MCQ
For every integer $\mathbf{n} \geq 1,\left(3^{2 n}-1\right)$ is always divisible by:
- A$2^{n 2}$
- B$2^{n+4}$
- ✓$2^{n+2}$
- D$2^{n+3}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\bar{z}-z^2=i\left(\bar{z}+z^2\right)$ is. . . . . .
| Column $I$ | Column $II$ |
| $(A)$ Circle | $(p)$ The locus of the point $(h, k)$ for which the line $h x+k y=1$ touches the circle $x^2+y^2=4$ |
| $(B)$ Parabola | $(q)$ Points $z$ in the complex plane satisfying $|z+2|-|z-2|= \pm 3$ |
| $(C)$ Ellipse | $(r)$ Points of the conic have parametric representation $x=\sqrt{3}\left(\frac{1-t^2}{1+t^2}\right), y=\frac{2 t}{1+t^2}$ |
| $(D)$ Hyperbola | $(s)$ The eccentricity of the conic lies in the interval $1 \leq x<\infty$ |
| $(t)$ Points $z$ in the complex plane satisfying $\operatorname{Re}(z+1)^2=|z|^2+1$ |