If $a, b, c$ are non-coplanar unit vectors such that $a \times (b \times c) = \frac{b + c}{\sqrt{2}}$,then what is the angle between $a$ and $b$?

Given below are two statements regarding silent heart attack.
Statement $I$: This type of heart attack shows symptoms like chest pain and shortness of breath.
Statement $II$: In this type of heart attack,usually person shows very mild symptoms and thus it is ignored.
In the light of above two statements,choose the correct answer from options given below.

$A$ uniform conductor of resistance $R$ is cut into $20$ equal pieces. Half of them are joined in series and the remaining half of them are connected in parallel. If the two combinations are joined in series,the effective resistance of all the pieces is

The temperature in $K$ at which $\Delta G = 0$ for a given reaction with $\Delta H = -20.5 \ kJ \ mol^{-1}$ and $\Delta S = -50.0 \ J \ K^{-1} \ mol^{-1}$ is:

How many major groups have recent researchers classified the plant kingdom into?

$A$ straight conductor of length $4 ~m$ moves at a speed of $10 ~m/s$. When the conductor makes an angle of $30^{\circ}$ with the direction of the magnetic field of induction $0.1 ~Wb/m^2$,the induced emf is: (in $~V$)