List of top Questions asked in AP EAMCET- 2024

If \( l, m, n \) are the direction cosines of a line that is perpendicular to the lines having the direction ratios \( (1,2,-1) \) and \( (-2,1,1) \), then \( (l+m+n)^2 \) =
If \( y = f(x) \) is a thrice differentiable function and a bijection, then \[ \frac{d^2x}{dy^2} \left(\frac{dy}{dx}\right)^3 + \frac{d^2y}{dx^2} = ? \]
A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph and the same braking force is applied, the stopping distance is:
If \( Q(h, k) \) is the inverse point of \( P(1,2) \) with respect to the circle \( x^2 + y^2 - 4x + 1 = 0 \), then \( 2h + k \) is:
Evaluate: \[ \cosh^{-1} 2 \]
If the system of equations: $$ a_1 x + b_1 y + c_1 z = 0, \quad a_2 x + b_2 y + c_2 z = 0, \quad a_3 x + b_3 y + c_3 z = 0 $$ has only the trivial solution, then the rank of the matrix:  \[\left[ \begin{array}{ccc} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{array} \right] \] is
Evaluate \( \cosh (\log 4) \):
Given the partial fraction decomposition: \[ \frac{4x^2 + 5}{(x - 2)^4} = \frac{A}{(x - 2)} + \frac{B}{(x - 2)^2} + \frac{C}{(x - 2)^3} + \frac{D}{(x - 2)^4} \] then the value of \[ \sqrt{\frac{A}{C} + \frac{B}{C} + \frac{D}{C}} \] is:
The range of the real-valued function \( f(x) = \sin^{-1} \left( \frac{1 + x^2}{2x} \right) + \cos^{-1} \left( \frac{2x}{1 + x^2} \right) \) is:
In a triangle ABC, if \( r : R = 1 : 3 : 7 \), then \( \sin(A + C) + \sin B = \)
2.644 g of metal (M) was deposited when 8040 coulombs of electricity was passed through molten MF\(_2\) salt. What is the atomic mass of M? (F = 96500 C mol\(^{-1}\))
The set of all values of \(k\) for which the inequality \(x^2 - (3k+1)x + 4k^2 + 3k - 3>0\) is true for all real values of \(x\) is
If \(\sec \theta + \tan \theta = \frac{1}{3}\), then the quadrant in which \(2\theta\) lies is:
Among the 4-digit numbers formed using the digits \( 0, 1, 2, 3, 4 \) when repetition of digits is allowed, the number of numbers which are divisible by 4 is:
At 300 K, \( \Delta_r G^\circ \) for the reaction \( A(g) \rightleftharpoons B(g) \) is \( -11.5 \) kJ mol\(^{-1}\). The equilibrium constant at 300 K is approximately: \((R = 8.314 \text{ J mol}^{-1} \text{ K}^{-1})\)
A slab consists of two identical plates of copper and brass. The free face of the brass is at \( 0^\circ C \) and that of copper at \( 100^\circ C \). If the thermal conductivities of brass and copper are in the ratio \( 1:4 \), then the temperature of the interface is:

If

 
and \( AA^T = I \), then \( \frac{a}{b} + \frac{b}{a} = \):

125 identical charged small spheres coalesce to form a big charged sphere. If the electric potential on each small sphere is 60 mV, then the electric potential on the bigger sphere formed is:
If a direct common tangent is drawn to the circles \( x^2 + y^2 - 6x + 4y + 9 = 0 \) and \( x^2 + y^2 + 2x - 2y + 1 = 0 \) that touches the circles at points \( A \) and \( B \), then \( AB = \):
In the expansion of \( \frac{2x+1}{(1+x)(1-2x)} \), the sum of the coefficients of the first 5 odd powers of \( x \) is:
The number of ways a committee of 8 members can be formed from a group of 10 men and 8 women such that the committee contains at most 5 men and at least 5 women is:
There were two women participating with some men in a chess tournament. Each participant played two games with the other. The number of games that the men played among themselves is 66 more than the number of games the men played with the women. Then the total number of participants in the tournament is:
If the probability distribution of a random variable \( X \) is given as follows, then find \( k \):
probability distribution of a random variable X
In \( \triangle ABC \), if \( (a+c)^2 = b^2 + 3ca \), then \( \frac{a+c}{2R} \) is:
The probability that A speaks truth is 75\% and the probability that B speaks truth is 80\%. The probability that they contradict each other when asked to speak on a fact is: