Equation of the tangent to the hyperbola 2x² - 3y² = 6. Which is parallel to the line y - 3x - 4 = 0 is

• y = 3x + 8

• y = 3x - 8

• y = 3x + 2

• None of these

If the coefficient of correlation between two variables is 0.32, covariance is 8 andvariance of x is 25, then variance of y is

• 36

• 25

• 64

• None of these

Ten coins are thrown simultaneously, the probability of getting atleast 7 heads is

• $\frac{63}{256}$

• $\frac{121}{172}$

• $\frac{113}{512}$

• $\frac{11}{64}$

When b_yx = 0.03 and b_xy = 0.3, then r is equal to approximately

• 0.003

• 0.095

• 0.3

• - 0.3

The feasible region represented x₁ + x₂ $\le$ 1, - 3x₁ + x₂ $\ge$ 3, (${\mathrm{x}}_1, {\mathrm{x}}_2 \ge 0$) is

• a polygon

• a singleton set

• empty set

• None of these

If x = $\frac{1}{2}\left(\sqrt{3} + \mathrm{i}\right)$, then x³ is equal to

• 1

• - 1

• i

• - i

If the complex numbers sin(x) + icos(2x) and cos(x) - isin(2x) are complex conjugate to each other, then the value of x is

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{8}$

• $\frac{3\mathrm{\pi }}{4}$

• None of these

8.

$\underset{\mathrm{x}\to 2^{+}}{\lim }\frac{\left|\mathrm{x} - 2\right|}{\mathrm{x} - 2}$ is equal to

• - 1

• 1

• 2

• - 2

${\cos }^4\left(\frac{\mathrm{\pi }}{8}\right) + {\cos }^4\left(\frac{3\mathrm{\pi }}{8}\right) +\hspace{0.17em}{\cos }^4\left(\frac{5\mathrm{\pi }}{8}\right) + {\cos }^4\left(\frac{7\mathrm{\pi }}{8}\right)$ is equal to

• $\frac{3}{2}$

• $- \frac{2}{3}$

• - 1

• 1

Number of solutions of the equationan $\tan \left(\mathrm{x}\right) + \sec \left(\mathrm{x}\right) = 2\cos \left(\mathrm{x}\right)$ lying in the interval $\left[0, 2\mathrm{\pi }\right]$ is

• 0

• 1

• 2

• 3