If A(z₁), B(z₂), C(z₃) and P(z) represent complex numbers such that $\left|{\mathrm{z}}_1 - \mathrm{z}\right| = \left|{\mathrm{z}}_2 - \mathrm{z}\right| = \left|{\mathrm{z}}_3 - \mathrm{z}\right|$, then, A, B, C lies on

• a straight line

• a circle

• a parabola

• an ellipse

If the complex numbers z, z, and origin form vertices of an equilateral triangle, then the value of z₁² + z₂² will be

• z₁z₂

• z₁ + z₂

• 2z₁z₂

• z₁ - z₂

Three numbers form an increasing GP. If the middle term is doubled, then the new numbers are in AP. The commonratio of the GP will be

• $2 - \sqrt{3}$

• $2 \pm \sqrt{3}$

• $3\sqrt{2}$

• $2 + \sqrt{3}$

If the equations ax² + 2cx + b = 0 and ax² + 2bx + c = 0 $\left(\mathrm{b} \ne \mathrm{c}\right)$ have a common root, then the value of a + 4b + 4c will be

• 2

• 1

• - 1

• Non eof these

If one root of ax² + bx + c = 0 is twice the other root, then

• b² = 9ac

• 2b² = 9ac

• 2b² = ac

• b² = ac

The number of ways of distributing 8 distinct toys among 5 children will be

• 5⁸

• 8⁵

• ${}^8\mathrm{P}_5$

• 40

The value of C₁ - 2 . C₂ + 3 . C₃ - 4 . C₄ + ... where C_r = ${}^{\mathrm{n}}\mathrm{C}_{\mathrm{r}}$ will be

• - 1

• 1

• 0

• None of these

In a $∆\mathrm{ABC}, \mathrm{if} \tan \left(\frac{\mathrm{A}}{2}\right) = \frac{5}{6} \mathrm{and} \tan \left(\frac{\mathrm{C}}{2}\right) = \frac{2}{5}$, then the sides a, b, c are in

• AP

• GP

• HP

• None of these

The value of $\cos \left(\frac{\mathrm{\pi }}{5}\right)\cos \left(\frac{2\mathrm{\pi }}{5}\right)\cos \left(\frac{4\mathrm{\pi }}{5}\right)\cos \left(\frac{8\mathrm{\pi }}{5}\right)$ will be

• $\frac{1}{16}$

• $- \frac{1}{16}$

• 0

• $\frac{1}{2}$

The distance between the lines 3x + 4y = 9 and 6x + 8y = 15 will be

• $\frac{3}{2}$

• $\frac{3}{8}$

• $\frac{3}{10}$

• 6