Cube root of 18 by using Newton-Raphson method will be

• 2.26

• 2.620

• 2.602

• None of these

The difference of the numbers (1100110011)₂ and (1101001011)₂ in binary system is

• (100000)₂

• (101010)₂

• (11000)₂

• (10111)₂

If the function f · $\mathrm{f} . [1, \infty ) \to [1, \infty )$ is defined by f(x) = 2^{x(x - 1)}, then f^-1(x) is defined by

• ${\left(\frac{1}{2}\right)}^{\mathrm{x}\left(\mathrm{x} - 1\right)}$

• $\frac{1}{2}\left(1 \pm \sqrt{4{\log }_2\left(\mathrm{x}\right)}\right)$

• $\frac{1}{2}\left(1 - \sqrt{1 - 4{\log }_2\left(\mathrm{x}\right)}\right)$

• None of these

By Newton-Raphson method, the positive root of the equation x⁴ - x - 10 = 0 is

• 1.871

• 1.868

• 1.856

• None of these

Which of the following function is inverse of itself

• $\mathrm{f}\left(\mathrm{x}\right) = \frac{1 - \mathrm{x}}{1 + \mathrm{x}}$

• g(x) = 5^log(x)

• h(x) = 2^{x(x - 1)}

• None of the above

Let f : R $\to$ R be the function defined by f(x) = $\sqrt{\mathrm{x} - 3} \forall , \mathrm{x} \in \mathrm{R}$. Then f^-1(x) = ?

• x + 3

• x² + 3

• $\frac{\mathrm{x} + 3}{2}$

• $\frac{{\mathrm{x}}^2 + 3}{2}$

Let Z denote the set of integers define f : $\mathrm{Z} \to \mathrm{Z}$ by f(x) = $$\begin{gathered} \left\{\frac{\mathrm{x}}{2}, \mathrm{x} \mathrm{is} \mathrm{even} \\ 0, \mathrm{x} \mathrm{is} \mathrm{odd}\right\} \end{gathered}$$, then f is

• onto but not one-one

• one-one but not onto

• one-one and onto

• neither one-one nor onto

Let f : $\mathrm{R} \to \mathrm{R}$ be defined by

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right) =\left\{ \mathrm{x} +\hspace{0.17em}2, \mathrm{x} \le - 1 \\ {\mathrm{x}}^2, - 1 < \mathrm{x} < 1 \\ 2 - \mathrm{x}, \mathrm{x} \ge 1\right\} \end{gathered}$$

Then, the value of f(- 1.75) + f(0.5) + f(1.5) is

• 0

• 1

• 2

• - 1

Two functions f : $\mathrm{R} \to \mathrm{R}$, g : $\mathrm{R} \to \mathrm{R}$ are defined as follows

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right) = \left\{0, \mathrm{x} \mathrm{is} \mathrm{rational} \\ 1, \mathrm{x} \mathrm{is} \mathrm{irational}\right\} \\ \mathrm{g}\left(\mathrm{x}\right) = \left\{- 1, \mathrm{x} \mathrm{is} \mathrm{rational} \\ 0, \mathrm{x} \mathrm{is} \mathrm{irrational}\right\} \end{gathered}$$

Then, (fog) $\left(\mathrm{\pi }\right)$ + (gof) (e) is equal to

• 0

• - 1

• 2

• 1

If the functions f and g are defined by f(x) = 3x - 4, g(x) = 2 + 3x for x $\in$ R respective, then g^-1(f^-1(5)) is equal to

• 1

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$