Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is $$\frac{1}{3}$$.

Reason (R): Let E and F be two events with a random experiment, then $$\mathrm{P}(\mathrm{F} / \mathrm{E})=\frac{\mathrm{P}(\mathrm{E} \cap \mathrm{F})}{\mathrm{P}(\mathrm{E})}$$.

Assertion (A): $$\int_\limits2^8 \frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}} d x=3$$

Reason (R): $$\int_\limits a^b f(x) d x=\int_a^b f(a+b-x) d x$$

Write the domain and range (principle value branch) of the following functions: $$f(x)=\tan ^{-1} x$$

(a) If $$f(x)=\left\{\begin{array}{ll}x^2, & \text { if } x \geq 1 \\ x, & \text { if } x<1\end{array}\right.$$, then show that $$f$$ is not differentiable at $$x=1$$.

OR

(b) Find the value(s) of '$$\lambda$$', if the function

$$f(x)=\left\{\begin{array}{cc} \frac{\sin ^2 \lambda x}{x^2}, & \text { if } x \neq 0 \\ 1, & \text { if } x=0 \end{array} \text { is continuous at } x=0 .\right.$$