List of top Mathematics Questions asked in AP EAPCET

If P\(\left(\frac{\pi}{4}\right)\) and Q\(\left(\frac{3\pi}{4}\right)\) are two points on the hyperbola $4x^2-y^2-8x-2y-13=0$ in parametric form, then the distance between P and Q is:
If the point $(1, 1)$ and the origin lie in the same region with respect to the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{1} = 1$ $(a>0)$, then the range of $a$ is:
Let \([t]\) represent the greatest integer not exceeding \( t \) and \( C = 1 - 2e^2 \).
If the function \[ f(x) = \begin{cases} [e^x], & x < 0 \\ ae^x + [x - 2], & 0 \leq x < 2 \\ [e^x] - C, & x \geq 2 \end{cases} \] is continuous at \(x = 2\), then \(f(x)\) is discontinuous at:
An equation of a plane parallel to the plane \( x - 2y + 2z - 5 = 0 \) and which is at one unit distance from the origin is:
A circle S touches the Y-axis at \( (0, 3) \) and makes an intercept of length 8 units on the X-axis. If the center C of the circle S lies in the second quadrant, then the distance of C from the point \( (-2, -1) \) is:
If the angle between the circles \( x^2 + y^2 + 2x - 4y + 1 = 0 \) and \( x^2 + y^2 - 4x - 2y + c = 0 \) is \( \frac{\pi}{4} \), then \( c \) is:
Let a focal chord \( 12x + 5y - 27 = 0 \) of the parabola \( y^2 = kx \) intersect the parabola at points \( P \) and \( P' \). If \( S \) is the focus of the parabola, then \( 9(SP + SP') \) = ?
The polar of a point with respect to the circle \( x^2 + y^2 - 10x + 12y - 3 = 0 \), which is not a tangent and not a chord of contact, is:
If the equation of the circle of radius 3 units which touches the circle \( x^2 + y^2 + 6x - 8y - 11 = 0 \) externally at (3, 0) is \( x^2 + y^2 + 2gx + 2fy + c = 0 \), then \( 3g - 4f + c = \):
Tangent \( L_1 = 3x - 4y - 8 = 0 \) and the chord \( L_2 = x + y - 1 = 0 \) are at a distance of 2 and \( \sqrt{2} \) units respectively from the centre of a circle \( S \). \((h, k)\) is the centre of \( S \) such that \( h^2 + k^2 = 13 \). If the midpoint of the chord \( L_2 = 0 \) is \( (\alpha, \beta) \) and the radius of the circle is \( r \), then \( \alpha + \beta + r = \):
If ad ≠ 0 and two of the lines represented by \( ax^3 + 3bx^2y + 3cxy^2 + dy^3 = 0 \) are perpendicular, then:
The absolute value of the tangent of the difference of the angles made by the lines \( 4x^2 - 24xy + 11y^2 = 0 \) with the X-axis is:
If the extremities of a diagonal of a square are \( (1, -2, 3) \) and \( (2, -3, 5) \), then the length of its side is:
Coordinate planes and the planes \( \pi_1, \pi_2, \pi_3 \), which are respectively parallel to YZ, ZX, XY planes at distances a, b, c, form a rectangular parallelepiped. If \( d_1 \) is a diagonal of the face on XY-plane not passing through origin and \( d_2 \) is diagonal of plane \( \pi_2 \), then the cosine of the angle between \( d_1 \) and \( d_2 \) is:
If p and q are the x and y intercepts respectively of the line passing through the points \( (a \cos \alpha, b \sin \alpha) \) and \( (a \cos \beta, b \sin \beta) \), then:
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:
If the y-intercept of the perpendicular bisector of the line segment joining P(1,4) and Q(k,3) is -4, then a possible value of k is:
If the mean and variance of a binomial variable X are 2.4 and 1.44 respectively, then the parameters \( n \) and \( p \) are respectively:
If a Bernoulli trial is conducted n times, then which one of the following is not suitable to use Poisson distribution?
If \( S \) is the sample space of a random experiment \( \xi \) and \( P \) is a probability function defined on the power set \( P(S) \) of \( S \), then which one of the following is not satisfied by \( P \)?
If A and B simultaneously toss one coin each every time, each 50 times, then the probability of not getting a tail on both the coins is:
A pair of dice is thrown. Then the probability that either of the dice shows 2 when their sum is 6 is:
If A and B are any two events of a sample space, then set-theoretic description for the event "Exactly one of the events A, B to occur" is:
The locus of the point which is equidistant from the point \( (1, 1) \) and the line \( x + y + 1 = 0 \) is:
If each of the observations \( x_1, x_2, \dots, x_n \) is increased or decreased by \( k \), where \( k \) is a positive number, then the variance of the data thus obtained: