The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

The maximum value of the function $f(x) = 3x^3 - 18x^2 + 27x - 40$ on the set $S = \{x \in R : x^2 + 30 \le 11x\}$ is

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

The total revenue in Rupees received from the sale of $x$ units of a product is given by $R(x) = 3x^2 + 36x + 5$. The marginal revenue,when $x = 15$,is

The acceleration of a moving body can be found from

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross-sectional area $A = 10 \, cm^2$ and length $\ell = 20 \, cm$. If one of the solenoids has $N_1 = 300$ turns and the other has $N_2 = 400$ turns,their mutual inductance is (given $\mu_0 = 4\pi \times 10^{-7} \, T \cdot m \cdot A^{-1}$):