$A = \{x_1, x_2, x_3, x_4\}$; $B = \{y_1, y_2, y_3, y_4\}$. $A$ function $f: A \to B$ is defined. The number of one-one functions such that $f(x_i) \neq y_i$ for $i = 1, 2, 3, 4$ is equal to:

If the roots of the equation $4x^3 - 12x^2 + 11x + k = 0$ are in arithmetic progression,then $k$ is equal to

The suspension of slaked lime in water is known as

The decreasing order of nucleophilicity among the following nucleophiles is:
$(I)$ $CH_3-COO^-$
$(II)$ $CH_3-O^-$
$(III)$ $CH_3-CH_2^-$
$(IV)$ $CH_3-SO_3^-$

$A$ particle of mass $m$ and charge $q$ is in an electric and magnetic field,given by $\vec{E} = 2 \hat{i} + 3 \hat{j}$ and $\vec{B} = 4 \hat{j} + 6 \hat{k}$. The charged particle is shifted from the origin to the point $P(1, 1)$ along a straight path. The magnitude of the total work done on it is: (in $q$)

Which of the following is the correct order of lattice energy for the given ionic compounds?