$A$ straight wire of length $20 \ cm$ carrying a current of $\frac{3}{\pi^2} \ A$ is bent in the form of a circle. The magnetic field at the centre of the circle is

$A$ moving coil galvanometer of resistance $100 \ \Omega$ shows full-scale deflection when a current of $100 \ \mu A$ passes through it. If it is intended to show full-scale deflection when a current of $1 \ mA$ passes through it,the value of shunt resistance in ohms to be connected to the galvanometer is:

The condition that $f(x)=a x^3+b x^2+c x+d$ has no extreme value,is

If $y=y(x)$ is the solution of the differential equation $\frac{5+e^x}{2+y} \cdot \frac{dy}{dx} + e^x = 0$ satisfying $y(0)=1$,then a value of $y(\log_e 13)$ is

Match the following and choose the correct answer:-
$(A)$ Implantation $(i)$ Vagina
$(B)$ Capacitation (ii) Ovary
$(C)$ Folliculogenesis (iii) Uterus
$(D)$ Fertilisation (iv) Fallopian tube

$A$ square matrix $[a_{ij}]$ in which $a_{ij} = 0$ for $i \neq j$ and $a_{ij} = k$ (constant) for $i = j$ is called a