The interior angles of a polygon of n sides are in AP. The smallest angle is 120° and the common difference is 5°. What is the largest interior angle of the polygon ?

• 160$°$ only

• 195$°$ only

• either 160$°$ or 195$°$ 

• neither 160$°$ nor 195$°$

$\mathrm{If} {\mathrm{x}}^{\ln \left(\frac{\mathrm{y}}{\mathrm{z}}\right)}. {\mathrm{x}}^{\ln {\left(\mathrm{xz}\right)}^2}. {\mathrm{z}}^{\ln \left(\frac{\mathrm{x}}{\mathrm{y}}\right)} = {\mathrm{y}}^{4\ln \left(\mathrm{y}\right)} \mathrm{for} \mathrm{any} \mathrm{x} > 1, \mathrm{y} > 1 \mathrm{and} \mathrm{z} > 1,$

then which one of the following is correct ?

• ln(y) is the GM of ln(x), ln(x), ln(x) and ln(z)

• ln(y) is the AM of ln(x), ln(x), ln(x) and ln(z)

• ln(y) is the GM of ln(x), ln(x), ln(x) and ln(z)

• ln(y) is the AM of ln(x), ln(x), ln(z) and ln(z)

If 3^rd, 8^th and 13^th terms of a GP are p, q and r respectively, then which one of the following is correct ?

• q² = pr

• r² = pq

• pqr = 1

• 2q = p + r

Let S_n be the sum of the first n terms of an AP. If S_2n = 3n + 14ⁿ², then what is the common difference ?

• 5

• 6

• 7

• 9

How many two-digit numbers are divisible by 4 ?

• 21

• 22

• 24

• 25

Let a, b, c be in AP and k ≠ 0 be a real number. Which of the following are correct ?

1) ka, kb, kc are in AP

2) k –a, k -b, k –c are in AP

3) $\frac{\mathrm{a}}{\mathrm{k}}, \frac{\mathrm{b}}{\mathrm{k}}, \frac{\mathrm{c}}{\mathrm{k}} \mathrm{are} \mathrm{in} \mathrm{AP}$ are in AP

Select the correct answer using the code given below :

• 1 and 2 only

• 2 and 3 only

• 1 and 3 only

• 1, 2 and 3 

If n! has 17 zeros, then what is the value of n ?

• 95

• 85

• 80

• No such value of n exists

If the middle term in the expansion of ${\left({\mathrm{x}}^2 + \frac{1}{\mathrm{x}}\right)}^{2\mathrm{n}}$ is 184756x¹⁰, then what is the value of n ?

• 10

• 8

• 5

• 4

79.

How many terms are there in the expansion of (1 + 2x + x²)⁵ + (1 + 4y + 4y²)⁵ ?

• 12

• 20

• 21

• 22

What is the value of ?

$2 + \frac{1}{2 + {\displaystyle \frac{1}{2 + {\displaystyle \frac{1}{2 + ... \infty }}}}} = ?$

• $\mathrm{x} = \sqrt{2} - 1$

• $1 \pm \sqrt{2}$

• 3

• 4