21.

If S₁, S₂ and S₃ are the sums of n, 2n and 3n terms of an arithmetic progression respectively, then

• S₂ = 3S₃ - 2S₁

• S₃ = 4(S₁ + S₂)

• S₃ = 3(S₂ - S₁)

• S₃ = 2(S₂ + S₁)

If ${}^{\mathrm{n}}\mathrm{C}_{\mathrm{r} - 1} = 36, {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r}} = 84 \mathrm{and} {}^{\mathrm{n}}\mathrm{C}_{\mathrm{r} + 1} = 126$, then n is equal to

• 8

• 9

• 10

• 11

The sides AB, BC, CA of triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be constructed using these points as vertices

• 201

• 120

• 205

• 435

Coefficient of xⁿ in the expansion of $1 + \frac{\mathrm{a} + \mathrm{bx}}{1!} + \frac{{\left(\mathrm{a} + \mathrm{bx}\right)}^2}{2!} + \frac{{\left(\mathrm{a} + \mathrm{bx}\right)}^3}{3!} + ...$

• $\frac{{\mathrm{e}}^{\mathrm{a}} . {\mathrm{b}}^{\mathrm{n}}}{\mathrm{n}!}$

• $\frac{{\left(\mathrm{b} . \mathrm{a}\right)}^{\mathrm{n}}}{\mathrm{n}}$

• $\frac{{\mathrm{e}}^{\mathrm{b}} . {\mathrm{b}}^{\mathrm{n}}}{\left(\mathrm{n} - 1\right)!}$

• $\frac{{\mathrm{a}}^{\mathrm{n}} . {\mathrm{b}}^{\mathrm{n} - 1}}{\mathrm{n}!}$

$\frac{{\mathrm{C}}_0}{1} + \frac{{\mathrm{C}}_2}{3} + \frac{{\mathrm{C}}_4}{5} + \frac{{\mathrm{C}}_6}{7} + ...$ is equal to

• $\frac{2^{\mathrm{n} - 1}}{\mathrm{n} - 1}$

• $\frac{2^{\mathrm{n} + 1}}{\mathrm{n} + 3}$

• $\frac{2^{\mathrm{n}}}{\mathrm{n} + 1}$

• $\frac{2^{\mathrm{n} - 2}}{\mathrm{n}}$

The equation of the parabola having the focus at the point (3, - 1) and the vertex at (2, - 1)is

• y² - 4x - 2y + 9 = 0

• y² + 4x + 2y - 9 = 0

• y² - 4x + 2y + 9 = 0

• y² + 4x - 2y + 9 = 0

The equation of lines joining the origin to the points of intersection of y = x + 3 and 4x² + 4y² = 1 is

• 36(x² + y²) = (x - y)²

• 12(x² + y²) = (x + y)²

• 9(x² + y²) = 4(x - y)²

• None of the above

The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 10s, the angle of elevation changes to 30°. If thejet is flying at a speed of 432 km/h. Find the constant height at which thejet is flying.

• $200\sqrt{3} \mathrm{m}$

• $400\sqrt{3} \mathrm{m}$

• $600\sqrt{3} \mathrm{m}$

• $800\sqrt{3} \mathrm{m}$

Find the equation of tangents to the ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2} + \frac{{\mathrm{y}}^2}{{\mathrm{b}}^2} = 1$ which cut off equal intercepts on the axes.

• $\mathrm{y} = \sqrt{3}\mathrm{x} \pm \sqrt{3{\mathrm{a}}^2 + {\mathrm{b}}^2}$

• $\mathrm{y} = \pm \mathrm{x} \mp \sqrt{{\mathrm{a}}^2 + {\mathrm{b}}^2}$

• $\mathrm{y} = \sqrt{3}\mathrm{x} \pm \sqrt{{\mathrm{a}}^2 + 3{\mathrm{b}}^2}$

• None of the above

The points on the curve x² = 2y which are closest to the point (0, 5) are

• (2, 2), (- 2, 2)

• $\left(2\sqrt{2}, 4\right), \left(- 2\sqrt{2}, 4\right)$

• $\left(\sqrt{6}, 3\right), \left(- 6\sqrt{3}, 3\right)$

• $\left(2\sqrt{3}, 6\right), \left(- 2\sqrt{3}, 6\right)$