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1.

The negation of   $\sim S \vee (\sim r\wedge S)$ is  equivalent to

A) $S\wedge \sim r$

B) $S\wedge (r\wedge\sim S)$

C) $S\vee (r\vee\sim S)$

D) $S\wedge r$

2.

Let $\tan ^{-1}y= \tan ^{-1} x+\tan ^{-1}\left(\frac{2x}{1-x^{2}}\right)$ where  $|x|<\frac{1}{\sqrt{3}}$. Then, the value of y is

A) $\frac{3x-x^{3}}{1-3x^{2}}$

B) $\frac{3x+x^{3}}{1-3x^{2}}$

C) $\frac{3x-x^{3}}{1+3x^{2}}$

D) $\frac{3x+x^{3}}{1+3x^{2}}$

3.

If the angles of elevation of the top of a tower from three  collinear points A, B and C on a line leading  to the foot of the tower are 30° , 45° and 60° respectively , then the ratio AB:BC is

A) $\sqrt{3}:1$

B) $\sqrt{3}:\sqrt{2}$

C) $1:\sqrt{3}$

D) 2:3

4.

The mean of the data set comprising of 16 observations in 16. If one of the observation valued 16 is deleted and three new observations valued 3,4 and 5 are added to the data, then the mean of the resultant data is

A) 16.8

B) 16.0

C) 15.8

D) 14.0

5.

If 12 identical  balls are to be placed in 3 identical boxes, then the probability  that one of the boxes contains exactly 3 balls, is

A) $\frac{55}{3}\left(\frac{2}{3}\right)^{11}$

B) $\frac{55}{3}\left(\frac{2}{3}\right)^{10}$

C) $220\left(\frac{1}{3}\right)^{12}$

D) $22\left(\frac{1}{3}\right)^{11}$

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