Wat is compiler?

• Applcaton software

• System software

• Utility software

• All of these

The coefficient of x⁴ in (1 + x + x³ + x⁴)¹⁰ is

• 210

• 100

• 310

• 110

The locus of centre of circles which cuts orthogonally the circle x² + y² - 4x + 8 = 0 and touches x + 1 = 0, is

• y² + 6x + 7 = 0

• x² + y² + 2x + 3 = 0

• x² + 3y + 4 = 0

• None of the above

The condition for the line lx + my + n = 0 to be a normal to $\frac{{\mathrm{x}}^2}{25} + \frac{{\mathrm{y}}^2}{9} = 1$ is

• $\frac{{\mathrm{l}}^2}{9} + \frac{{\mathrm{m}}^2}{\mathrm{l}25} = \frac{{\mathrm{n}}^2}{256}$

• $\frac{9}{{\mathrm{m}}^2} + \frac{25}{{\mathrm{l}}^2} = \frac{256}{{\mathrm{n}}^2}$

• $\frac{{\mathrm{l}}^2}{9} - \frac{{\mathrm{m}}^2}{\mathrm{l}25} = \frac{{\mathrm{n}}^2}{256}$

• None of these

The least value of a, for which the function a $\frac{4}{\sin \left(\mathrm{x}\right)} + \frac{1}{1 - \sin \left(\mathrm{x}\right)}$ has at east one solution in the interval $\left(0, \frac{\mathrm{\pi }}{2}\right)$, is

• 9

• 4

• 5

• 1

16.

If one line ofregression coefficient is less than unity, then the other will be

• less than unity

• equal to unity

• greater than unity

• All of these

Roots of equation x³ - 6x + 1 = 0 lie in the interval

• (2, 3)

• (3, 4)

• (3, 5)

• (4, 6)

RAM is a

• volatile memory

• non-volatile memory

• cash memory

• dynamic memory

If $\underset{\mathrm{n}\to \infty }{\lim }\sum \frac{\log \left(\mathrm{n} + \mathrm{r}\right) - \log \left(\mathrm{n}\right)}{\mathrm{n}} = 2\left(\log \left(2\right) - \frac{1}{2}\right)$, then $\underset{\mathrm{n}\to \infty }{\lim }\frac{1}{{\mathrm{n}}^{\mathrm{\lambda }}}{\left[{\left(\mathrm{n} + 1\right)}^{\mathrm{\lambda }}{\left(\mathrm{n} + 2\right)}^{\mathrm{\lambda }} ... {\left(\mathrm{n} + \mathrm{n}\right)}^{\mathrm{\lambda }}\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{n}$}\right.}$ is equal to

• $\frac{4\mathrm{\lambda }}{\mathrm{e}}$

• ${\left(\frac{4}{\mathrm{e}}\right)}^{\mathrm{\lambda }}$

• ${\left(\frac{4}{\mathrm{e}}\right)}^{\frac{1}{\mathrm{\lambda }}}$

• ${\left(\frac{\mathrm{e}}{4}\right)}^{\mathrm{\lambda }}$

$\underset{\mathrm{x}\to 0}{\lim }\frac{\sin \left(\sin \left(\mathrm{x}\right)\right) - \sin \left(\mathrm{x}\right)}{{\mathrm{ax}}^3 + {\mathrm{bx}}^5 + \mathrm{c}} = \frac{- 1}{12}$, then

• $\mathrm{a} = 2, \mathrm{b} \in \mathrm{R}, \mathrm{c} = 0$

• $\mathrm{a} = - 2, \mathrm{b} \in \mathrm{R}, \mathrm{c} = 0$

• $\mathrm{a} = 1, \mathrm{b} \in \mathrm{R}, \mathrm{c} = 0$

• $\mathrm{a} = - 1, \mathrm{b} \in \mathrm{R}, \mathrm{c} = 0$