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(a) HN 2 SO 3 H
(b) (NH 2 ) 2 CO
(c) C 6 H 5 SO 3 H
(d) (NH 4 ) 2 SO 4
PARAGRAPH 2
In stereoisomerism, the isomers differ only in the
spatial arrangement of groups about the central metal
atom. It is of two types : (i) Geometrical isomerism, this
isomerism arises in heteroleptic complexes due to the
difference in geometrical complexes and geometrical
arrangement of the ligands around the central atom.
(ii) Optical isomerism, this isomerism is shown by chiral
molecules, i.e., the molecules which do not have plane
of symmetry.
35. The number of isomers exhibited by [Cr(NH 3 ) 3 Cl 3 ] is
(a) 2 (b) 3 (c) 4 (d) 5
36. Which of the following will exhibit optical
isomerism?
(a) [Cr(en)(H 2 O) 4 ] 3+
(b) [Cr(en) 3 ] 3+
(c) trans-[Cr(en)Cl 2 (NH 3 ) 2 ] +
(d) trans-[Cr(en) 2 Cl 2 ] +
MATHEMATICS
SECTION 1 (Maximum Marks : 18)
• This section contains SI questions.
• Each question has FOUR options (a), (b), (c) and (d). ONLY ONE
of these four options is correct.
• For each question, darken the bubble corresponding to the
correct option in the ORS.
• For each question, marks will be awarded in one of the following
categories :
Full Marks : +3 If only the bubble corresponding to the correct
option is darkened.
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –1 In all other cases.
39. If the angle between the curves y = 2 x and y = 3 x is
α, then the value of tanα is equal to
log( 3/ 2)
6
(a)
(b)
1+
(log 2)(log 3)
7
1
log( 6)
(c)
(d)
7
1+
(log 2)(log 3)
40. The solution of the differential equation
ysin(x/y)dx = (xsin(x/y) – y)dy satisfying y(/4) = 1
is
x
(a) cos = loge
y + 1 y
2 (b) x
sin = loge
y + 1 y
2
x
(c) sin = loge
x − 1 y
2
x
(d) cos =−loge
x − 1 y
2
41. Let a, b be two distinct roots of acosq + bsinq = c,
where a, b and c are three real constants and q [0, 2].
Then a+ bis also a root of the same equation, if
(a) a + b = c
(b) b + c = a
(c) c + a = b
(d) c = a
42. If x 1 , x 2 , ..., x 18 are observations such that
18
j=
1
18
∑( x j − 8)
= 9 and ∑( x j − 8) 2 = 45,
then the
j=
1
standard deviation of these observations is
81
(a) (b) 5 (c) 5 (d) 3/2
34
SECTION 2 (Maximum Marks : 32)
• This section contains EIGHT questions.
• Each question has FOUR options (a), (b), (c) and (d). ONE OR
MORE THAN ONE of these four option(s) is(are) correct.
• For each question, darken the bubble(s) corresponding to all the
correct option(s) in the ORS.
• For each question, marks will be awarded in one of the following
categories :
Full Marks : +4 If only the bubble(s) corresponding to all the
⎛1
− x ⎞
correct option(s) is(are) darkened.
⎜ ⎟
⎛ 1 + x ⎞⎝
1 − x ⎠
Partial Marks : +1 For darkening a bubble corresponding
37. lim
to each correct option, provided NO incorrect option is
x
⎜
→ ⎝ + x
⎟
1 2 ⎠
darkened.
(a) is 1
(b) does not exist
Zero Marks : 0 If none of the bubbles is darkened.
Negative Marks : –2 In all other cases.
• For example, if (a), (c) and (d) are all the correct options for
2
(c) is
(d) is ln 2
a question, darkening all these three will result in +4 marks;
3
darkening only (a) and (d) will result in +2 marks; and darkening
(a) and (b) will result in –2 marks, as a wrong option is also
1
dx
darkened.
38. If I = ∫ , then
1
π/ 2
0
+ x
43. Let PQR be a triangle. Let
a= QRb , = RP and c = PQ.
(a) log e 2 < I < π/4 (b) log e 2 > I a= QRb , = RP and c = PQ.
If |
a| = 12,| b|
= 4 3 and
b⋅
c =24, then
(c) I = π/4 (d) I = log e 2
which of the following is (are) true?
76 CHEMISTRY TODAY | APRIL ‘17