Correct Answer: D. {36}

Explanation

P = {3,6,9,12,18,36}; Q = { 4,36}

P n Q = {36}

Correct Answer: C. \(\frac{-33}{65}\)

Explanation

From Pythagoras' theorem

when sin x = \(\frac{12}{13}\), cos x = \(\frac{5}{13}\)

Using cos (x + y) = cosx cosy - sinxsiny

\(\frac{5}{13}\) * \(\frac{3}{5}\) - \(\frac{12}{13}\) * \(\frac{4}{5}\)

= \(\frac{-33}{65}\)

Correct Answer: B. 75N

Explanation

Let the normal reaction be R

R = Wcosø = mgcosø

= 15 * 10cos 60°

= 150 * 0.5000

= 75N

Correct Answer: C. 31.5m

Explanation

S = 12t + \(\frac{5}{2t^2}\) - t\(^3\);

ds/dt = 12 + 5t - 3t\(^2\)

At max height ds/dt = 0

i.e 12 + 5t - 3t\(^2\)

(3t + 4)(t -3) = 0;

t = -4/3 or 3

Hmax = 12[3] + \(\frac{5}{2[3]^2}\) - 3\(^3\)

= 36 + 45/2 - 27

= 31.5m

Explanation

Let. X = Prob. that a good mango is selected = 18/24= 3/4

Y Prob. that a bad mango is selected = 6/24 1/4

Using the binomial probability distribution, we have:

(X+Y)\(^6\) = X\(^6\) + \(^6{C}_1 {X}^5 Y\) + \(^6{C}_2 {X}^4 {Y}^2\) + \(^6{C}_3 {X}^3 {Y}^3\) + \(^6{C}_4 {X}^2 {Y}^4\) + \(^6{C}_5 {X} {Y}^5\) + \(^6{C}_6 {Y}^6\)

Probability that not more than 3 are bad is

= \(^6{C}_1 {X}^5 Y\) + \(^6{C}_2 {X}^4 {Y}^2\) + \(^6{C}_3 {X}^3 {Y}^3\)

= 6(3/4)\(^5\) (1/4) + 15(3/4)\(^4\) (1/4)\(^2\) + 20(3/4)\(^3\) (1/4)\(^3\)

= 6(243/1024)(1/4) + 15(81/256)(1/16) + 20(27/64)(1/64)

= 0.36 + 0.30 + 0.13

≈ 0.79

Correct Answer: D. \(\frac{8}{15}\)

Explanation

Prime number in the experiment are 2,3 and 5 with frequencies 10,14 and 8

P(obtaining a prime number) = \(\frac{10+14+8}{60}\)

= \(\frac{32}{60}\) or \(\frac{8}{15}\)

Explanation

\(^9{∫}_1\) \(\frac{x(2x-3)}{√x}\) dx = \(\frac{2x^2 - 3x)}{x^{1/2}}\)

= x\(^{-1/2}\) (2x\(^2\) - 3x)

= 2x\(^{3/2}\) - 3x\(^{1/2}\)

= \(\frac{2x^{3/2}}{3/2 + 1}\) - \(\frac{3x^{1/2}}{1/2 + 1}\)

= \(\frac{2x^{3/2}}{5/2}\) - \(\frac{3x^{1/2}}{3/2}\)

= \(^9{∫}_1\) [\(\frac{4x^{3/2}}{5}\) - \(\frac{6x^{1/2}}{3}\)]

[ \(\frac{4(9)^{3/2}}{5}\) - \(\frac{6^(9){1/2}}{3}\) ] - [ \(\frac{4(9)^{1/2}}{5}\) - \(\frac{6(1)^{1/2}}{3}\) ]

= [ \(\frac{4(27)}{5}\) - \(\frac{6(3)}{3}\) - [ \(\frac{4}{5}\) - 2 ]

= [ \(\frac{108}{5}\) - 2 ] - [ \(\frac{6}{5}\) ]

= \(\frac{78}{5}\) + \(\frac{6}{5}\) = \(\frac{84}{5}\)

16\(^{4/5}\)

Correct Answer: C. 6?3

Correct Answer: C. 4

Correct Answer: A. \(\frac{7}{6}\)

Explanation

3x\(^2\) - 7x + 6 = 0

α + β = \(\frac{7}{3}\);

αβ = 2;

\(\frac{1}{α}\) + \(\frac{1}{β}\) = \(\frac{α +β}{αβ}\)

\(\frac{7}{3}\) ÷ 2

= \(\frac{7}{6}\)