What is the n^th term of the sequence 25, - 125, 625, - 3125, ... ?

• ${\left( - 5\right)}^{2\mathrm{n} - 1}$

• ${\left( - 1\right)}^{2\mathrm{n}}{5}^{\mathrm{n} + 1}$

• ${\left( - 1\right)}^{2\mathrm{n} - 1}{5}^{\mathrm{n} + 1}$

• ${\left( - 1\right)}^{\mathrm{n} - 1}{5}^{\mathrm{n} + 1}$

What is the fourth term of an AP of n terms whose sum is n(n + 1) ?

• 6

• 8

• 12

• 20

What is the number of terms in the expansion of ${\left[{\left(2\mathrm{x} - 3\mathrm{y}\right)}^2{\left(2\mathrm{x} + 3\mathrm{y}\right)}^2\right]}^2 = ?$

• 4

• 5

• 8

• 16

In the expansion of (1 + ax)ⁿ, the first three terms are respectively 1, 12x and 64x². What is n equal to ? 

• 6

• 9

• 10

• 12

5.

The numbers 1, 5 and 25 can be three terms (not necessarily consecutive) of : 

• only one AP

• More than one but finite numbers of APs

• infinite number of APs

• finite number of APs

$\mathrm{The} \mathrm{sum} \mathrm{of} (\mathrm{p} + \mathrm{q}) \mathrm{and} (\mathrm{p} - \mathrm{q}{)}^{\mathrm{th}} \mathrm{terms} \mathrm{of} \mathrm{an} \mathrm{AP} \mathrm{is} \mathrm{equal} \mathrm{to} :$

• (2p)^th term

• (2q)^th term

• Twice the p^th term

• Twice the q^th term

$\mathrm{If} \mathrm{n} \in \mathrm{N}, \mathrm{then} {121}^{\mathrm{n}} - {25}^{\mathrm{n}} + {1900}^{\mathrm{n}} - {\left( - 4\right)}^{\mathrm{n}} \mathrm{is} \mathrm{divisible} \mathrm{by} \mathrm{which} \mathrm{one} \mathrm{of} \mathrm{the} \mathrm{following} ?$

• 1904

• 2000

• 2002

• 2006

$\mathrm{If} \mathrm{n} = \left(2007\right)!, \mathrm{then} \mathrm{what} \mathrm{is} \frac{1}{{\log }_2\left(\mathrm{n}\right)} + \frac{1}{{\log }_3\left(\mathrm{n}\right)} + \frac{1}{{\log }_4\left(\mathrm{n}\right)} + ... + \frac{1}{{\log }_{2017}\left(\mathrm{n}\right)} = ?$

• 0

• 1

• $\frac{\mathrm{n}}{2}$

• n

If the ratio of AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to :

• 3 : 5

• 2 : 9

• 9 : 1

• 5 : 3

$\mathrm{If} \mathrm{x} + {\log }_{15}\left(1 +3^{\mathrm{x}}\right) = {\mathrm{xlog}}_{15}\left(5\right) + {\log }_{15}\left(12\right), \mathrm{where} \mathrm{x} \mathrm{is} \mathrm{an} \mathrm{integer}, \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{x} =?$

• - 3

• 2

• 1

• 3