List of top Questions asked in AP EAPCET

If \( ^9C_3 + ^9C_5 = ^{10}C_r \) for some \( r \in \mathbb{N} \), then \( r = \) ?

The number of real values of \( m \) such that the equation \[ x^2 + (2m + 1)x + m = 0 \] has equal roots is:

The number of solutions of the equations \[ x + y + z = 1,\quad x^2 + y^2 + z^2 = 1,\quad x^3 + y^3 + z^3 = 1 \] is:

There are 4 oranges, 5 apples, and 7 mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is:

All pairs \( (x, y) \) that satisfy the inequality \[ 2\sqrt{\sin^2x - 2\sin x + 5} \cdot \frac{1}{4^{\sin^2 y}} \leq 1 \] also satisfy the equation:

Given 5 different green toys, 4 different blue toys, and 3 different red toys, how many combinations of toys can be chosen taking at least one green and one blue toy?

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:

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

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

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 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 \( b \) 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 \( \det(A + B) = \) ?

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

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

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

$50\, mL$ 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 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