List of top Questions asked in TS EAMCET

Two capacitors of capacitances $ 1\mu F $ and $ 2\mu F $ can separately withstand potentials of $ 6 $ kV and $ 4 $ kV respectively. The total potential, they together can withstand when they are connected in series is:

A constant force of \[ \mathbf{F} = (8\hat{i} - 2\hat{j} + 6\hat{k}) \text{ N} \] acts on a body of mass 2 kg, displacing it from \[ \mathbf{r_1} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ m to } \mathbf{r_2} = (4\hat{i} - 3\hat{j} + 6\hat{k}) \text{ m}. \] The work done in the process is:

If the excess pressures inside two soap bubbles are in the ratio $ 2:3 $, then the ratio of the volumes of the soap bubbles is:

The electric flux due to an electric field \[ \vec{E} = (8\hat{i} + 13\hat{j}) \text{ NC}^{-1} \] through an area 3 m$^2$ lying in the XZ plane is:

A voltmeter of resistance $400 \, \Omega$ is used to measure the emf of a cell with an internal resistance of $4 \, \Omega$. The error in the measurement of emf of the cell is:

Four bodies of masses 8 kg, 2 kg, 4 kg and 2 kg are placed at the four corners A, B, C and D respectively of a square ABCD of diagonal 80 cm. The distance of the center of mass of the system from the corner A is:

A copper wire of cross-sectional area 0.01 cm$^2$ is subjected to a tension of 22 N. If Young’s modulus and Poisson’s ratio of copper are $1.1 \times 10^{11}$ Nm$^2$ and 0.32 respectively, then the change in the cross-sectional area of the wire is:

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

$$ x^5 + 4x^4 - 13x^3 - 52x^2 + 36x + 144 = 0 $$

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with the name of his own wife is ?

A plane $ (\pi) $ passing through the point $ (1,2,-3) $ is perpendicular to the planes $ x + y - z + 4 = 0 $ and $ 2x - y + z + 1 = 0 $. If the equation of the plane $ (\pi) $ is $ ax + by + cz + 1 = 0 $, then $ a^2 + b^2 + c^2 $ is equal to:

If $ \theta $ is the acute angle between the curves $ y^2 = x $ and $ x^2 + y^2 = 2 $, then $ \tan \theta $ is:

If the real-valued function

\[ f(x) = \sin^{-1}(x^2 - 1) - 3\log_3(3^x - 2) \]

is not defined for all $ x \in (-\infty, a] \cup (b, \infty) $, then what is $ 3^a + b^2 $?

The length of the latus rectum of the ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ $ (a>b) $ is $ \frac{8}{3} $. If the distance from the center of the ellipse to its focus is $ \sqrt{5} $, then $ \sqrt{a^2 + 6ab + b^2} = \text{?} $

The slope of the tangent drawn from the point $ (1,1) $ to the hyperbola $ 2x^2 - y^2 = 4 $ is:

If $ y = a \cos 3x + b e^{-x} $, then $ y'(3\sin 3x - \cos 3x) = $:

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

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

is:

In a triangle $ABC$, if