From a point on the level ground, the angle of elevation of top of a pole is $30°$ on moving 20metres nearer,the angle of elevation is $45°$. Then,the height of the pole $\left(\mathrm{in} \mathrm{metres}\right)$, is

• $10\left(\sqrt{3} - 1\right)$

• $10\left(\sqrt{3} - 1\right)$

• 15

• 20

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected at random, the probability that it is a black or a red ball, is

• $\frac{1}{3}$

• $\frac{1}{4}$

• $\frac{5}{12}$

• $\frac{2}{3}$

The probability of getting qualified in IITJEE and EAMCET by a student are respectively $\frac{1}{5} \mathrm{and} \frac{3}{5}$. The probability that the student gets qualified for atleast one of these test, is

• $\frac{3}{25}$

• $\frac{8}{25}$

• $\frac{17}{25}$

• $\frac{22}{25}$

One die and a coin (both unbiased) are tossed simultaneously. The probability of getting 5 on the top of the die and tail on the coin is

• $\frac{1}{2}$

• $\frac{1}{12}$

• $\frac{1}{6}$

• $\frac{1}{8}$

5.

If the axes are rotated through an angle 45° in the positive direction without changing the origin,then the co-ordinates of the point ($\sqrt{2}$, 4) in the old system are

• $\left(1 - 2\sqrt{2}, 1 + 2\sqrt{2}\right)$

• $\left(1 + 2\sqrt{2}, 1 - 2\sqrt{2}\right)$

• $\left(2\sqrt{2}, \sqrt{2}\right)$

• $\left(\sqrt{2}, 2\right)$

If a straight line perpendicular to 2x - 3y + 7 = 0 forma triangle with the co-ordinate axes whose area is 3 sq. units, then the equation of the straight line is

• $3\mathrm{x} + 2\mathrm{y} = \pm 2$

• $3\mathrm{x} + 2\mathrm{y} = \pm 6$

• $3\mathrm{x} + 2\mathrm{y} = \pm 4$

• $3\mathrm{x} + 2\mathrm{y} = \pm 8$

• ${\left({\mathrm{x}}^2\mathrm{y}\right)}^{2/3} + ({\mathrm{xy}}^2{)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} = 1$

• $\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right) = 4\mathrm{xy}$

• $\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right) = 12\mathrm{xy}$

• ${\left({\mathrm{x}}^2 - {\mathrm{y}}^2\right)}^2 = 16\mathrm{xy}$

If ( - 2, 6) is the image of the point (4, 2) with respect to the line L = 0, then L is equal to

• 6x - 4y - 7 = 0

• 2x + 3y - 5 = 0

• 3x - 2y + 5 = 0 

• 3x - 2y + 10 = 0

If the co-ordinate axes are the bisectors of the angles between the pair of lines ${\mathrm{ax}}^2 + 2\mathrm{hxy} + {\mathrm{by}}^2 = 0 \mathrm{where} {\mathrm{h}}^2 >\mathrm{ab} \mathrm{and} \mathrm{a} \ne \mathrm{b}, \mathrm{then}$

• a + b = 0 

• h = 0

• $\mathrm{h} \ne 0, \mathrm{a} + \mathrm{b} = 0$

• $\mathrm{a} + \mathrm{b} \ne 0$

If the angle 20 is acute, then the acute angle between the pair of straight lines ${\mathrm{x}}^2\left(\cos \left(\mathrm{\theta }\right) - \sin \left(\mathrm{\theta }\right)\right) + 2\mathrm{xycos}\left(\mathrm{\theta }\right) + {\mathrm{y}}^2\left(\cos \left(\mathrm{\theta }\right) + \sin \left(\mathrm{\theta }\right)\right) = 0$

• $2\mathrm{\theta }$

• $\frac{\mathrm{\theta }}{2}$

• $\frac{\mathrm{\theta }}{3}$

• $\mathrm{\theta }$