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13. 15g of a solute in 100g water makes a solution freeze<br />
at –1ºC. What will be the depression in freezing point<br />
if 30g of a solute is dissolved in 100g of water ?<br />
14. The half lives of decomposition of gaseous CH 3 CHO<br />
at constant temperature but at initial pressure of<br />
364mm and 170mm Hg were 410 second and 880<br />
second respectively. Hence what is the order of<br />
reaction.<br />
15. The number of S–S bonds in sulphur trioxide trimer<br />
(S 3 O 9 ) is ....... .<br />
16. The number of peroxo linkages present in the<br />
[H 4 B 2 O 8 ] 2– is ..... .<br />
17. The maximum number of structural isomers (acyclic<br />
and cyclic) possible for C 4 H 8 are ....... .<br />
18. What is the no. of lone pair of electrons present on N<br />
in Trisilylamine ?<br />
19. A small amount of solution containing 24 Na with<br />
activity 2 × 10 3 dps was administered into the blood<br />
of patient in a hospital. After 5 hour a sample of the<br />
blood drawn out from the patient shared an activity<br />
of 16 dps per cm 3 . (t 1/2 of 24 Na = 15 hrs.) Find the<br />
volume (in L) of blood in patient.<br />
[Given : log 1.2598 = 0.1003]<br />
MATHEMATICS<br />
Questions 1 to 4 are multiple choice questions. Each<br />
question has four choices (A), (B), (C) and (D), out of<br />
which ONLY ONE is correct.<br />
1. The largest term in the expansion of (3 + 2x) 50 , where<br />
x = 1/5, is -<br />
(A) 5th<br />
(B) 6th<br />
(C) 8th<br />
(D) 9th<br />
1<br />
2. If sin<br />
–1 ⎡ 3sin 2θ<br />
⎤<br />
2<br />
⎢ ⎥ = tan –1 x, then x =<br />
⎣5+<br />
4cos 2θ⎦<br />
(A) tan 3θ<br />
(B) 3 tan θ<br />
(C) (1/3) tan θ<br />
(D) 3 cot θ<br />
3.<br />
(cos x −1)(cos x − e<br />
The integer n for which lim<br />
x→0<br />
n<br />
x<br />
a finite nonzero number is -<br />
(A) 1 (B) 2<br />
(C) 3 (D) 4<br />
x<br />
)<br />
is<br />
x<br />
4. If f(x) = and g(x) =<br />
sin x<br />
then in this interval -<br />
x<br />
tan x<br />
where 0 < x ≤ 1,<br />
(A) both f(x) and g(x) are increasing functions<br />
(B) both f(x) and g(x) are decreasing functions<br />
(C) f(x) is an increasing function<br />
(D) g(x) is an increasing function<br />
Questions 5 to 9 are multiple choice questions. Each<br />
question has four choices (A), (B), (C) and (D), out of<br />
which MULTIPLE (ONE OR MORE) is correct.<br />
5. If a, b, c are in A.P., and a 2 , b 2 , c 2 are in H.P., then<br />
(A) a = b = c<br />
(C) a, b, c are in H.P.<br />
(B) a, b, – 2<br />
1 c are in G.P.<br />
(D) – 2<br />
1 a, b, c are in G.P.<br />
6. The system of equations<br />
–2x + y + z = a<br />
x – 2y + z = b<br />
x = y – 2z = c<br />
has<br />
(A) no solution if a + b + c ≠ 0<br />
(B) unique solution if a + b + c = 0<br />
(C) infinite number of solutions if a + b + c = 0<br />
(D) none of these<br />
7.<br />
x<br />
The function f(x) =<br />
1+<br />
| x |<br />
is differentiable on -<br />
(A) (0, ∞) (B) [0, ∞)<br />
(C) (–∞, 0)<br />
(D) (– ∞,∞)<br />
4 2<br />
x sinx + cos x⎛ x cos x x sin x cos x ⎞<br />
8. If l = e ⎜<br />
− +<br />
⎟<br />
∫<br />
dx<br />
2 2<br />
x cos x<br />
⎝<br />
⎠<br />
then l equals -<br />
(A) e x s in x ⎛ sec x ⎞<br />
+ cos x ⎜x<br />
− ⎟ + C<br />
⎝ x ⎠<br />
(B) e x s in x ⎛ cosx<br />
⎞<br />
+ cos x ⎜x<br />
sin x − ⎟<br />
⎝ x ⎠<br />
(C) e x s in x ⎛<br />
+ cos x ⎜<br />
⎝<br />
(D) xe x sin x+cos x –<br />
∫<br />
x<br />
tan x<br />
e<br />
secx<br />
⎞<br />
− ⎟ + C x ⎠<br />
x sinx + cos x<br />
⎛ cos x − x sin x ⎞<br />
⎜1−<br />
⎟ dx<br />
2 2<br />
⎝ x cos x ⎠<br />
XtraEdge for <strong>IIT</strong>-<strong>JEE</strong> 61 DECEMBER 2009
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