List of top Questions asked in TS EAMCET

A 60 kg man standing on a bridge, jumps vertically down onto a 540 kg boat moving in the river below him with a speed of 10 m/s. The change in the speed of the boat is:

Evaluate the limit: \[ \lim_{\theta \to \frac{\pi}{2}} \frac{8\tan^4\theta + 4\tan^2\theta + 5}{(3 - 2\tan\theta)^4} \]

The number of solutions of the equation \[ \sin 7\theta - \sin 3\theta = \sin 4\theta \] that lie in the interval $ (0, \pi) $ is:

Given two planes with equations $ \mathbf{r} \cdot (\mathbf{i} - \mathbf{j} + \mathbf{k}) = 5 $ and $ \mathbf{r} \cdot (2\mathbf{i} + \mathbf{j} - \mathbf{k}) = 3 $. A plane $ \pi $ passing through the line of intersection of these two planes also passes through the point (0,1,2). If the equation of $ \pi $ is $ \mathbf{r} \cdot (a\mathbf{i} + b\mathbf{j} + c\mathbf{k}) = m $, determine the value of $ \frac{bc}{a^2} $:

Let $ \bar{a}, \bar{b}, \bar{c} $ be three vectors each having $ \sqrt{2} $ magnitude such that

\[ (\bar{a}, \bar{b}) = (\bar{b}, \bar{c}) = (\bar{c}, \bar{a}) = \frac{\pi}{3}. \]

If

\[ \bar{x} = \bar{a} \times (\bar{b} \times \bar{c}) \quad \text{and} \quad \bar{y} = \bar{b} \times (\bar{c} \times \bar{a}), \]

then:

$ \vec{a}, \vec{b}, \vec{c} $ are three vectors such that $|\vec{a}| = 3$, $|\vec{b}| = 2\sqrt{2}$, $|\vec{c}| = 5$, and $ \vec{c} $ is perpendicular to the plane of $ \vec{a} $ and $ \vec{b} $.

If the angle between the vectors $ \vec{a} $ and $ \vec{b} $ is $ \frac{\pi}{4} $, then

\[ |\vec{a} + \vec{b} + \vec{c}| = \ ? \]

If $ x = \cos 2t + \log (\tan t) $ and $ y = 2t + \cot 2t $, then $ \frac{dy}{dx} $ is:

If the inverse point of the point $P(3,3)$ with respect to the circle $x^2 + y^2 - 4x + 4y + 4 = 0$ is $Q(a,b)$, then $a + 5b =$

If on average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in a specific hour is:

Given $ \cos B - \sin A = \frac{\sqrt{3}+1}{4\sqrt{2}} $ and $ 2 \cos A \cos B = \frac{1+\sqrt{2}+\sqrt{3}}{2\sqrt{2}} $, calculate $ \cos^2 \frac{4B}{3} - \sin^2 \frac{4A}{5} $:

When the origin is shifted to the point $ (2,b) $ by translation of axes, the coordinates of the point $ (4,4) $ have changed to $ (6,8) $. When the origin is shifted to $ (a,b) $ by translation of axes, if the transformed equation of $ x^2 + 4xy + y^2 = 0 $ is $ X^2 + 2HXY + Y^2 + 2GX + 2FY + C = 0 $, then $ 2H(G + F) = $ ?

If $ y = \frac{\tan x \cos^{-1}x}{\sqrt{1 - x^2}} $, then the value of $ \frac{dy}{dx} $ when $ x = 0 $ is:

If $m\cos(\alpha + \beta) - n\cos(\alpha - \beta) = m\cos(\alpha - \beta) + n\cos(\alpha + \beta)$, then $\tan \alpha \tan \beta$ is:

The centroid of a variable triangle ABC is at the distance of 5 units from the origin. If A = (2,3) and B = (3,2), then the locus of C is:

If

\[ \cosh^{-1}\left(\frac{5}{3}\right) + \sinh^{-1}\left(\frac{3}{4}\right) = k, \]

then $ e^k $ is:

Arrange the following halides in decreasing order of their reactivity towards dehydrohalogenation:

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

The general solution of the differential equation $$ \frac{dy}{dx} = \frac{2y^2 + 1}{2y^3 - 4xy + y}. $$

The wavelength of an electron is $ 10^3 $ nm. What is its momentum in kg m s$^{-1}$?

A 31.4 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter of 2 cm. The pressure exerted by the heel on the horizontal floor is (Acceleration due to gravity = 10 m/s$^2$):

If $ 3^{2n+2} - 8n - 9 $ is divisible by $ 2^p $ $\forall n \in \mathbb{N}$, then the maximum value of $ p $ is

If $ \int x^3 \sin 3x \,dx = f(x) \cos 3x + g(x) \sin 3x + c $, then evaluate $ 27(f(x) + xg(x)) $:

A circle passing through the points $ (1, 1) $ and $ (2, 0) $ touches the line $ 3x - y - 1 = 0 $. If the equation of this circle is $ x^2 + y^2 + 2gx + 2fy + c = 0 $, then a possible value of $ g $ is

The approximate value of $ \sqrt[3]{730} $ obtained by the application of derivatives is:

Identify the wrong pair: