If $f: R \rightarrow R$ is defined by $f(x) = \frac{1}{2 - \cos 3x}$ for each $x \in R$,then the range of $f$ is

$A$ circular disc of radius $R$ is removed from a bigger uniform circular disc of radius $2R$ such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

The number of geometrical isomers for octahedral $[Co(NH_3)_2Cl_4]^-$,square planar $[AuCl_2Br_2]^-$ and $[Pt(en)Cl_2]$ are

Assertion $(A)$: $-NH_2$ group of aniline is ortho,para directing in electrophilic substitutions.
Reason $(R)$: $-NH_2$ group stabilises the arenium ion formed by the ortho,para attack of the electrophile.
The correct answer is

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to generate caustic soda. When $CO_2$ is bubbled through $A$,it turns cloudy,what is $A$?