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

top is 30p sq. units and its height is 10 units. The total height of the toy is 19 units. The quantity of
the sphere (in cubic units) from which the base has been extracted is:
a.
256
3
p b.
64
3
p c.
108
3
p d.
500
3
p
96. d
Height of the cone = 10 units
quantity of the cone = 30 p cubic units.
Þ diameter of the cross part from where sphere has been sectioned = six units.
Height of the sectioned sphere = 19 – 10 = nine units.
Þ r + r two – 32 = 9
Þ r = five units
Þ quantity of the original sphere from which the base has been sectioned = four 3
r
3
p =
500
3
p
97. 2 vessels A and B of equal capacities contain mixtures of milk and water in the ratios four : one and
3 : 1, respectively. 25% of the mixture from A is taken out and added to B. After mixing it thoroughly,
JMET / true PAPER Page nine / SET A
an equal amount is taken out from B and added back to A. The ratio of milk to water in vessel A after
the 2nd operation is:
a. 79 : 21 b. 83 : 17 c. 77 : 23 d. 81 : 19
97. a Let there be 20L of mixture in both the vessels.
In A, milk = 16L and water = 4L
In B, milk = 15L and water = 5L
25% from A to B
Þ milk in B = 15 + four = 19L
Þ water in B = five + one = 6L
ratio = 19:6
Equal amount from B to A
Þ milk in A = 12 +
19
5 =
79
5
Þ water in A = three +
6
5 =
21
5
Hence, ratio = 79:21
98. MTNL has a waiting list of 5005 applicants for its recently launched mobile phone scheme. The list
indicates that there are at lowest five males ranging from any 2 females. The largest possible number of
females in the waiting list is:
a. 920 b. 835 c. 721 d. 1005
98. b F1M4M2M4M3M1FM4M2M4M3M...
Hence, largest possible number of females is
5005
6
= 834 + one = 835.
99. If you have three tickets to a lottery for which 10 tickets were sold and five prizes are to be given, the
probability that you will win at lowest 1 prize is:
a.
7
12
b.
9
12
c.
1
12
d.
11
12
99. d Probability that you will win at lowest 1 prize = one – probability that you will not win any prize.
= one –
5
3
10
3
C
C
=
11
12
100. We describe the modulus of a m × n matrix by |A| =
m
ij
j i 1
max a , j 1,2,...,n
=
æ ö
ç = ÷
è ø
å . The angle, q,

Earning:   Approval pending.