If the points (1, 1), (- 1, - 1), $\left(- \sqrt{3}, \sqrt{3}\right)$ are the vertices of a triangle, then this triangle is

• a right-angled triangle

• an isosceles triangle

• an equilateral triangle

• None of the above

The point of intersection of the lines $\frac{\mathrm{x} - 5}{3} = \frac{\mathrm{y} - 7}{- 1} = \frac{\mathrm{z} + 2}{1}$ and $\frac{\mathrm{x} + 3}{- 36} = \frac{\mathrm{y} - 3}{2} = \frac{\mathrm{z} - 6}{4}$ is

• (2, 10, 4)

• (21, 5/3, 10/3)

• (5, 7, - 2)

• (- 3, 3, 6)

The distance between the point (1, - 5, - 10) and the point of intersection of the plane x - y + z = 5 and the line $\frac{\mathrm{x} - 2}{3} = \frac{\mathrm{y} + 1}{4} = \frac{\mathrm{z} - 2}{12}$, will be

• 10

• 11

• 12

• 13

$\underset{\mathrm{h}\to 0}{\lim }\frac{\sqrt{\mathrm{x} +\hspace{0.17em}\mathrm{h}} - \sqrt{\mathrm{x}}}{\mathrm{h}}$ is equal to

• $\frac{1}{2\sqrt{\mathrm{x}}}$

• $\frac{1}{\sqrt{\mathrm{x}}}$

• $2\sqrt{\mathrm{x}}$

• $\sqrt{\mathrm{x}}$

$\underset{\mathrm{\theta }\to 0}{\lim }\frac{5\mathrm{\theta cos}\left(\mathrm{\theta }\right) - 2\sin \left(\mathrm{\theta }\right)}{3\mathrm{\theta } + \tan \left(\mathrm{\theta }\right)}$ is equal to

• 3/4

• - 3/4

• 0

• None of these

If cos(x + y) = ysin(x), then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is equal to

• $- \frac{\sin \left(\mathrm{x} +\hspace{0.17em}\mathrm{y}\right) + \mathrm{ycos}\left(\mathrm{x}\right)}{\sin \left(\mathrm{x}\right) + \sin \left(\mathrm{x} + \mathrm{y}\right)}$

• $\frac{\sin \left(\mathrm{x} +\hspace{0.17em}\mathrm{y}\right) + \mathrm{ycos}\left(\mathrm{x}\right)}{\sin \left(\mathrm{x}\right) + \sin \left(\mathrm{x} + \mathrm{y}\right)}$

• $\frac{- \sin \left(\mathrm{x} +\hspace{0.17em}\mathrm{y}\right) + \mathrm{ycos}\left(\mathrm{x}\right)}{\sin \left(\mathrm{x}\right) + \sin \left(\mathrm{x} + \mathrm{y}\right)}$

• None of the above

A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white, is

• $\frac{4}{49}$

• $\frac{1}{7}$

• $\frac{4}{7}$

• $\frac{12}{49}$

38.

A coin is tossed 4 times. The probability that atleast one head turns up 1s

• $\frac{1}{16}$

• $\frac{2}{16}$

• $\frac{14}{16}$

• $\frac{15}{16}$

A speaks truth in 75% cases and B speaks truth in 80% cases, The probability that they contradict each other in a statement, is

• $\frac{7}{20}$

• $\frac{13}{20}$

• $\frac{3}{5}$

• $\frac{2}{5}$

The probability that a leap year will have 53 Friday or 53 Saturday, is

• $\frac{2}{7}$

• $\frac{3}{7}$

• $\frac{4}{7}$

• $\frac{1}{7}$