21.

The expression $\frac{{\left(1 + \mathrm{i}\right)}^{\mathrm{n}}}{{\left(1 - \mathrm{i}\right)}^{\mathrm{n} - 2}}$

• $- {\mathrm{i}}^{\mathrm{n} + 1}$

• ${\mathrm{i}}^{\mathrm{n} + 1}$

• $- 2{\mathrm{i}}^{\mathrm{n} + 1}$

• 1

Let z = .x + iy, where x and y are real. The  points (x, y) in the X-Y plane for which $\frac{\mathrm{z} + \mathrm{i}}{\mathrm{z} - \mathrm{i}}$ is purely imaginary, lie on

• a straight line

• An ellipse

• a hyperbola

• a circle

If p, q are odd integers, then the roots of the equation 2px² + (2p + q) x + q= 0 are

• rational

• irrational

• non-real

• equal

Out of 7 constants and 4 vowels, words are formed each having 3 constants 2 vowels. The number of such words that can be formed is

• 210

• 25200

• 2520

• 302400

If one of the diameters of the curve x² + y² - 4x - 6y + 9 = 0 is a chord of a circle with centre (1, 1), the radius of this circle is

• 3

• 2

• $\sqrt{2}$

• 1

Let A(- 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $\angle \mathrm{MBA} = 2\angle \mathrm{MAB}$. Then, the point M moves along

• a straight line

• a parabola

• an ellipse

• a hyperbola

The area of the figure bounded by the parabolas x = - 2y ² and x = 1- 3y² is

• $\frac{4}{3}$ sq. units

• $\frac{2}{3}$ sq. units

• $\frac{3}{7}$ sq. units

• $\frac{6}{7}$sq. units

Tangents are drawn to the ellipse $\frac{{\mathrm{x}}^2}{9} + \frac{{\mathrm{y}}^2}{5} = 1$ at the ends of both latusrectum. The area of the quadrilateral, so formed is

• 27 sq. units

• $\frac{13}{2}$ sq. units

• $\frac{15}{4}$ sq. units

• 45 sq. units

If a, b $\in$ {1, 2, 3} and the equation ax² + bx + 1 = 0 has real roots, then

• a > b

• $\mathrm{a} \le \mathrm{b}$

• number of possible ordered pairs (a, b) is 3

• a<b

If the tangent to y² = 4ax at the point (at², 2at) where $\left|\mathrm{t}\right|$ > 1 is a normal to x² - y² = a² at the point ($\mathrm{a} \sec \left(\mathrm{\theta }\right), \mathrm{a} \tan \left(\mathrm{\theta }\right)$), then

• $\mathrm{t} = - \csc \left(\mathrm{\theta }\right)$

• $\mathrm{t} = - \sec \left(\mathrm{\theta }\right)$

• $\mathrm{t} = 2\tan \left(\mathrm{\theta }\right)$

• $\mathrm{t} = 2\cot \left(\mathrm{\theta }\right)$