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

= Rs. 17100
His amount from 1-4-2006 to 31-3-2007
10250 10 10250 10 1
100 100 2
´ ´
= + ´
= 12300 + 6150 = Rs. 18450
Total amount = 16200 + 17100 + 18450 = Rs. 51750
84. ( )1
n n n
n
lim two 7
®¥
+ is equal to:
a. 7e b. seven c. 2e d. 2
84. b ( )1
n nn
n
lim two 7
®¥
+
= seven ×
1
n n
n
2
lim 1
®¥ 7
æ æ ö ö ç + ç ÷ ÷ çè è ø ÷ø
= seven × (1 + 0)0
= 7
JMET / true PAPER Page three / SET A
85. A complex number z lies on the curve z + six = 3. The largest magnitude of z + three will be:
a. six b. three c. 36 d. 12
85. a
–6 –3 –2 –1
z+ six = three represents circle with centre (–6, 0) and radius 3.
z lies as the boundary of circle.
|z + 3| is maximum when it is at (–9, 0) and max |z + 3| = 6
86.
l–1
k 1
sin 2k –icos 2k
= l l
é æ p ö æ p öù
ê çè ÷ø çè ÷øú ë û å is equal to (where i = –1)
a. one b. –1 c. –i d. i
86. a
l 1
k 1
2k 2k
sin icos
l l
-
=
æ p pö
ç - ÷
è ø å
l 1
k 1
2k 2k
i cos isin
l l
-
=
æ p pö
= - ç + ÷
è ø å
l 1
k 0
2k 2k
i cos isin 1
l l
-
=
æ ö
ç æ p p ö ÷ = - ç ç + ÷ - ÷ ç è ø ÷
è ø
å
= -i(0 - 1) = i
87. An equilateral triangle is inscribed in a circle such that its vertices lie on the circumference of the
circle. A point is opted at random from within the circle. The probability of finding the point inside
the triangle is:
a.
3
2p
b.
3 3
4p
c.
2
3
p
d.
4
3 3p
Page four / SET A JMET / true PAPER
87. b The needed probability is the ratio of area of triangle to the area of the circle.
=
2
1 3
r three r
2 2
r
´ ´
p
=
3 3
4p
88. Set A consists of n elements. A subset X1 Í A is constituted. Elements of X1 are changed in A and
a 2nd subset X2 Í A is constituted. This process is repeated to form m subsets X1, X2, ...Xm of
A. The number of ways in which we can form X1, X2, ...Xm such that
m
1
i l
X A
=
U = are:
a. ( )m n 2– one b. mn two –1 c. ( )n m 2– one d. n!m!–1
88. c A = {1, 2}
\ n = 2
Let m = 2
x1 = f, x2 = {1, 2}

Earning:   Approval pending.