The value of $\frac{\cot \left(\mathrm{x}\right) - \tan \left(\mathrm{x}\right)}{\cot \left(2\mathrm{x}\right)}$ is

• 1

• 2

• - 1

• 4

The number of points of intersection of 2y = 1 and y = sin(x), in $- 2\mathrm{\pi } \le \mathrm{x} \le 2\mathrm{\pi }$ is

• 1

• 2

• 3

• 4

The value of $\frac{2}{3!} +\hspace{0.17em}\frac{4}{5!} + \frac{6}{7!} + ...$

• ${\mathrm{e}}^{\frac{1}{2}}$

• e^{- 1}

• e

• ${\mathrm{e}}^{- \frac{1}{3}}$

If sum of an infinite geometric series is 4/3 and its Ist term is 3/4, then its common ratio is

• 7/16

• 9/16

• 1/9

• 7/9

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

• 96

• 144

• 512

• 576

6.

If ${}^{\mathrm{n} - 1}\mathrm{C}_{3 }+ {}^{\mathrm{n} - 1}\mathrm{C}_4 > {}^{\mathrm{n}}\mathrm{C}_3$ then n is just greater than integer

• 5

• 6

• 4

• 7

If in the expansion of (a- 2b)ⁿ, the sum of the 5th and 6th term is zero, then the value of $\frac{\mathrm{a}}{\mathrm{b}}$ is

• $\frac{\mathrm{n} - 4}{5}$

• $\frac{2\left(\mathrm{n} - 4\right)}{5}$

• $\frac{5}{\mathrm{n} - 4}$

• $\frac{5}{2\left(\mathrm{n} - 4\right)}$

(2³ⁿ - 1) will be divisible by $\left(\forall \mathrm{n} \in \mathrm{N}\right)$

• 25

• 8

• 7

• 3

Sum of the last 30 coefficients in the expansion of (1 + x)⁵⁹ , when expanded in ascending power of x is

• 2⁵⁹

• 2⁵⁸

• 2³⁰

• 2²⁹

If (1 - x + x²)ⁿ = a₀ + a₁x + ... + a_2nx²ⁿ, then the value of a₀ + a₂ + a₄ + ... + a_2n is

• $3^{\mathrm{n}} + \frac{1}{2}$

• $3^{\mathrm{n}} - \frac{1}{2}$

• $\frac{3^{\mathrm{n}} - 1}{2}$

• $\frac{3^{\mathrm{n}} + 1}{2}$