List of top Questions asked in AP EAMCET- 2024

If $ M_1 $ and $ M_2 $ are the maximum values of $ \frac{1}{11 \cos 2x + 60 \sin 2x + 69} $ and $ 3 \cos^2 5x + 4\sin^2 5x $ respectively, then $ \frac{M_1}{M_2} = $:

The mass % of urea solution is 6. The total weight of the solution is 1000 g. What is its concentration in mol L$^{-1}$? (Density of water = 1.0 g mL$^{-1}$)
(Given: C = 12u, N = 14u, O = 16u, H = 1u)

The gravitational potential energy of a body on the surface of the Earth is $E$. If the body is taken from the surface of the Earth to a height equal to $150%$ of the radius of the Earth, its gravitational potential energy is:

The mass of particle X is four times the mass of particle Y. The velocity of particle Y is four times the velocity of X. The ratio of de Broglie wavelengths of X and Y is:

The focal length of a thin converging lens in air is 20 cm. When the lens is immersed in a liquid, it behaves like a concave lens of power 1 D. If the refractive index of the material of the lens is 1.5, the refractive index of the liquid is

A line $ L $ passing through the point $ P(-5,-4) $ cuts the lines $ x - y - 5 = 0 $ and $ x + 3y + 2 = 0 $ respectively at $ Q $ and $ R $ such that \[ \frac{18}{PQ} + \frac{15}{PR} = 2, \] then the slope of the line $ L $ is:

If the origin is shifted to remove the first degree terms from the equation $2x^2 - 3y^2 + 4xy + 4x + 4y - 14 = 0$, then with respect to this new co-ordinate system, the transformed equation of $x^2 + y^2 - 3xy + 4y + 3 = 0$ is

An object of mass 'm' is projected with an initial velocity 'u' with an angle of '$\theta$' with the horizontal. The average power delivered by gravity in reaching the highest point is

Two objects having masses in $1:4$ ratio are at rest. When both of them are subjected to the same force separately, they achieved the same kinetic energy during times $t_1$ and $t_2$ respectively. The ratio of $\frac{t_2}{t_1}$ is

A boat man finds that he can save 8 s in crossing a river by quickest path than by the shortest path. If the velocity of the boat and the river flow are 13 m/s and 12 m/s respectively, then the width of the river is:

A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is 7 m/s and the coefficient of restitution is 0.75, the total distance travelled by the ball before it comes to rest (acceleration due to gravity = 10 ms$^{-2}$) is

The length of a metal bar is 20 cm and the area of cross-section is $ 4 \times 10^{-4} $ m$^2$. If one end of the rod is kept in ice at $ 0^\circ C $ and the other end is kept in steam at $ 100^\circ C $, the mass of ice melted in one minute is 5 g. The thermal conductivity of the metal in Wm$^{-1}$K$^{-1}$ is (Latent heat of fusion = 80 cal/gm)

The number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples is:

If the sum of two roots $ \alpha, \beta $ of the equation \[ x^4 - x^3 - 8x^2 + 2x + 12 = 0 \] is zero and $ \gamma, \delta $ ($ \gamma\delta $) are its other roots, then $ 3\gamma + 2\delta $ is:

For real values of $ x $ and $ a $, if the expression $ \frac{x+a}{2x^2 - 3x + 1} $ assumes all real values, then:

If the determinant of a 3rd order matrix $ A $ is $ K $, then the sum of the determinants of the matrices $ (AA^T) $ and $ (A - A^T) $ is:

For all positive integers $ n $, if $ 3(5^{2n+1}) + 2^{3n+1 $ is divisible by $ k $, then the number of prime numbers less than or equal to $ k $ is:}

If $ f(x) = \sqrt{x - 1 $ and $ g(f(x)) = x + 2\sqrt{x} + 1 $, then $ g(x) $ is:}

If a function $ f: \mathbb{R} \to \mathbb{R} $ is defined by $ f(x) = x^3 - x $, then $ f $ is:

If $ f(x + h) = 0 $ represents the transformed equation of $$ f(x) = x^4 + 2x^3 - 19x^2 - 8x + 60 = 0 $$ and this transformation removes the term containing $ x^3 $, then $ h $ is:

A body is thrown with a velocity $ (5\hat{i} + 6\hat{j}) \, \text{m/s} $. Its maximum height is (given that acceleration due to gravity = $ 10 \, \text{m/s}^2 $):

Which of the following is NOT a unit of permeability?

Observe the following reactions:
I. $ \text{CaCO}_3(s) \rightarrow \text{CaO}(s) + \text{CO}_2(g) $
II. $ \text{Cl}_2(g) \rightarrow 2 \text{Cl}(g) $
III. $ \text{H}_2\text{O}(l) \rightarrow \text{H}_2O(s) $
Identify the reactions in which entropy increases.

If a real valued function $ f: [a, \infty) \to [b, \infty) $ is defined by $ f(x) = 2x^2 - 3x + 5 $ and is a bijection, then find the value of $ 3a + 2b $:

Let $ \alpha \in \mathbb{R} $. If the line $ (a + 1)x + \alpha y + \alpha = 1 $ passes through a fixed point $ (h, k) $ for all $ a $, then $ h^2 + k^2 = $: