If $4\,P(A) = 6\,P(B) = 10\,P(A \cap B) = 1,$ then $P\left( \frac{B}{A} \right) = $

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :

If all the seven letters of the word $LEADING$ are permuted in all possible ways and the words thus formed are arranged as in the dictionary order,then the word in $2017^{\text{th}}$ place is

If the lines $2x + 3y + 12 = 0$ and $x - y + k = 0$ are conjugate with respect to the parabola $y^2 = 8x$,then $k$ is equal to

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is

In the circuit shown,the heat produced in $5 \Omega$ resistance due to current $I_2$ is $50 \text{ J/s}$. Then,the heat generated per second in $2 \Omega$ resistance is (in $text{ J/s}$)