Indian Institute of Technology Kanpur (IIT-K) 2006 JT Quant - Question Paper

3 3
= ´ + ´ = + =
107. The position vector of the mirror image of the point represented by the position vector r = 2ˆi + 3ˆj+ 4kˆ r
across the plane mirror x + y = 0 is:
a. -3ˆi -2ˆj + 4kˆ b. 2iˆ + 3ˆj - 4kˆ c. -2ˆi -3ˆj + 4kˆ d. 3iˆ + 2ˆj - 4kˆ
107. a ( ) x two y three z 4
say
1 one 0
- - -
= = = l
Let (l + 2, l + 3, 4) be the needed point then mid-point of line joining this point with provided point i.e. (2, 3, 4) lies on the
plane provided.
i.e.
2 two three 3
0
2 2
l+ + l+ +
+ =
Þ2l +10 = 0
Þ l = -5
Hence needed points is provided by (–3, –2, 4)
JMET / true PAPER Page 13 / SET A
108. A man six feet tall standing 50 feet away from the base of a tower observes that the angle subtended
by the tower at his eye level is tan–1 2. A flagstaff atop the tower subtends an angle of tan–1 0.1 at the
identical point. The height (in feet) of the flagstaff is nearest to:
a. 18 b. 20 c. 25 d. 22
108.
6
50
6
T - 6
h
q - b
a
90( ) q - b
b
q
Tanq = two and Tana =
1
10
T six 6 3
tan( ) , tan
50 50 25
-
q - b = b= =
tanq = tan(q - b + b)
T six 3
50 25 25(T 6) 150 2
1 T six three 50.25 3(T 6)
50 25
- + - +
Þ = =
- - × - -
Þ 2500 - 6(T - 6)= 25T
2536 = 31 T
2350 47
tan( )
31.50 31
q - b- =
Now ( ) h T 6
tan( )
50
+ -
q - b +a =
1 1
h 2536 six tan tan 47 tan one 31
31 10 50
- -
æ ö + - Þ æ ö + æ ö = ç ç ÷ ç ÷ ÷
è è ø è ø ø
1
47 1
31 10 31h 2536 186 tan tan
47 31 50 1
31 10
-
æ æ öö ç ç + ÷÷ + -
Þ ç ç ÷÷ =
ç ç - ÷÷ ´ ç ç ÷÷ è è ´ øø
470 31 31h 2536 186
310 47 31 50
+ + -
Þ =
- ´
501 31h 2350
263 31 50
+
Þ =
´
Þh =19.44
Hence h » 18 ft.
109. A, B and C are assigned a piece of work which they can complete by working together in 15 days.
Their efficiencies (measured in terms of rate of doing work) are in the ratio one : two : 3. After
1
3 of the
work is completed, 1 of them has to be withdrawn due to budget constraint. Their wages per day
are in the ratio three : five : 6. The number of days in which the remaining 2 persons can complete the
work (at optimal cost) is:
a. 18 b. 20 c. 15 d. 12
109. d
A, B and C together in 15 days.
Þ A alone in 90 days

Earning:   Approval pending.