List of top Questions asked in AP EAPCET

If one root of the equation \( ax^2 + bx + c = 0 \) is twice another root, then the equation \( ax^2 + bx + c = 0 \) is:

If \( -1 \) is a twice repeated root of the equation \( ax^3 + bx^2 + cx + 1 = 0 \), then \( ax^3 + bx^2 + cx + 1 = 0 \) represents:

If \( C_j = \binom{n}{j} \), then \( C_0 C_t + C_1 C_{t+1} + C_2 C_{t+2} + \dots + C_n = \)

The coefficient of the highest power of \( x \) in the expansion of \[ \left( x + \sqrt{x^2 - 1} \right)^3 + \left( x - \sqrt{x^2 - 1} \right)^8 \text{ is:} \]

The number of non-negative integral solutions of \( x_1 + x_2 + x_3 + x_4 = 10 \) is:

If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), where \( a, b, c, d \in \{-1, 1\} \), then the number of singular matrices in \( A \) is:

If \( \cot x \cot y = a \) and \( x + y = \frac{\pi}{6} \), then the quadratic equation satisfying \( \cot x \) and \( \cot y \) is:

If \( \tan A + \tan B = x \) and \( \cot A + \cot B = y \), then \( \tan(A + B) = \)

If \( \triangle ABC \) is a right-angled isosceles triangle and \( \angle C = 90^\circ \), then \( r = \frac{1}{5} \) is:

If \( 7i - 4j - 5k \) is the position vector of vertex A of a tetrahedron ABCD and \( -i + 4j - 3k \) is the position vector of the centroid of the triangle BCD, then the position vector of the centroid of the tetrahedron ABCD is:

Let \( \mathbf{OA = i + 2j - 2k} \) and \( \mathbf{OB = -2i - 3j + 6k} \) be the position vectors of two points A and B. If C is a point on the bisector of \( \angle AOB \) and \( OC = \frac{\sqrt{42}}{2} \), then \( OC = \)

The distance of a point \( \vec{a} \) from the plane \( r \cdot m = q \) is given by \( \frac{| \vec{a} \cdot m - q |}{|m|} \). If the distance of the point \( i + 2j + 3k \) from the plane \( \vec{r} \cdot (2i + 6j - 9k) = -1 \) is \( p \) and the distance of the origin from this plane is \( q \), then \( p - q = \dots \)

Three screws are drawn at random from a lot of 50 screws containing 5 defective ones. Then the probability of the event that all 3 screws drawn are non-defective, assuming that the drawing is (a) with replacement (b) without replacement respectively is:

A coin is tossed three times. Let A be the event of "getting three heads" and B be the event of "getting a head on the first toss". Then A and B are:

The minimum number of times a fair coin needs to be tossed, so that the probability of getting at least two heads is at least 0.96 is:

If \( P(X = x) = k \left( \frac{3}{8} \right)^x \), where \( x = 1, 2, 3, \dots \) is the probability distribution function of a discrete random variable X, then \( k = \)

If \( A(4, 0) \) and \( B(-4, 0) \) are two points, then the locus of a point \( P \) such that \( PA - PB = 4 \) is:

The lines \( p(x^2 + 1) + x - y + q = 0 \) and \( (p^2 + 1)x^2 + (p^2 + 1)y + 2q = 0 \) are perpendicular to a line L. Then the equation of the line L is:

If \( 2x^2 - 3xy + y^2 = 0 \) represents two sides of a triangle and \( x + y - 1 = 0 \) is its third side, then the distance between the orthocenter and the circumcenter of that triangle is:

If \( S \) is the set of all real values of \( a \) such that a plane passing through the points \( (-a^2, 1, 1), (1, -a^2, 1), (1, 1, -a^2) \) also passes through the point \( (-1, -1, 1) \), then \( S = \dots \)

The distance between the centres of similitude of the circles \( x^2 + y^2 + 6x - 8y + 16 = 0 \) and \( x^2 + y^2 - 2x - 2y + 1 = 0 \) is:

Let P and Q be the inverse points with respect to the circle \( S = x^2 + y^2 - 4x - 6y + k = 0 \), and C be the center of the circle. If \( CP.CQ = 4 \), and \( P = (1, 2) \), then \( Q = (a, b) \) and \( 2a = \dots \)

The perpendicular distance from the origin to the focal chord drawn through the point \( (4, 5) \) to the parabola \( y^2 - 4y - 3x + 7 = 0 \) is:

If \( S = \frac{x^2}{k - 7} - \frac{y^2}{11 - k} = 0, k \in \mathbb{R}, k \neq 7,11 \), then which one of the following statements is incorrect?

The function \( f(x) = \frac{\sqrt{3x^2 - 5x - 2}}{2x^2 - 7x + 5} \) has discontinuous points at \( x = \dots \)