$\cos \left[\cos ^{-1}\left(-\frac{1}{7}\right)+\sin ^{-1}\left(-\frac{1}{7}\right)\right]$ is equal to

In a triangle,if $r_1 = 2r_2 = 3r_3$,then $\frac{a}{b} + \frac{b}{c} + \frac{c}{a}$ is equal to

Assertion : Bond angle of $H_2S$ is smaller than $H_2O$.
Reason : Electronegativity of the central atom increases,bond angle decreases.

An air column in a tube $32 ~cm$ long,closed at one end,is in resonance with a tuning fork. The air column in another tube,open at both ends,of length $66 ~cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together,they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

The velocities of two particles $A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de-Broglie's wavelength is

The steps of a plant breeding program are given below. Arrange them in the correct sequence.
$(a)$ Cross-hybridization among the selected parents
$(b)$ Testing,release,and commercialization of new cultivars
$(c)$ Collection of variability
$(d)$ Selection and testing of superior recombinants
$(e)$ Evaluation and selection of parents