21.

According to Newton-Raphson method, the value of $\sqrt{12}$. upto three places of decimal will be

• 3.463

• 3.462

• 3.467

• None of these

If $\frac{{\left(3 - \mathrm{i}\right)}^2}{2 + \mathrm{i}} = \mathrm{A} + \mathrm{iB}$ where A and B are real numbers, then A and Bare equal to

• A = - 4, B = 2

• A = 2, B = - 4

• A = 2, B = 4

• None of these

The radical centre of the system of circles

            x² + y² + 4x + 7 = 0,

2(x² + y²) + 3x + 5y + 9 = 0

and               x² + y² + y = 0 is

• (- 2, - 1)

• (1, - 2)

• (- 1, - 2)

• None of these

The sum of n terms of the series 1 + 5 + 12 + 22 + 35 + ... is

• $\frac{{\mathrm{n}}^2\left(\mathrm{n} + 1\right)}{8}$

• $\frac{{\mathrm{n}}^2\left(\mathrm{n} + 1\right)}{6}$

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

• None of these

If lines of regression are 3x+ 12y = 19 and 3y+ 9x = 46, then value of r_xy will be

• 0.289

• - 0.289

• 0.209

• None of these

If 1, w and w² are the cube roots of unity, then the value of (1 - w + w²)(1 + w - w²) is equal to

• 4

• 0

• 2

• 3

If geometric mean and harmonic mean of two numbers a and b are 16 and 64/5 respectively, then the value of a : b is

• 4 : 1

• 3 : 2

• 2 : 3

• 1 : 4

If the sum offour numbers in GP is 60 and the arithmetic mean of the first and last numbers is 18, then the numbers are

• 3, 9, 27, 81

• 4, 8, 16, 32

• 2, 6, 18, 54

• None of these

If f'(x) > 0, $\mathrm{x} \in \mathrm{R}, \mathrm{f}\text{'}\left(3\right) = 0$ and g(x) = $\mathrm{f}\left({\tan }^2\left(\mathrm{x}\right) - 2\tan \left(\mathrm{x}\right) + 4\right), 0 < \mathrm{x} < \frac{\mathrm{\pi }}{2}$, then g(x) is increasing in

• $\left(0, \frac{\mathrm{\pi }}{4}\right)$

• $\left(\frac{\mathrm{\pi }}{6}, \frac{\mathrm{\pi }}{3}\right)$

• $\left(0, \frac{\mathrm{\pi }}{3}\right)$

• $\left(\frac{\mathrm{\pi }}{4}, \frac{\mathrm{\pi }}{2}\right)$

If $\mathrm{f}\left(\mathrm{x}\right) = \log \left(\frac{1 + \mathrm{x}}{1 - \mathrm{x}}\right) \mathrm{and} \mathrm{g}\left(\mathrm{x}\right) = \frac{3\mathrm{x} +\hspace{0.17em}{\mathrm{x}}^3}{1 + 3{\mathrm{x}}^2}$, then fog(x) is equal to

• - f(x)

• 3f(x)

• [f(x)]³

• None of these