List of top Mathematics Questions asked in AP EAPCET

The general solution of \( \frac{dy}{dx} = \cos^2(x - y - 1) \) is given by \( x = \):
If \[ S = 2x^2 + 2y^2 - 8x + 8y - 7 = 0 \] is the circle passing through the points of intersection of the circles \[ x^2 + y^2 - kx - ky + 1 = 0 \quad \text{and} \quad x^2 + y^2 - kx + ky - 2 = 0, \] then the length of the tangent drawn from the point \( (k, k) \) to the circle \( S \) is:
Let \( a, b, c, d \) be non-zero numbers. If the point of intersection of the lines \( 4ax + 2ay + c = 0 \) and \( 5bx + 2by + d = 0 \) lies in the fourth quadrant and is equidistant from the two coordinate axes, then the relationship between \( a, b, c, d \) 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
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
In \( \triangle ABC \), if \( \sin B = \sin C \) and \( 3 \cos B = 2 \cos C \), then \( \triangle ABC \) is:
If \( \cos\theta \), \( \sin\theta \), and \( \cot\theta \) are in geometric progression, then: \[ \sin^9\theta + \sin^6\theta + 3\sin^5\theta + \sin^3\theta + \sin^2\theta = \]
Let \( A(-1, 1, 2), B(1, 2, 3), C(1, 1, 6) \) be three points. If \( l_1, m_1, n_1 \) are the direction cosines of \( AB \) and \( l_2, m_2, n_2 \) are the direction cosines of \( AC \), then \( |l_1 l_2 + m_1 m_2 + n_1 n_2| = \)
If the lines joining the origin to the points of intersection of $ 2x + 3y = k $ and $ 3x^2 - xy + 3y^2 + 2x - 3y - 4 = 0 $ are at right angles, then:
\(f(x)\) 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 coefficient of \( x^2 \) in the expansion of \( (1 - 3x)^{\frac{1}{3}} (1 + 2x)^{\frac{1}{2}} \) is:
The modulus of the conjugate of \( z = \frac{-2 + i}{(1 - 2i)^2} \) 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 \( \overline{\mathbf{a}} = 2\overline{\mathbf{i}} + 3\overline{\mathbf{j}} + 4\overline{\mathbf{k}} \), \( \overline{\mathbf{b}} = 3\overline{\mathbf{i}} + 4\overline{\mathbf{k}} \), 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
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 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 \( \alpha \) 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 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
If eight coins are tossed simultaneously, then the probability of getting at least six heads is:
If the number of diagonals of a regular polygon of \( n \) sides is 104, then \( n = \)
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 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 there exists a \( k^{th} \) order non-singular sub-matrix in a matrix \( P \) of order \( m \times n \), then the rank \( (\rho) \) of \( P \)