The solution set of $(5+4 \cos \theta)(2 \cos \theta+1)=0$ in the interval $[0, 2 \pi]$ is:

When an object is placed at a distance of $25 \, cm$ from a concave mirror,the magnification is $m_1$. The object is moved $15 \, cm$ farther away with respect to the earlier position,and the magnification becomes $m_2$. If $m_1/m_2 = 4$,the focal length of the mirror is $..... \, cm$ (Assume image is real,$m_1$ and $m_2$ are numerical values).

The number of distinct real values of $\lambda$,for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\hat{k}$,$\hat{i}-\lambda^2 \hat{j}+\hat{k}$ and $\hat{i}+\hat{j}-\lambda^2 \hat{k}$ are coplanar,is

In the circuit shown,the readings of the ammeter and voltmeter are $4\,A$ and $20\,V$ respectively. The meters are non-ideal. Then $R$ is:

Who is known as the father of Indian Bryology?

If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0$,then the angle between the lines is: