11.

System software : Utility software : :

• Operating system· Anti-virus

• Anti-virus Operating system

• Anti-virus MS office

• MS office Anti-virus

If f(x) = $$\begin{gathered} \left\{\frac{\sin \left[\mathrm{x}\right]}{\left[\mathrm{x}\right]}, \left[\mathrm{x}\right] \ne 0 \\ 0, \left[\mathrm{x}\right] = 0\right\} \end{gathered}$$, where [x] denotes the gretest function less than or equal to x, then $\underset{\mathrm{x}\to 0}{\lim }\mathrm{f}\left(\mathrm{x}\right)$ is equal to

• 1

• 0

• - 1

• Does not exist

The number of common tangents to two circles x² + y² = 4 and x² + y² - 8x + 12 = 0 is

• 1

• 2

• 3

• 4

If for all x, y $\in$ N, there exists a function f(x) satisfying f(x + y) = f(x) · f(y) such that f(1) = 3 and $\sum _{\mathrm{x}=1}^{\mathrm{n}}\mathrm{f}\left(\mathrm{x}\right) = 120$, then value of n will be

• 4

• 5

• 6

• None of these

If sin(a) and cos(a) are the roots of the equation ax² + bx + c = 0, then

• a² - b² + 2ac = 0

• (a - c)² = b² + c²

• a² + b² - 2ac = 0

• a² + b² + 2ac = 0

In $∆\mathrm{ABC}$, if cot(A), cot(B) and cot(C) are in AP, then a², b² and c² are in

• HP

• AP

• GP

• None of the above

A die is rolled three times. The probability of getting a larger number than the previous number is

• $\frac{5}{216}$

• $\frac{5}{54}$

• $\frac{1}{6}$

• $\frac{5}{36}$

If f(x) = ${\log }_{\mathrm{e}}\left(6 - \left|{\mathrm{x}}^2 + \mathrm{x} - 6\right|\right)$, then domain of f(x) has how many integral values of x ?

• 5

• 4

• infinite

• None of these

The graph of the equation y² + z² = 0 in three dimensional space is

• YZ-plane

• Z-axis

• Y-axis

• X-axis

If Z₁ = 1 + i, Z₂ = - 2 + 3i and Z₃ = $\frac{\mathrm{ai}}{3}$ are  collinear, where i² = - 1, then the value of a will be

• - 1

• 3

• 4

• 5