List of top Questions asked in TS EAMCET

The sum of all the 4-digit numbers formed by taking all the digits from 0, 3, 6, 9 without repetition is:

If the slope of the tangent drawn at any point $(x, y)$ on the curve $y = f(x)$ is $y = 6x^2 + 10x - 9$ and $f(2) = 0$, then $f(-2) = $?

The tension applied to a metal wire of one metre length produces an elastic strain of 1%. The density of the metal is $ 8000 \, kg/m^3 $ and Young's modulus of the metal is $ 2 \times 10^{11} \, Nm^{-2} $. The fundamental frequency of the transverse waves in the metal wire is:

If the period of the function \[ f(x) = 2\cos(3x+4) - 3\tan(2x-3) + 5\sin(5x) - 7 \] is $ k $, then $ f(x) $ is periodic with fundamental period $ k $. Find $ k $.

If $ \sqrt{5} - i\sqrt{15} = r(\cos\theta + i\sin\theta), -\pi < \theta < \pi, $ then

\[ r^2(\sec\theta + 3\csc^2\theta) = \]

The sphere A of mass $ m $ moving with a constant velocity hits another sphere B of mass $ 2m $ at rest. If the coefficient of restitution is 0.4, the ratio of the velocities of the spheres A and B after collision is

If \[ f(x) = 3x^{15} - 5x^{10} + 7x^5 + 50\cos(x - 1), \] then \[ \lim_{h \to 0} \frac{f(1 - h) - f(1)}{h^2 + 3h} \] is:

Identify the wrong statement of the following:

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

In the contact process of manufacturing $\text{H}_2\text{SO}_4$, the arsenic purifier used in the industrial plant contains:

When $ |x| < 2 $, the coefficient of $ x^2 $ in the power series expansion of

\[ \frac{x}{(x-2)(x-3)} \]

is:

By shifting the origin to the point $ (h,5) $ by the translation of coordinate axes, if the equation \[ y = x^2 - 9x^2 + cx - d \] transforms to $ Y = X^2 $, then $ \left( \frac{d - c}{h} \right) $ is: \

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

The equation of the circle passing through the origin and cutting the circles $x^2 + y^2 + 6x - 15 = 0$ and $x^2 + y^2 - 8y - 10 = 0$ orthogonally is:

Identify the number of molecules having permanent dipole moment from the following: $$ CCl_4, NF_3, H_2S, HBr, SF_4, SiF_4, XeF_4, BeCl_2, SnCl_2, BrF_5, SO_2 $$

If two electromagnetic waves with electric fields given by $$ \vec{E_1} = E_0 \sin (kx - \omega t) \hat{j} $$ and $$ \vec{E_2} = E_0 \sin (kx - \omega t + \pi) \hat{j} $$ - interfere, then the peak value of the electric field of the resultant wave is

If the tangent drawn at a point $P(t)$ on the hyperbola $$ x^2 - y^2 = c^2 $$ cuts the X-axis at $T$ and the normal drawn at the same point $P$ cuts the Y-axis at $N$, then the equation of the locus of the midpoint of $TN$ is:

A hydrocarbon containing C and H has 92.3\% of C. When 52 g of hydrocarbon is completely burnt in oxygen, $ x $ moles of water and $ y $ moles of CO$_2$ were formed. The liberated water is sufficient to liberate one mole of H$_2$ when reacted with sodium metal. What is the weight (in g) of O$_2$ consumed?

The maximum interval in which the slopes of the tangents drawn to the curve \[ y = x^4 + 5x^3 + 9x^2 + 6x + 2 \] increase is:

If the extremities of the latus recta having positive ordinate of the ellipse $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a > b) $$ lie on the parabola $$ x^2 + 2ay - 4 = 0, $$ then the points $(a, b)$ lie on the curve:

If $$ \int \frac{1}{x^4 + 8x^2 + 9} \, dx = \frac{1}{k} \left[ \frac{1}{\sqrt{14}} \tan^{-1} (f(x)) - \frac{1}{\sqrt{2}} \tan^{-1} (g(x)) \right] + c, $$ then $$ \frac{k}{\sqrt{2}} + f(\sqrt{3}) + g(1) = $$

The domain of the real-valued function $$ f(x) = \sin^{-1} \left( \log_2 \left( \frac{x^2}{2} \right) \right) $$ is:

If the function

$ f(x) = \begin{cases} \frac{\cos ax - \cos 9x}{x^2}, & \text{if } x \neq 0 \\ 16, & \text{if } x = 0 \end{cases} $

is continuous at $ x = 0 $, then $ a = ? $

Ategmic, Unitegmic, and Bitegmic ovules are present serially in: