List of top Mathematics Questions asked in AP EAPCET

\(\int (\sqrt{\tan x} + \sqrt{\cot x}) \, dx =\)
\(\int \frac{\sqrt{x - 2}}{2x + 4} \, dx =\)
\(\int \frac{x}{\sqrt{x^2 - 2x + 5}} \, dx =\)
If the surface area of a spherical bubble is increasing at the rate of 4 sq.cm/sec, then the rate of change in its volume (in cubic cm/sec) when its radius is 8 cms is
\(\lim_{x \to 0} \frac{x \tan 2x - 2x \tan x}{(1 - \cos 2x)^2} =\)
If \( f(x) = \begin{cases} \frac{(e^x - 1) \log(1 + x)}{x^2} & \text{if } x>0 \\ 1 & \text{if } x = 0 \\ \frac{\cos 4x - \cos bx}{\tan^2 x} & \text{if } x<0 \end{cases} \) is continuous at \( x = 0 \), then \(\sqrt{b^2 - a^2} =\)
The locus of a point at which the line joining the points (-3, 1, 2), (1, -2, 4) subtends a right angle, is
Let A = (2, 0, -1), B = (1, -2, 0), C = (1, 2, -1), and D = (0, -1, -2) be four points. If \(\theta\) is the acute angle between the plane determined by A, B, C and the plane determined by A, C, D, then \(\tan\theta =\)
If \( 3\sqrt{2}x - 4y = 12 \) is a tangent to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and \(\frac{5}{4}\) is its eccentricity, then \( a^2 - b^2 = \)
Let \([x]\) represent the greatest integer function. If \(\lim_{x \to 0^+} \frac{\cos[x] - \cos(kx - [x])}{x^2} = 5\), then \(k =\)
If A(1, 2, 3), B(2, 3, -1), C(3, -1, -2) are the vertices of a triangle ABC, then the direction ratios of the bisector of $\angle$ABC are
If the equation of the circle passing through the point $(8, 8)$ and having the lines $x + 2y - 2 = 0$ and $2x + 3y - 1 = 0$ as its diameters is $x^2 + y^2 + px + qy + r = 0$, then $p^2 + q^2 + r =$
Tangents are drawn at three points P($t_1$), Q($t_2$), R($t_3$) on the parabola $y^2 = x$. Let these tangents intersect each other at the points L, M, N. If $t_1 = 2$, $t_2 = -4$, $t_3 = 6$, then the area of the triangle LMN is
$3x+4y-43=0$ is a tangent to the circle $S = x^2+y^2-6x+8y+k=0$ at a point P. If C is the center of the circle and Q is a point which divides CP in the ratio -1:2, then the power of the point Q with respect to the circle S=0 is
If $2x - 3y + 1 = 0$ is the equation of the polar of a point $P(x_1, y_1)$ with respect to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$, then $3x_1 - y_1 =$
If a unit circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$ touches the circle $S' = x^2 + y^2 - 6x + 6y + 2 = 0$ externally at the point $(-1, -3)$, then $g + f + c =$
If the angle between the pair of lines $2x^2 + 2hxy + 2y^2 - x + y - 1 = 0$ is $\tan^{-1}\left(\frac{3}{4}\right)$ and $h$ is a positive rational number, then the point of intersection of these two lines is
If the radical axis of the circles $x^2+y^2+2gx+2fy+c=0$ and $2x^2 + 2y^2 + 3x + 8y + 2c = 0$ touches the circle $x^2 + y^2 + 2x + 2y + 1 = 0$, then
If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2) =$
If the pair of lines $ax^2 - 7xy - 3y^2 = 0$ and $2x^2 + xy - 6y^2 = 0$ have exactly one line in common and '$a$' is an integer, then the equation of the pair of bisectors of the angles between the lines $ax^2 - 7xy - 3y^2 = 0$ is
A($a$, 0) is a fixed point, and $\theta$ is a parameter such that $0<\theta<2\pi$. If P($a \cos \theta$, $a \sin \theta$) is a point on the circle $x^2 + y^2 = a^2$ and Q($b \sin \theta$, $-b \cos \theta$) is a point on the circle $x^2 + y^2 = b^2$, then the locus of the centroid of the triangle APQ is
The point P(4, 1) undergoes the following transformations in succession: (i) origin is shifted to the point (1, 6) by translation of axes, (ii) translation through a distance of 2 units along the positive direction of the x-axis, (iii) rotation of axes through an angle of $90^\circ$ in the positive direction. Then the coordinates of the point P in its final position are
If $(h, k)$ is the image of the point $(2, -3)$ with respect to the line $5x - 3y = 2$, then $h + k =$
Let $\mathbf{a} = 4\mathbf{i} + 3\mathbf{j}$ and $\mathbf{b}$ be two perpendicular vectors in the XOY-plane. A vector $\mathbf{c}$ in the same plane and having projections 1 and 2 respectively on $\mathbf{a}$ and $\mathbf{b}$ is
In a school there are 3 sections A, B, and C. Section A contains 20 girls and 30 boys, section B contains 40 girls and 20 boys, and section C contains 10 girls and 30 boys. The probabilities of selecting section A, B, and C are 0.2, 0.3, and 0.5, respectively. If a student selected at random from the school is a girl, then the probability that she belongs to section A is