If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k}$,$\overrightarrow{b}=\hat{i}+\hat{j}$,$\overrightarrow{c}=\hat{i}$ and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c}=\lambda \overrightarrow{a}+\mu \overrightarrow{b}$,then $\lambda+\mu$ is equal to:

Let a random variable $X$ have a Binomial distribution with mean $8$ and variance $4$. If $P(X \leq 2) = \frac{k}{2^{16}}$,then $k$ is equal to:

The lengths of tangent,subtangent,normal,and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are $A, B, C$,and $D$ respectively. Then their increasing order is:

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to

Which of the following organisms derives energy for $N_2$ fixation through photosynthesis?

If $a = \hat{i} + \hat{j} + t \hat{k}$ and $b = \hat{i} + 2 \hat{j} + 3 \hat{k}$,then the values of $t$ for which $(a+b)$ and $(a-b)$ are perpendicular are: