If f : [2, 3] $\to$ R is defined by f(x) = x³ + 3x - 2, then the range of f(x) is contained in the interval

• [1, 12]

• [12, 34]

• [35, 50]

• [- 12, 12]

The number of subsets of {1, 2, 3, ..., 9} containing atleast one odd number is

• 324

• 396

• 496

• 512

A binary sequence is an array of 0's and 1's. The number of n-digit binary sequences which contain even number of 0's is

• 2^{n - 1}

• 2ⁿ - 1

• 2^{n - 1} - 1

• 2ⁿ

If x is numerically so small so that x² and higher power of x can be neglected, then ${\left(1 + \frac{2\mathrm{x}}{3}\right)}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} . {\left(32 + 5\mathrm{x}\right)}^{- \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}$ is approximately equal to

• $\frac{32 + 31\mathrm{x}}{64}$

• $\frac{31 + 32\mathrm{x}}{64}$

• $\frac{31 - 32\mathrm{x}}{64}$

• $\frac{1 - 2\mathrm{x}}{64}$

The locus of z satisfying the inequality $\left|\frac{\mathrm{z} +\hspace{0.17em}2\mathrm{i}}{2\mathrm{z} +\hspace{0.17em}\mathrm{i}}\right| < 1$, where z = x + iy, is

• x² + y² < 1

• x² - y² < 1

• x² + y² > 1

• 2x² + 3y² < 1

If n is an integer which leaves remainder one when divided by three, then ${\left(1 + \sqrt{3}\mathrm{i}\right)}^{\mathrm{n}} + {\left(1 - \sqrt{3}\mathrm{i}\right)}^{\mathrm{n}}$ equals

• - 2^{n + 1}

• 2^{n + 1}

• - (- 2)ⁿ

• - 2ⁿ

The period of ${\sin }^4\left(\mathrm{x}\right) + {\cos }^4\left(\mathrm{x}\right)$ is

• $\frac{{\mathrm{\pi }}^4}{2}$

• $\frac{{\mathrm{\pi }}^2}{2}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

8.

If 3 cos x $\ne$ 2 sin x, then the general solution of ${\sin }^2\left(\mathrm{x}\right) - \cos \left(2\mathrm{x}\right) = 2 - \sin \left(2\mathrm{x}\right)$ is

• $\mathrm{n\pi } + {\left(- 1\right)}^{\mathrm{n}}\frac{\mathrm{\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\frac{\mathrm{n\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• $\left(4\mathrm{n} \pm 1\right)\frac{\mathrm{\pi }}{2}, \mathrm{n} \in \mathrm{Z}$

• (2n - 1)$\mathrm{\pi }, \mathrm{n} \in \mathrm{Z}$

If X is a binomial variate with the range {0, 1, 2, 3, 4, 5, 6} and P(X = 2) = 4P(X = 4), then the parameter p of X is

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$

• $\frac{3}{4}$

The area (in square unit) of the circle which touches the lines 4x + 3y = 15 and 4x + 3y = 5 is

• 4$\mathrm{\pi }$

• $3\mathrm{\pi }$

• $2\mathrm{\pi }$

• $\mathrm{\pi }$