If the vectors $\hat{i}+3 \hat{j}+4 \hat{k}$ and $\lambda \hat{i}-4 \hat{j}+\hat{k}$ are orthogonal to each other, then $\lambda$ is equal to:

$A$ line with positive direction cosines passes through the point $P(2,-1,2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x+y+z=9$ at point $Q$. The length of the line segment $PQ$ equals

In a binomial distribution, the probability of success is $\frac{1}{4}$ and the standard deviation is $3$. Then, its mean is

For the same total mass,which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body?

Which of the following crops have been brought to India from the New World?