List of top Questions asked in AP EAPCET

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 \( x = \dots \)

If \( f(x) \) is defined as follows:

\[ f(x) = \begin{cases} \frac{x - \lfloor x \rfloor}{x - 2} & \text{if } x = 2 \\ \frac{|x - \lfloor x \rfloor|}{a^2 + (x - \lfloor x \rfloor)^2} & \text{if } 1 < x < 2 \\ 2a - b & \text{if } x = 1 \end{cases} \]

Then the limit \( \displaystyle \lim_{x \to 0} \frac{\sin(ax) + x \tan(bx)}{x^2} \) is:

Let \( [x] \) represent the greatest integer not more than \( x \). The discontinuous points of the function \[ f(x) = \frac{5 + [x]}{\sqrt{11 + [x]} - 6x + 2 + [x]} \] lie in the interval:

If \( x^x y^y = e^e \), then \( \left( \frac{d^2 y}{dx^2} \right)_{(e, e)} = \):

If \( f(x) = |x - 5| + |x + 5| + |x - 4| + |x + 4| \), then \[ \frac{f'(1) - f'(-6)}{f'(1) + f'(-6)} \]

If \( f(x + ay) + g(x - ay) = 0 \), then \( \frac{dy}{dx} = \):

If the angle between the curves \( y = e^{(x+4)} \) and \( x^2 y = 1 \) at the point \( (1, 1) \) is \( \theta \), then \[ \sin \theta + \cos \theta = \dots \]

If a line is moving between the coordinate axes such that the sum of the intercepts made by it on the coordinate axes is always 12, then the equation of that line which forms a triangle of maximum area with the coordinate axes is:

If the points of contact of the tangents drawn from \( (0,0) \) to the curve \( y = x^2 + 3x + 4 \) are \( (\alpha, \beta) \) and \( (\gamma, \delta) \), then \( \beta + \delta = \):