List of top Questions asked in AP EAPCET

If the rank of the matrix \[ A = \begin{bmatrix} 1 & 2 & 1 & -1 \\ -1 & 2 & 3 & 5 \\ 0 & 1 & k & k \end{bmatrix} \] is 2 and \( k \) is a real number, then \( k \) is a root of which of the following quadratic equations?

If the solution of the system of simultaneous equations \[ \frac{1}{x} + \frac{2}{y} - \frac{3}{z} = 1, \quad \frac{2}{x} - \frac{4}{y} + \frac{3}{z} = 1, \quad \frac{3}{x} + \frac{6}{y} - \frac{6}{z} = 4 \] is \( x = \alpha, y = \beta, z = \gamma \), then the value of \( \alpha^2 + \gamma^2 \) is:

Evaluate: \[ \sum_{k=1}^{6} \left[ \sin\left( \frac{2\pi k}{7} \right) - i \cos\left( \frac{2\pi k}{7} \right) \right] \]

If \( (x - iy)^{1/3} = a - ib \), then the value of \( \frac{x}{2a} + \frac{y}{2b} \) is:

A true statement among the following identities is:

If \( x = -5 + 2\sqrt{-4} \), then the value of \( x^4 + 9x^3 + 35x^2 - x + 4 \) is:

If \( \alpha, \beta \) are the roots of \( x^2 - 10x - 8 = 0 \), with \( \alpha>\beta \), and \( a_n = \alpha^n - \beta^n \), then the value of: \[ \frac{a_{10} - 8a_8}{5a_9} \] is:

The range of the real valued function \( f(x) = \frac{x^2 + x + 1}{x} \) is

If a function \( f: \mathbb{R} - \{l\} \to \mathbb{R} - \{m\} \) defined by \( f(x) = \frac{x+3}{x-2} \) is a bijection, then \( 3l + 2m = \) ?

If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?

If \( b \) and \( c \) are non-zero real numbers, and \[ A = \begin{bmatrix} 1 & b & c \\ b & 2 & 3 \\ c & 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0 \end{bmatrix}, \] then \( \det(A + B) = \) ?

A box contains $30$ toys of same size in which $10$ toys are white and all the remaining toys are blue. A toy is drawn at random horn the box and it is replaced in the box after noting down its colour. If $5$ toys are drawn in tills way, then the probability of getting atmost $2$ white toys is

$50\, mL$ of $0.02\, M \,NaOH$ solution is mixed $50\, mL$ of $0.06 \,M$ acetic acid solution, the $pH$ of resulting solution is $\left( p K_{a}\right.$ of acetic acid is $4.76, \log 5=0.70$ )

The number of species of the following that can act both as Bronsted acids and bases is $HCl , ClO _{4}^{-},{ }^{-} OH , H ^{+}, H _{2} O , HSO _{4}^{-}, SO _{4}^{2-}$, $H _{2} SO _{4}, Cl ^{-}$

The molecule/ion having diamagnetic nature and a bond order of $1.0$ is

Which one of the following properties has same value for $H_2$ and $D_2$ ?

$6g$ of graphite is burnt in a bomb calorimeter at $25^{\circ}C$ and $1\, atm$ pressure. The temperature of water increased from $25^{\circ}C$ to $30^{\circ}C$. If $\Delta H$ of this reaction is $-248 \,kJ\, mol^{-1}$, find out $C_v$ (in $kJ\, K^{-1}$) of bomb calorimeter.

If the kinetic energy of $O_2$ gas is $4.0 \,kJ \; mol^{-1}$ . its RMS speed in $cm \; s^{-1}$ is

The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is

In which of the following the election gain enthalpy of elements is correctly arranged?

An $\alpha$-particle moves in a circular path of radius $1\, cm$ in a uniform magnetic field of $0.125\, T$. The de Broglie wavelength associated with the $\alpha$-particle is

A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )

At $1000\, K$, the equilibrium constant. $K_{C}$ for the reaction $2 NOCl (g) \rightleftharpoons 2 NO (g)+ Cl _{2}(g)$ is $4.0 \times 10^{-6} mol\, L ^{-1}$. The $K_{P}$ (in bar) at the same temperature is $\left(R=0.083 \,L\right.$ bar $\left. K ^{-1}\, mol ^{-1}\right)$

A body of mass 2 kg thrown vertically upward from the ground with a velocity of $8 \, ms^{-1}$ reaches a maximum height of 3 in. The work done by the air resistance is_______ (Acceleration due to gravity = $10 \, ms^{-2}$)

A body is projected with a speed 'u? at an angle $'\theta'$ with the horizontal. The radius of curvature of the trajectory when it makes an angle $\left(\frac{\theta}{2} \right)$ with the horizontal is (g - acceleration due to gravity)