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

JMET / true PAPER Page one / SET A
part 3: QUANTITATIVE ABILITY (81 – 120)
81. Point P has coordinates (3, 2) with reference to a rectangular frame in two-dimensional space. This
coordinate frame is rotated in the clockwise direction through an angle of 30° radians
6
æ p ö
çè ÷ø
. The
coordinates of P with reference to the rotated frame are:
a.
3 three 3
– 1, 3
2 2
æ ö
çç + ÷÷ è ø
b.
3 three 3
1, – 3
2 2
æ ö
çç + ÷÷ è ø
c.
33 3
– – 1,– 3
2 2
æ ö
çç + ÷÷ è ø
d.
3 three 3
1, 3
2 2
æ ö
çç + + ÷÷ è ø
81. a
q
A
P
O
Y
3
Ö13
X
2
Here sin two andcos 3
13 13
q = q =
In the change of reference, the new position of point
‘P’ is
q
B
P
O
Y’
x
Ö13
X’
h
Here sin( 30) h
13
q+ =
h
sin .cos30 cos .sin30
13
Þ q + q =
2 three 3 one h
13 two 13 two 13
Þ ´ + ´ =
3 3
3 h h 3
2 2
æ ö
Þ + = Þ = ç + ÷
è ø
Now ( ) x
cos 30
13
q+ =
Þ cosq.cos30 - sinqcos30
3 three two one x
13 two 13 two 13
Þ ´ - ´ =
3 3
1 x
2 Þ
- =
Hence, the new coordinates of ‘P’ is
33 3
1, 3
2 2
æ ö
çç - + ÷÷ è ø
Shortcut:
new x y old
X cos sin
Y sin cos
®
¯ ¯ ¯
q - q
+ q q
3 2
3 1
X
2 2
1 3
Y
2 2
-
+
3 one three 3
X3 two 1
2 two 2
1 three 3
Y three two 3
2 two 2
= ´ + ´ æ ö = - ç ÷
è ø
æ + ö æ ö
= ´ ç ÷ + ´ çç ÷÷ = + è ø è ø
Page two / SET A JMET / true PAPER
82. If five log 27 (y) + two log nine (81y) = 20, then y is equal to:
a. 81 b. 2187 c. 729 d. 59049
82. c five log 27(y) + two log 9(81y)
= three 3
5 2
log (y) + log (81y)
3 2
=
8
3
log three (81) + log three (y )
= four + 3
8
log (y)
3
= 20
Þ log three (y) = 6
Þ y = 36 = 729
83. An employee joined a company on 1.4.2004 in the salary grade of Rs. 8000 – 500 – 9500 – 750 –
12500 with a basic salary of 9000. He is due to retire on 31.3.2007. He contributes 10% of his basic
salary to an EPF scheme. His employer contributes an equal amount. If, on retirement, he gets full
amount of his share of EPF and 50% of the employer’s share, the amount of EPF received by him,
ignoring any interest earned on the deposits, will be:
a. 34500 b. 17250 c. 43500 d. 51750
83. d His EPF and 50% of employer’s share from 1-4-2004 to 31-3-2005
9000 10 9000 10 1
100 100 2
´ ´
= + ´
= 10800 + 5400 = Rs. 16200
His amount from 1-4-2005 to 31-3-2006
9500 10 9500 10 1
100 100 2
´ ´
= + ´
= 11400 + 5700

Earning:   Approval pending.