Indian Institute of Information Technology 2006 Entrance Exams IIT Entrance Exams JAM BIOTECHNOLOGY TEST - Question Paper
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be 2 vectors. The sine of the angle ranging from a
and b is:
(A) ?
2
(B) 6
7
(C) 5
7
(D) 1
7
85. The angle ranging from the lines
x - one ? y ? two ? z - 3
and
x ? one ? y - two ? z ? three is:
(A) ?
2
(B) ?
6
(C) ?
4
(D) ?
3
1 - two 3
6 2 4
86. Let a and b be 2 non-zero real numbers such that z = a + ib and z1 = iz. Which of the subsequent statements is TRUE:
?
(A) The principal part of the arguments of z and z1 differ by
2
(B) The principal part of the arguments of z and z1 differ by ?
(C) z1 is the complex conjugate of z
(D) z1 is a pure imaginary number
87. 4 horses A, B, C and D participated in a race. Horses A and B have equal chances to win. C is twice as likely to win as A and D is twice as likely to win as C. The probability that either B or C wins is
(A) 1
8
(B) 2
8
(C) 3
8
(D) 5
8
4
? ?
88. The component (value) which is independent of x in the expansion of ?1 ?
x ? one ?
is:
?? x ?
(A) 7
(B) 12
(C) 18
(D) 19
89. The area of the region bounded by the circle
x two ? y two ? a, (a ? 0) and ranging from the lines
x ? - a
2
and
x ? a is
2
2 ? ? ?
(A)
a ? three - two ?
2 ? ? ?
(B)
a ? three ? two ?
2 ? ? ?
? ?
(C)
2 ? three - two ?
a two ? ? ?
(D)
2 ? three ? two ?
8 ? r ? n
90. If S ? ??
? cos n ? , which of the subsequent statements is actual
(A)
n?1 ? a ?
S ?? r
, if (r, ?) are the polar coordinates such that r
(B) (C) (D)
a cos? ? r
S ?? r
a cos? ? r
S ?? r
a sec? - r
S ?? r
a sec? - r
, if (r, ?) are the polar coordinates such that r>a
, if (r, ?) are the polar coordinates such that r
, if (r, ?) are the polar coordinates such that r>a
91. Let a and ß be 2 real numbers satisfying a cos? ? b sin ? ? c , where a, b and c are three
real constants. Also a – ß ? 2n?, (n is an integer). The value of sin(? ? ? ) is:
(A) (B) (C)
(D)
2ab
a two ? b 2
ab
a two ? b 2
2ab
a two - b 2
a two - b 2
a two ? b 2
92. If the point (x, y) = (2, 4) minimizes Z = 6x + 10y subject to the constraints
2 x ? y = 4,
x ? two y = 10,
x ? y = six , then which of the provided constraints does NOT
effect the minimization point (2, 4) in minimizing Z = 6x + 10y. (A) no constraint can be omitted
(B) (C) (D)
93. ? ?
x ? two y = 10
x ? y = 6
2 x ? y = 4
i - 1
cos ? ? i sin ?
is 1 of the roots of the quadratic formula
x two ? bx ? c ? 0,
where b
3 3
and c are real constants. The value of b is:
(A)
1 - 3
(B)
3 -1
(C)
1 - 3
2
(D)
3 -1
2
94. Let f be a function provided by
f ( x) ? x - [ x],
where
x ? R and [x] is the greatest integer
described as [x] = n for all n = x < n+1. Then which of the subsequent statements is TRUE: (A) f is discontinuous at all integer values
(B) f is continuous everywhere
(C) f is discontinuous at all integer values other than at ‘0’ (D) f is discontinuous only at positive integer values
95. Let a, b, c, d and e be real and non-zero. For the provided matrix the subsequent statements is TRUE:
(A) Matrix A is non-singular for all distinct a, b, c, d and e
? a
?
A ? ? 0
? d
0 b ?
?
c 0 ? which of
0 ?
(B) The minor of every element of A is equal to the cofactor of the corresponding element
(C) The number of non-zero elements of the matrix
1 ?A - AT ? is 5
2
(D) The matrix
1 ?A - AT ? is symmetric
2
96. provided
x ln(x) dy - y ? 0, ( x ? 0),
dx
y(e) ? e , then y(4) is
(A) (B) (C) (D)
ln(4)
e ln(4)
e two ln(4)
e four ln(4)
? e cos x sin x
97. Let
?
f ( x) ? ?
1 ? x 2
for
| x |? 2
4
. The value of the integral ? f ( x) dx is:
(A)
?
?
?
1 - 3e 2
xe x-2
otherwise -2
(B) (C)
(D)
3e two ? 1
3e two - 1
3e 2
98. If y is a function of x described as
x is:
y ? a x ?
a x ?
1 . The derivative of y with respect to
1
a x ? L
(A)
(B)
ya x ln a
2 y ? a x
ya x ln a
2 y - a x x
(C)
ya ln a
2( y - a x )
x
(D)
ya ln a
2( y ? a x )
99. Let A, B, C and D be 4 points in a vertical line such that
AB ? one BC ? one CD. If a body
3 5
falls from rest from A, the ratio of the times of descending AB, BC and CD is: (A) 1 : four : 9
(B) 1 : three : five (C) 1 : two : three (D) 1 : one : 1
100. The resulting of 2 forces of 20N and 40N is acting vertically at ‘O’ as shown in the subsequent figure. If the angle XOP is 300, then the angle X'OQ is:
Y
Q
40N
P
20N
(A)
cos
X'? X O
-1 ?? ?
?
? two ?
(B)
cos
-1 ?? ?
?
? four ?
(C)
sin
-1 ?? ?
?
? two ?
(D)
sin
-1 ?? ?
?
? four ?
| Earning: Approval pending. |
