FMS Actual Paper – 2007 (Memory Based Questions)

logx logy logz
20. b Let = = = k
2 2 2 2 2 2 1
a + b + ab b + c + bc c + a + ac
21. d
and x (a–b) .y (b – c) . z (c–a) = k 2
( a–blogx ) + ( b–clogy ) + ( c–alogz ) = logk2
2 2 2 2
{ ( ) ( ) ( ) ( )
⇒ k1 a–b a + b + ab + b–c b + c + bc
2 2
( ) ( )}
= c–a c + a + ac logK2
2
⇒ logK g= 0
⇒ K2 = 1
Hence, (b) is the answer.
1 –1
2x3 + 2x 3 = 5
1
3
Let x t
=
2
2t 5or 2t
2
⇒ + = –5t + 2= 0
t
1
3 1
⇒ t = x = 2or
2
1
⇒ x = 8or
8
Hence, (d).
⎡ ⎤
⎢ –6 2⎥ 1
⎢ ⎥3
⎢⎣ ⎥⎦
22. a ( ) 1
0.000064 = 64× 10
1
⎡ 1⎤3 ⎢⎡ 2
–3 ⎤2⎥
= ⎢⎢( 8× 10 ) ⎥ ⎥
⎢⎣ ⎦ ⎥
⎢⎣ ⎥⎦
1 1
=
–3
8× 10 3 =
–1
2× 10 3 –1
= 2× 10
( ) ( ) × 3
= 0.2
Hence (a).
23. a (1 + i) 6 + (1 + i) 4 = (1 + i) 4 [(1 + i) 2 + 1]
= (1 2 + i 2 + 2i)2 [1 2 + i + 2i + 1]
= [4 (i) 2 ] [1 + 2i]
= (–4) (1 + 2i)
= (–4 – 8i)
24. a Let N = total number of students
Number of married students
FMS ACTUAL PAPER 2007 Page 3
N
=
20
Number of unmarried students 19 = N
20
Number of married female students
N
=
80
Number of unmaried male students 12 = N
20
Number of unmaried female students
7
= N
20
Number of married female student N 20 1
⇒ = × = .
Number of un-married female student 80 7N 28
Number of married male students 3N 20 1
& = × = .
number of un-married male students 80 12N 16
⇒ Only (I) is valid .
⇒ Option (a) is correct
26. b Final price, A = 8748 Rs.
Time = n = 3 years
depreciation rate = r = –10%
Let the price, 3 years ago be, P
n
⎛ r ⎞
Then, A = P⎜1+ ⎟
⎝ 100⎠
3
⎛ 10 ⎞
or 8748 = P⎜1– ⎟
⎝ 100⎠
⇒ P = 12,000
Hence (b) is correct.
27. c Volume of cylinder = 2
r h
π×
22 2
= × ( 8) × ( 14)
7
= 2816 cc.
Volume of cuboid = a2 × h
= (8) 2 × (14)
= 896 cc.
The difference is 1920 cc.
Hence (c) is correct.
28. c Let the number of balls be N,
9× 10× 11
= N = = 8750
3
4 22 ⎛ 3 ⎞
× × ⎜ ⎟
3 7 ⎝10⎠ Hence (c) is correct.