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

è ø è ø
= two +1 - one + two = two 2
JMET / true PAPER Page seven / SET A
93. For 0
2
p
< f < , let
2n 2n
n 0 n 0
sin ; cos
¥ ¥
= =
a = å f b = å f , then the value of a–1 + b–1 will be:
a. one b. i c. –1 d. 0
93. Here 2n 2n
n 0 n 0
sin and cos
¥ ¥
= =
a =å f b =å f
So, two 4
2
1
1 sin sin ...
1 sin
a= + f+ f+ ¥ =
- f
2 4
2
1
and one cos sin ...
1 cos
b=+ f+ f+ ¥ =
- f
Now, a-1 + b-1 = 1- sin2f + 1- cos2f = 2- 1= 1
94. describe ( )
n
1
i 1
x ( x – x )
=
f =Õ then the value of
n
i
i one i
x
x – x =
å is:
a. ( ) ( )
( )
n ' x –x x
x
f f
f
b. ( ) ( )
( )
n x – x ' x
x
f f
f
c. ( ) ( )
( )
x x – n ' x
x
f f
f
d. ( ) ( )
( )
x ' x –n x
x
f f
f
94. d ( ) ( ) ( ) ( ) ( )
n
i one two 4
i 1
x x x x x x x ... x x
=
f =Õ - = - - -
f'( x) = ( x - x2 )...( x - xn ) + (x - x1) (x - x3 ) ...( x- xn )
+... +(x - x1)...(x - xn-1)
( )
( ) one two n
' x one 1 1
...
x x x x x x x
f
= + + +
f - - -
( )
( )
1 one two 2 n n
1 two n
x ' x x x x x x x x x x
...
x x x x x x x
f - + - + - +
= + + +
f - - -
1 two n
1 two n
x x x
1 one ... 1
x x x x x x
=+ ++ + + +
- - -
n
i
i one i
x
n
x x
=
= +
- å
( )
( )
n
i
i one i
x x ' x
n
x x x
=
f
= -
- f å
( ) ( )
( )
x ' x n x
x
f - f
=
f
Page eight / SET A JMET / true PAPER
95.
a/n n
n –a/n
lim one 1
®¥ n 1
æ ö
çç ÷÷ è ø
is equal to:
a.
0 0
0 0
æ ö
ç ÷
è ø
b.
1 0
0 1
æ ö
ç ÷
è ø
c.
1 0
0 –1
æ ö
ç ÷
è ø
d.
0 1
–1 0
æ ö
ç ÷
è ø
95. a
n
n
1 a
1 n lim
n a
1
n
®¥
æ ö
ç ÷
ç ÷
ç- ÷ çè ÷ø
n
a a
1 1
lim one n n ntimes
n a a
1 1
n n
®¥
æ ö æ ö
ç ÷ ç ÷
= ç ÷ ´ ç ÷¼
ç - ÷ ç - ÷ çè ÷ø çè ÷ø
2 2
n two 2
1 a na na a
lim one nterms nterms nterms one nterm
® ¥ n n n n n
æ æ ö æ öæ ö ö = çç - +¼ ç -¼ ÷ - ç -¼ ÷çç - +¼ ÷÷ ÷÷ è è ø è øè ø ø
0 0
0 0
æ ö
=ç ÷
è ø
96. A toy consists of a base that is the part of sphere and a conical top. The quantity of the conical

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