FMS Actual Paper – 2007 (Memory Based Questions)

–1 3
1. d Slope of the, line = =
–2 2
3
Equation is
y–1 3
= or 3x – 2y = 1
x–1 2
Hence (d) is the correct answer.
–1
2. b Slope of the line = = 1
–1
3. d
4. c
Answers and Explanations
equation is y–2 1
x–3 =
or x – y = 1
Hence (b).
(0, 4) C
A
(–1, –1)
y
( )
B(3,
5)
3 1
Slopes of lines AB, BC & AC are , and5 .
2 3
The length of the sides AB, BC and AC are
52 units, 10 units and 26 units.
As. AC 2 + BC 2 < AB 2 ; It is an obtuse triangle. Hence (d).
A
a
60°
h
B D C
a= 3 3units
2 2 2
AB BD AD
= +
2
2 ⎛a⎞ 3 3
or h = a – ⎜ ⎟ = a = × ( 3 3)
⎝2⎠ 2 2
or h = 4.5 units. hence (c) is correct.
x
FMS ACTUAL PAPER 2007 Page 1
5. b
7 log7 log7 c
log6
= = =
log6 log2+ log3 a+ b
Hence, (b) is correct.
6. c If x lies between 2 and 3 then it is greater than 2 and
less than 3.
7. a
8. a
9. b
10. b
⇒ ( x–2) > 0and
(x – 3) < 0
⇒ ( x–2) ( x–3) < 0 . Hence (b) is always correct.
(a) is incorrect and (c) is correct for some values of x,
only.
2
6 x–x 0
+ ≥
2
⇒ x –x–6 ≤0
or ( x+ 2) ( x–3) ≤0
⇒–2≤x ≤3
Hence (a) is correct.
1
3
+ 2
3
+ 3
3
+ ........12
3
2 2 2 2
1 + 2 + 3 + ........ + 12
2
⎧⎪12( 12+ 1)
⎫⎪
⎨ ⎬
⎪ 2 ⎪ 234
=
⎩ ⎭
=
12 12 1 12 2 1 25
( + ) ( × + )
6
Hence (a) is correct.
2 2
1+° i 1+° i + 2i°
= = =° i
1–i° 2 2 1+ 1
( 1+° i )
( 1 ) – ( i°
)
2 ( )
100
⎛1+° i ⎞
50
⎜ ⎟ = i° = 1
⎝1–i° ⎠
Hence (b) is correct.
6 6
⎛ –1+ i 3 ⎞ ⎛ –1–i 3⎞
=
⎜ ⎟ +
⎜ ⎟
⎝ 2 ⎠ ⎝ 2 ⎠
( +
2
)
( ) ( )
( )
( ) ( )
⎛ ⎞ ⎛ ⎞
⎜ 1 i 3 ⎟ ⎜ 1–i 3 ⎟
= ⎜ ⎟ +
2 2 ⎜ 2 2⎟
⎜ 1 – i 3 ⎟ ⎜ 1 – i 3 ⎟
⎝ ⎠ ⎝ ⎠