Equation of tangent to the circle x² + y² - 2x - 2y + 1 = 0 perpendicular to y = x is given by

• $\mathrm{x} + \mathrm{y} \pm 1 = 0$

• $\mathrm{x} + \mathrm{y} = 2 \pm \sqrt{3}$

• $\mathrm{x} + \mathrm{y} \pm 3 = 0$

• None of these

If A and B are two such events that $\mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) = \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$, then which of the following is true?

• P(a) + P(B) = 0

• P(A) + P(B) = P(A)P(B/A)

• P(A) + P(B) = 2P(A)P(B/A)

• None of the above

The y - coordinate of a point P on the line joining A(7, 2,1) and B(10, 5, 7) is 4. Then, x and z - coordinates of the point are

• x = 9, z = 5

• x = 3, z = 7

• x = 2, z = 3

• None of these

If point D divides the base BC of a $∆$ABC in the ratio n : m, then the value of mBD² + nCD² + (m + n)AD² is

• mAC² + nAB²

• (m + n)(AC² + AB²)

• nAC² + mAB²

• None of these

A man is standing on the horizontal plane. The angle of elevation of top of the pole is $\mathrm{\alpha }$. If he walks a distance double the height of the pole, then the elevation of the pole is $2\mathrm{\alpha }$. The value of $\mathrm{\alpha }$ is

• $\frac{\mathrm{\pi }}{12}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{6}$

6.

If f(x) = $$\begin{gathered} \left\{\frac{\sin \left[\mathrm{x}\right]}{\left[\mathrm{x}\right]} \mathrm{for} \left[\mathrm{x}\right] \ne 0 \\ 0 \mathrm{for} \left[\mathrm{x}\right] = 0\right\} \end{gathered}$$

where [x] denotes the greatest integer less than or eual to x, then $\underset{\mathrm{x}\to 0}{\lim }\mathrm{f}\left(\mathrm{x}\right)$ is equal to

• 1

• - 1

• 0

• Does not exist

The value of the angle between two straight lines y = $\left(2 - \sqrt{3}\right)\mathrm{x} + 5$ and $\mathrm{y} = \left(2 + \sqrt{3}\right)\mathrm{x} - 7$ is

• $30°$

• $60°$

• $45°$

• $90°$

Which of the following is a universal gate?

• NAND

• OR

• AND

• NOT

The value of sin(50°) cos (10°) + cos(50°) sin(10°) is

• $\frac{1}{2}$

• $\sqrt{3}$

• $\frac{\sqrt{3}}{2}$

• 1

Probability of getting a total of 7 or 9 in a single throw of two dice is

• $\frac{5}{18}$

• $\frac{1}{6}$

• $\frac{1}{9}$

• None of these