Which bond angle $\theta$ gives maximum dipole moment for a triatomic molecule $XY_2$?

The half-life of a radioactive substance against $\alpha$-decay is $1.2 \times 10^7 \ s$. What is the decay rate for $4 \times 10^{15}$ atoms of the substance?

For any integer $n \geq 1$,the number of positive divisors of $n$ is denoted by $d(n)$. Then,for a prime $P$,$d(d(d(P^7)))$ is equal to

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

Two opposite and equal charges $4 \times 10^{-8} \, C$ are placed $2 \times 10^{-2} \, cm$ apart,forming a dipole. If this dipole is placed in an external electric field of $4 \times 10^8 \, N/C$,what are the values of the maximum torque and the work done in rotating it through $180^o$?

In which group of organisms do the cell walls form two thin overlapping shells that fit together?