If a, b, c are in arithmetic progression, then $\frac{\mathrm{a}}{\mathrm{bc}}, \frac{1}{\mathrm{c}}, \frac{2}{\mathrm{b}}$ will be in

• arithmetic proression

• geometric progression

• harmonic progresssion

• None of the above

If G is the geometric mean of x and y, then $\frac{1}{{\mathrm{G}}^2 - {\mathrm{x}}^2} + \frac{1}{{\mathrm{G}}^2 - {\mathrm{y}}^2}$ will be

• - G²

• $- \frac{1}{{\mathrm{G}}^2}$

• $\frac{1}{{\mathrm{G}}^2}$

• G²

If a > 1, b > 1 and c > 1 are in geometric progression, then $\frac{1}{1 + {\log }_{\mathrm{e}}\left(\mathrm{a}\right)}, \frac{{\displaystyle 1}}{{\displaystyle 1 + {\log }_{\mathrm{e}}\left(\mathrm{b}\right)}}, \frac{{\displaystyle 1}}{{\displaystyle 1 + {\log }_{\mathrm{e}}\left(\mathrm{c}\right)}}$ will be in

• arithmetic proression

• geometric progression

• harmonic progresssion

• None of the above

154.

The lines 2x + 3y = 6 , 2x + 3y = 8 cut the X-axis at A and B, respectively. A line L drawn through the point (2, 2) meets the X-axis as C in such away that abscissae of A, B and C are in arithmetic progression. Then, the equation of the line L is

• 2x + 3y = 10

• 8x + 2y = 10

• 2x - 3y = 10

• 8x - 2y = 10

If the polar of a point on the circle x² + y² = p² with respect to the circle x² + y² = q² touches the circle x² + y² = r, then p, q, r are in

• AP

• GP

• HP

• AGP

If 2³ + 4³ + 6³ + ... + 2(n)³ = hn²(n + 1)², then h is equal to

• $\frac{1}{2}$

• 1

• $\frac{3}{2}$

• 2

$1 + \frac{1}{4} + \frac{1}{4} . \frac{3}{8} + \frac{1}{4} . \frac{3}{8} . \frac{5}{12 } + . . . \mathrm{is} \mathrm{equal} \mathrm{to}$

• $\sqrt{2}$

• $\frac{1}{\sqrt{2}}$

• $\sqrt{3}$

• $\frac{1}{\sqrt{3}}$

$\frac{2}{2!} + \frac{2 + 4}{3!} + \frac{2 + 4 + 6}{4!} + ...\mathrm{is} \mathrm{equal} \mathrm{to}$

• e

• ${\mathrm{e}}^{ - 1}$

• ${\mathrm{e}}^{ - 2}$

• ${\mathrm{e}}^{ - 3}$

The roots of the equation x³ - 14x² + 56x - 64 = 9 are in

• AGP

• HP

• AP

• GP

$1 + \frac{1 + 2}{2!} + \frac{1 + 2 + 2^2}{3!} + ...$ is equal to

• e² + e

• e²

• e² - 1

• e² - e