sin^6\theta + 3\sin^5\theta + \sin^3\theta + \sin^2\theta = \]
In \( \triangle ABC \), if \( \sin B = \sin C \) and \( 3 \cos B = 2 \cos C \), then \( \triangle ABC \) is:
If \( C \) is a point on the straight line joining the points \( A = -2+i \) and \( B = 3 - 4i \) in the Argand plane and } \[ \frac{AC}{CB} = \frac{1}{2}, \] then the argument of \( C \) is
The number of words that can be formed using the letters of the word VOWEL such that vowels always remain together is:
If the roots of the equation \( 16x^3 - 44x^2 + 36x - 9 = 0 \) are in harmonic progression, then its greatest root is
\(f(x)\) is a continuous function on \(\mathbb{R}\) and \(y = f(x)\) is a curve. If \((\alpha, \beta)\) is a point such that \(\beta = f(\alpha)\) and \(p\alpha + m\beta + n = 0\ (p \ne 0, m \ne 0)\), then which one of the following is True?
The general solution of \( \frac{dy}{dx} = \cos^2(x - y - 1) \) is given by \( x = \):
The coefficient of \( x^2 \) in the expansion of \( (1 - 3x)^{\frac{1}{3}} (1 + 2x)^{\frac{1}{2}} \) is:
If a card is drawn at random from a well shuffled pack of playing cards, then the probability that it is either an Ace or a Spade card is
Let \( C \) be the centre and \( A \) be one end of a diameter of the circle \( x^2 + y^2 - 2x - 4y - 20 = 0 \). If \( P \) is a point on \( AC \) such that \( CP : PA = 2 : 3 \), then the locus of \( P \) is:
If the mid-point of the chord intercepted by the circle \(x^2 + y^2 - 8x + 10y + 5 = 0\) on the line \(2x + y + 2 = 0\) is \((h, k)\), then \(k + 4h =\) ?
If a line \( L \) makes angles \( \frac{\pi}{3} \) and \( \frac{\pi}{4} \) with the positive X-axis and positive Y-axis respectively, then the angle made by \( L \) with the positive direction of the Z-axis is:
If \( \overline{\mathbf{a}} = 2\overline{\mathbf{i}} + 3\overline{\mathbf{j}} + 4\overline{\mathbf{k}} \), \( \overline{\mathbf{b}} = 3\overline{\mathbf{i}} + 4\overline{\mathbf{k}} \), and \( \overline{\mathbf{c}} = 5\overline{\mathbf{i}} + 4\overline{\mathbf{k}} \) are three vectors, then a vector which is perpendicular to \( \overline{\mathbf{a}} \) and \( \overline{\mathbf{b}} \times \overline{\mathbf{c}} \) is
The modulus of the conjugate of \( z = \frac{-2 + i}{(1 - 2i)^2} \) is:
If the number of diagonals of a regular polygon of \( n \) sides is 104, then \( n = \)
If $X_1, X_2, ..., X_n$ are $n$ independent events such that $P(X_r) = \frac{1}{r+1}$, for $r=1, 2, ..., n$, then the probability that none of the $n$ events occur is
If eight coins are tossed simultaneously, then the probability of getting at least six heads is:
If \( \alpha \) and \( \beta \) are the roots of \( x^2 - ax - b = 0 \), and \( \alpha^2 + \beta^2 \) and \( \alpha^3 + \beta^3 \) are the roots of \( Ax^2 + Bx + C = 0 \), then \( C = \ldots \)
The minimum value of \( f(x) = \frac{x^2 - 2x + 3}{x^2 - 4x + 7} \) is:
If the circles $x^2+y^2 - 4x + 2fy + 1 = 0$ and $x^2+y^2 + 2gx - 4y - 1 = 0$ cut orthogonally, then $r_1^2 + r_2^2 - 8=$
If \( f(x) = \begin{cases} x^2, & 0 \le x<1 \\ \sqrt{x}, & 1 \le x \le 2 \end{cases} \), then \( \int_0^2 f(x) dx = \)
A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and the perpendicular drawn from the origin to this line makes an angle of 60° with the line \( x + y = 0 \). Then the equation of the line L is:
Let X-axis be the transverse axis and Y-axis be the conjugate axis of a hyperbola H. Let \( x^2 + y^2 = 16 \) be the director circle of H. If the perpendicular distance from the centre of H to its latus rectum is \( \sqrt{34} \), then \( a + b = \):