List of top Questions asked in AP EAPCET- 2023

Let \( B = \begin{bmatrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & -1 & -1 \end{bmatrix} \), \( C = \begin{bmatrix} -1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{bmatrix} \), and if a matrix \( A \) is such that \( BAC = I \), then \( A^{-1} = \)
Let \( (a, b) \) denote the angle between vectors \( \mathbf{a} \) and \( \mathbf{b} \). If \( \mathbf{a} = 2i + 3j + 6k \), \( |\mathbf{a}| = 4 \), and \( (\mathbf{a}, \mathbf{b}) = \cos^{-1} \left( \frac{4}{21} \right) \), then \( \mathbf{a} + \mathbf{b} = \)
If \( A(3, -1, 1), B(0, 2, 3), C(4, 8, 11) \) are three points, then the coordinates of the foot of the perpendicular drawn from the point A to the line joining the points B and C is:
Evaluate the integral: \[ \int \frac{dx}{4 + 5 \cos x} \]
The magnetic force \( q [v \times B] \) is
If the unrtainty in velocity of an electron $(\Delta v)$ is $0.1 \text{ m/s}$, the unrtainty in its position $(\Delta x)$ is (given: $m_e = 9.1 \times 10^{-31} \text{ kg}$)
The temperature of the surface of Sun is 6000 K. The wavelength corresponding to the maximum energy is nearly (Wien's constant, \( b = 2.89 \times 10^{-3} \, \text{mK} \))
How many of the following are neutral oxides?
CO, NO, Na\(_2\)O, N\(_2\)O, Cl\(_2\)O\(_7\), Al\(_2\)O\(_3\), As\(_2\)O\(_3\)
Observe the following half cell reactions and choose the correct options
(I) 2H2O(l) → O2(g)+4H+ +4e− E0 = 1.23V
(II) H+(aq) + e− → 1/2 H2(g) E0 = 0.00V
(III) 2SO4^2− (aq) → S2O8^2− (aq)+2e− E0 = −1.96V
(a) In dilute H2SO4 solution, H+ ions are reduced at cathode.
(b) In concentrated H2SO4 solution, water is oxidized at anode.
(c) In dilute H2SO4 solution, water is oxidized at anode.
(d) In dilute H2SO4 solution, SO4^2− ions are oxidized at anode.
Which one of the following is not correct regarding diamond?
If the roots of the equation \[ 6x^3 - 11x^2 + 6x - 1 = 0 \] are in harmonic progression, then the roots of \[ x^3 - 6x^2 + 11x - 6 = 0 \] will be in
If $ X $ is a random variable with the probability distribution \[ P(X = k) = \frac{(k+1)c}{2^k}, \quad k = 0, 1, 2, ..., \] then $ P(X \geq 3) $ is:
$\int \frac{dx}{(x-1)\sqrt{x+2}} =$
The magnetic field lines of a bar magnet
A liquid of density 800 kg/m$^3$ is used instead of mercury in the Torricelli barometer. What is the height of the liquid column if atmospheric pressure is 76 cm of Hg? (Density of mercury = $13.6 \times 10^3$ kg/m$^3$)
A polymer sample contains 5 molecules of molar mass 1000, 3 molecules of molar mass 500 and 2 molecules of molar mass 250. What is its weight average molecular weight (Mw)?
Let \( f(x) = |x| \) and \( g(x) = |x| + a \), \( (a>0) \). For \( 0 \le x \le b \), \( \{(x, y) / g(x) \le y \le f(x)\} \) represents all the points in the interior of
If \( \alpha \) and \( \beta \) are the roots of the equation \( x^2 + x + 1 = 0 \), then the quadratic equation whose roots are \( \alpha^{2023} \) and \( \beta^{2012} \) is
A car is moving along a circular path having coefficient of friction 0.5 and radius of curvature 16.2 m. Then the maximum velocity of the car that can travel without falling outwards is (Acceleration due to gravity = 10 ms\(^{-2} \))
The time required (in hours) to reduce 3 mol of \( Fe^{3+} \) ions to \( Fe^{2+} \) ions with 2.0 amperes of current is (1 F = 96500 C mol\(^{-1} \))
If \( A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \), then \( A^{-1} \) = ?
If \[ \int \frac{x^3}{\sqrt{1 + x^2}} \, dx = A(1 + x^2)^{\frac{3}{2}} + B(1 + x^2)^{\frac{1}{2}} + C, \text{ then } A + B = \]
The condition that the lines joining the origin to the points of intersection of the line \( \frac{x}{a} + \frac{y}{b} = 2 \) and the circle \( (x - a)^2 + (y - b)^2 = r^2 \) are at right angles is:
If \( r_1 \) and \( r_2 \) are the angles of refraction at the first face and second face of a prism, then the angle of the prism is:
A body is thrown vertically upwards with an initial velocity \( u \). If \( g \) is the acceleration due to gravity, then the total time taken for the body to return to the starting point is: