# 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