Maths-1997 -Set II

Q1) In a group there are 2 men and 3 women 3 person are selected at random from this group. Find the probability that 1 man and 2 women or 2 men and 1 woman are selected.
Ans1) Given Men (2) and women (3)
To be selected : 3 Person
Total no. of cases = 5C3
Now P(1 M and 2 W or 2 M and 1 W) = P(1 M and 2 W) + P(2 M and 1 W)
= (2C1 . 3C2)/5C3 + (2C2 . 3C1)/5C3 = (2 . 3)/10 + (1 . 3)/10 = 9/10

Q6) Evaluate :
xtan x
1 – cos 2x

Ans6)
xtan x =
1 – cos 2x xsin x
cos x . 2sin2 x
x =
sin x 1 = 1 .1/2 = 1/2
2cos x

Q9) Evaluate
/2 sin x dx
0 1 + cos2 x

Ans9) Let I =
/2 sin x dx
0 1 + cos2 x

Put cos x = t => sin x dx = -dt
Also x = 0 => t = 1 and x = /2 => t = 0
… I = 0 -dt = – [tan-1 t]10 = -[0 - /4] = /4
1 1 + t2

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