List of top Questions asked in TS EAMCET

A circle passes through the points $(2, 0)$ and $(1, 2)$ . If the power of the point $(0, 2)$ with respect to this circle is 4, then the radius of the circle is

If the angle between the pair of lines given by the equation $ax^2 + 4xy + 2y^2 = 0$ is $45^\circ$ , then the possible values of 'a' are

The line $x + y + 1 = 0$ intersects the circle $x^2 + y^2 - 4x + 2y - 4 = 0$ at the points A and B. If $M(a, b)$ is the midpoint of AB, then $a - b =$ ?

A circle $S$ passes through the points of intersection of the circles $x^2 + y^2 - 2x - 3 = 0$ and $x^2 + y^2 - 2y = 0$ . If $x + y + 1 = 0$ is a tangent to the circle $S$ , then the equation of $S$ is:

If the common chord of the circles $x^2 + y^2 - 2x + 2y + 1 = 0$ and $x^2 + y^2 - 2x - 2y - 2 = 0$ is the diameter of a circle $S$ , then the centre of the circle $S$ is:

If $(1,1)$ is the vertex and $x + y + 1 = 0$ is the directrix of a parabola. If $(a, b)$ is its focus and $(c, d)$ is the point of intersection of the directrix and the axis of the parabola, then $a + b + c + d$ is:

The axis of a parabola is parallel to Y-axis. If this parabola passes through the points $(1,0), (0,2), (-1,-1)$ and its equation is $ax^2 + bx + cy + d = 0$ , then $\frac{ad}{bc}$ is:

If the focus of an ellipse is $(-1,-1)$ , equation of its directrix corresponding to this focus is $x + y + 1 = 0$ and its eccentricity is $\frac{1}{\sqrt{2}}$ , then the length of its major axis is:

If the normal drawn at the point $(2, -1)$ to the ellipse $x^2 + 4y^2 = 8$ meets the ellipse again at $(a, b)$ , then $17a$ is:

If $A(-2,4,a)$ , $B(1,3,b)$ , $C(0,4,c)$ , and $D(-5,6,1)$ are collinear points, then $a+b+c=$

A(1, -2, 1) and B(2, -1, 2) are the end points of a line segment. If $D(\alpha, \beta, \gamma)$ is the foot of the perpendicular drawn from $C(1, 2, 3)$ to AB, then $\alpha^2 + \beta^2 + \gamma^2 =$

$\lim_{x \to -\frac{3}{2}} \frac{(4x^2 - 6x)(4x^2 + 6x + 9)}{\sqrt{2x - \sqrt{3}}}$

$f(x) = \begin{cases} \frac{(4^x - 1)^4 \cot(x \log 4)}{\sin(x \log 4) \log(1 + x^2 \log 4)}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}$

Find $e^k$ if $f(x)$ is continuous at $x = 0$ .

A function $f : \mathbb{R} \rightarrow \mathbb{R}$ is such that $yf(x+y) + \cos mxy = 1 + yf(x)$ . If $m = 2$ , find $f'(x)$ .

$y = \sqrt{\sin(\log(2x)) + \sqrt{\sin(\log(2x)) + \sqrt{\sin(\log(2x))} + \dots \infty}}$

Find $\frac{dy}{dx}$ for the given function:

$y = \tan^{-1} \left( \frac{\sin^3(2x) - 3x^2 \sin(2x)}{3x \sin(2x) - x^3} \right).$

For a given function $y = f(x)$ , $\delta y$ denotes the actual error in $y$ corresponding to actual error $\delta x$ in $x$ and $dy$ denotes the approximate value of $\delta y$ . If $y = f(x) = 2x^2 - 3x + 4$ and $\delta x = 0.02$ , then the value of $\delta y - dy$ when $x = 5$ is: \vspace{0.5cm}

The length of the normal drawn at $t = \frac{\pi}{4}$ on the curve $x = 2(\cos 2t + t \sin 2t)$ , $y = 4(\sin 2t + t \cos 2t)$ is:

If water is poured into a cylindrical tank of radius 3.5 ft at the rate of 1 cubic ft/min, then the rate at which the level of the water in the tank increases (in ft/min) is:

The function $y = 2x^3 - 8x^2 + 10x - 4$ is defined on $[1,2]$ . If the tangent drawn at a point $(a,b)$ on the graph of this function is parallel to the X-axis and $a \in (1,2)$ , then $a =$ ?

If $m$ and $M$ are respectively the absolute minimum and absolute maximum values of a function $f(x) = 2x^3 + 9x^2 + 12x + 1$ defined on $[-3,0]$ , then $m + M$ is:

Evaluate the integral: $\int \frac{\sec x}{3(\sec x + \tan x) + 2} \,dx$

Evaluate the integral: $\int \frac{dx}{4 + 3\cot x}$

Evaluate the integral: $\int \frac{dx}{(x+1)\sqrt{x^2 + 4}}$

Evaluate the integral: $\int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{dx}{\sec^2 x + (\tan^{2022} x - 1)(\sec^2 x - 1)}$