$A$ pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of $a$ is

Two moles of ideal helium gas are in a rubber balloon at $30^\circ C$. The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $35^\circ C$. The amount of heat required in raising the temperature is nearly...... $J$ (take $R = 8.31$ $J/mol \cdot K$)

Antihistamines and steroids are administered for which of the following?

If $f(x) = \frac{x}{1+x}$ and $g(x) = f(f(x))$, then $g^{\prime}(x)$ is equal to

The equation of the directrix of the parabola ${y^2} + 4y + 4x + 2 = 0$ is

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge. The bridge is balanced when $C = 100 \ \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \ \Omega$. The value of $D$ is (in $\Omega$)