In how many ways can a committee of 3 women and 2 men be chosen from a group of 7 men and 5 women?
500
350
720
210
Correct answer is D
For choosing, its different 'combinations'
Options - 7 men, 5 women
To pick - 2 men, 3 women
∴ The number of ways to choose a committee of 3 women and 2 men from a group of 7 men and 5 women is:
=5C3×7C2
=5×4×33×2×7×62×1
=10×21
=210
An exponential sequence (G.P.) is given by 92,34,18,....Find its sum to infinity
525
415
1312
634
Correct answer is A
Sum to infinity of a G.P when /r/ < 1 = a1−r
a = 92,r=T2T1=34+92
r = 34×29=16
S∞=921−16=9256=275
∴
2.0
3.0
2.5
4.0
Correct answer is C
∑ clock wise moments =∑ anti clock wise moments
= 60 x 10 = 30 x m
= 600 = 30 m
m = \frac{600}{30} = 20 N
W = mg ==> m = \frac{W}{g}
∴ m = \frac{20}{10} = 2kg
If f : x → 2 tan x and g : x → √(x^2 + 8), find ( g o f )(45^o)
4
2√3
6
3√2
Correct answer is B
f : x → 2 tan x
g : x → √(x^2 + 8)
( g o f ) = √((2 tan x)^2 + 8)
( g o f )(45º) = √((2 tan 45º)^2 + 8)
= √(4 + 8) = √12
= √(4 x 3)
∴ 2√3
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