No Author Solutions for Exercise 1: EXAM GALLERY

The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is $2 \mathrm{cm}$ is

Let $S$ be the set of all real matrices, $A=\left[\begin{array}{ll}a& b\\ c& d\end{array}\right],$ such that $a+d=2$ and $A^T=A^2-2A$, then, $S$

If $z=i \left(i+\sqrt{2}\right)$, then the value of $z^4+4z^3+6z^2+4z$ is

Suppose, a population $A$ has $100$ observations $101,102,\dots ,$ $200$ and another population $B$ has $100$ observations $151,$ $152,\dots ,250$ If $V_A$ and $V_B$ represent the variances of two populations respectively, then the ratio $V_A:V_B$ is

$\int \left[\frac{7x^{13}+5x^{15}}{{\left(x^7+x^2+1\right)}^3}\right]dx$ equals to

If for some real number $a,\underset{x\to 0}{\lim }\frac{\sin 2x+a\sin x}{x^3}$ exists, then the limit is equal to

If a variable line passing through the point of intersection of the lines $x+2y-1=0$ and $2 x-y-1=0$, meets the coordinate axes in $A$ and $B$, then the locus of the mid-point of $AB$ is

Let $y^2=16x$ be a given parabola and $L$ be an extremity of its latus rectum in the first quadrant. If a chord is drawn through $L$ with slope $-1$, then the length of this chord is