1
IIT-JEE 2005
Subjective
+4
-0
At constant temperature and volume, X decomposes as 2X(g) $$\to$$ 3Y(g) + 2Z(g); Px is the partial pressure of X.
Observation No. Time (in minute) Px (in mm of Hg)
1 0 800
2 100 400
3 200 200

(i) What is the order of the reaction to X?
(ii) Find the rate constant
(iii) Find the time for 75% completion of the reaction.
(iv) Find the total pressure when pressure of X is 700 mm of Hg
2
IIT-JEE 2005
Subjective
+4
-0
If one the vertices of the square circumscribing the circle $$\left| {z - 1} \right| = \sqrt 2 \,is\,2 + \sqrt {3\,} \,i$$. Find the other vertices of the square.
3
IIT-JEE 2005
Subjective
+2
-0
Find the range of values of $$\,t$$ for which $$2\,\sin \,t = {{1 - 2x + 5{x^2}} \over {3{x^2} - 2x - 1}},\,\,\,\,\,t\, \in \,\left[ { - {\pi \over 2},\,{\pi \over 2}} \right].$$\$
4
IIT-JEE 2005
Subjective
+2
-0
If total number of runs scored in n matches is $$\left( {{{n + 1} \over 4}} \right)\,\,({2^{n + 1}} - n - 2)\,$$ where $$n > 1$$, and the runs scored in the $${k^{th}}$$ match are given by k. $$\,{2^{n + 1 - k}}$$, where $$1 \le k \le n$$. Find n.
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