1. Xtra Edge February 2012 - Career Point

28.
x
x
y
∴ x → side of square
y → rad. of circle
∴ 4x + 2πy = 36 ..... (1)
Now area A = x 2 + πy 2
A = x 2 ⎛18
– 2x
⎞
+ π ⎜ ⎟ [From (1)]
⎝ π ⎠
dA 4
= 2x – (18 – 2x)
dx π
2
d A
= 2 + 8/π > 0 ⇒ min 2
dx
m area
Form min m dA
area = 0
dx
36
⇒ x =
π + 4
18
From (1) , y =
π + 4
144
Length of one piece = 4x =
π + 4
36π
Length of other piece = 2πy =
π + 4
1
29. Let = u ;
x
2
1 1
= v; = w
y z
Given equation can be written in form
⎡ 2 3 10 ⎤ ⎡ u ⎤ ⎡4⎤
⎢
⎥
⎢
4 – 6 5
⎢ ⎥
⎥ ⎢
v
⎥
=
⎢ ⎥
⎢
1
⎥
⎢⎣
6 9 – 20 ⎥⎦
⎢⎣
w⎥⎦
⎢⎣
2⎥⎦
A ⋅ X = B
X = A –1 ⋅ B
Adj(
A)
X = . B, |A| = 1200
| A |
X =
⎡ 75
⎢
⎢
110
⎢⎣
72
150
– 100
0
1200
75
30
– 24
⎤ ⎡4⎤
⎥
.
⎢
1
⎥
⎥ ⎢ ⎥
⎥⎦
⎢⎣
2⎥⎦
⎡600⎤
⎡ u ⎤ ⎢
X =
⎢ ⎥ 400
⎥ ⎡1/
2⎤
⎢
v
⎥
= ⎢ ⎥ =
⎢ ⎥
⎢240⎥
⎢
1/
3
⎥
⎢⎣
w⎥
⎣ ⎦
⎦
⎢ ⎥
1200
⎣1/
5⎦
u = 1/2 ⇒ x = 2
v = 1/3 ⇒ y = 3
w = 1/5 ⇒ z = 5
At a Glance
Some Important Practical Units
1. Par sec : It is the largest practical unit of
distance.
1 par sec = 3.26 light year
2. X-ray unit : It is the unit of length.
1 X-ray unit = 10 –13 m
3. Slug : It is the unit of mass.
1 slug = 14.59 kg
4. Chandra Shekhar limit : It is the largest
practical unit of mass.
1 Chandra Shekhar limit = 1.4 × Solar mass
5. Shake : It is the unit of time.
1 Shake = 10 –6 second
6. Barn : It is the unit of area.
1 barn = 10 –28 m 2
7. Cusec : It is the unit of water flow.
1 cusec = 1 cubic foot per second flow
8. Match No. : This unit is used to express velocity
of supersonic jets.
1 match no. = velocity of sound
= 332 m/sec.
9. Knot : This unit is used to express velocity of
ships in water.
1 knot = 1.852 km/hour
10. Rutherford : It is the unit of radioactivity.
1 rutherford (rd) = 1 × 10 6 disintegrations/sec
11. Dalton : It is the unit of mass.
1 12
1 dalton = mass of C = 931 MeV
12
= 1 a.m.u.
12. Curie : It is the unit of radioactivity.
1 curie = 3.7 × 10 10 disintegration / sec
XtraEdge for IIT-JEE 101 FEBRUARY 2012