IIT-JEE 2010 - Career Point

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9. H 2 C 2 O 4 and NaHC 2 O 4 behave as acids as well as reducing agents which is/are correct statement (s) ? (A) Equivalent wt. of H 2 C 2 O 4 and NaHC 2 O 4 are equal to their molecular weights when behaving as reducing agent (B) 100 mL of 1N solution of each is neutralised by equal volumes of 1M Ca(OH) 2 (C) 100 mL of 1N solution of each is neutralised by equal volumes of 1N Ca(OH) 2 (D) 100 mL of 1M solution of each is oxidised by equal volumes of 1M KMnO 4 (B) (C) Cl Me Cl Me Me Me Me Me Me Me Me Br Me Me Me Me Br Cl Me Me Me Cl Me This section contains 2 questions (Questions 10 to 11). Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S, T) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, A-T, B-Q, B-R, C-P, C-Q and D-S, D-T then the correctly bubbled 4 × 5 matrix should be as follows : P Q R S T A B C D P P P P Q Q Q Q R R R R S S S S T T T T 10. Column-I Column-II ⎛ a ⎞ (A) If force of attraction (P) ⎜P + ⎟ ⎝ V 2 (V–b)= RT ⎠ among the gas molecules be negligible (B) If the volume of the (Q) PV = RT –a/V gas molecules be negligible (C) At STP (for real gas) (R) PV = RT + Pb (D) At low pressure and (S) PV = RT at high temperature (T) PV/RT = 1–a/VRT 11. Column-I Me Me Me Me Cl (D) Me Cl Me Me Br Me Me Br Me Me Column-II (P) Optically active (Q) Cis compound (R) Trans compound (S) Optically inactive (T) Chiral axis (element of chirality) Cl Me This section contains 8 questions (Questions 12 to 19). The answer to each of the questions is a SINGLE- DIGIT INTEGER, ranging from 0 to 9. The appropriate bubbles below the respective question numbers in the OMR have to be darkened. For example, if the correct answers to question numbers X, Y, Z and W (say) are 6, 0, 9 and 2, respectively, then the correct darkening of bubbles will look like the following : X Y Z W 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 (A) Me Me Me Me Me Me 12. What is the number of lone pair on the molecule XeO 2 F 2 ? XtraEdge for IIT-JEE 60 DECEMBER 2009
13. 15g of a solute in 100g water makes a solution freeze at –1ºC. What will be the depression in freezing point if 30g of a solute is dissolved in 100g of water ? 14. The half lives of decomposition of gaseous CH 3 CHO at constant temperature but at initial pressure of 364mm and 170mm Hg were 410 second and 880 second respectively. Hence what is the order of reaction. 15. The number of S–S bonds in sulphur trioxide trimer (S 3 O 9 ) is ....... . 16. The number of peroxo linkages present in the [H 4 B 2 O 8 ] 2– is ..... . 17. The maximum number of structural isomers (acyclic and cyclic) possible for C 4 H 8 are ....... . 18. What is the no. of lone pair of electrons present on N in Trisilylamine ? 19. A small amount of solution containing 24 Na with activity 2 × 10 3 dps was administered into the blood of patient in a hospital. After 5 hour a sample of the blood drawn out from the patient shared an activity of 16 dps per cm 3 . (t 1/2 of 24 Na = 15 hrs.) Find the volume (in L) of blood in patient. [Given : log 1.2598 = 0.1003] MATHEMATICS Questions 1 to 4 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct. 1. The largest term in the expansion of (3 + 2x) 50 , where x = 1/5, is - (A) 5th (B) 6th (C) 8th (D) 9th 1 2. If sin –1 ⎡ 3sin 2θ ⎤ 2 ⎢ ⎥ = tan –1 x, then x = ⎣5+ 4cos 2θ⎦ (A) tan 3θ (B) 3 tan θ (C) (1/3) tan θ (D) 3 cot θ 3. (cos x −1)(cos x − e The integer n for which lim x→0 n x a finite nonzero number is - (A) 1 (B) 2 (C) 3 (D) 4 x ) is x 4. If f(x) = and g(x) = sin x then in this interval - x tan x where 0 < x ≤ 1, (A) both f(x) and g(x) are increasing functions (B) both f(x) and g(x) are decreasing functions (C) f(x) is an increasing function (D) g(x) is an increasing function Questions 5 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which MULTIPLE (ONE OR MORE) is correct. 5. If a, b, c are in A.P., and a 2 , b 2 , c 2 are in H.P., then (A) a = b = c (C) a, b, c are in H.P. (B) a, b, – 2 1 c are in G.P. (D) – 2 1 a, b, c are in G.P. 6. The system of equations –2x + y + z = a x – 2y + z = b x = y – 2z = c has (A) no solution if a + b + c ≠ 0 (B) unique solution if a + b + c = 0 (C) infinite number of solutions if a + b + c = 0 (D) none of these 7. x The function f(x) = 1+ | x | is differentiable on - (A) (0, ∞) (B) [0, ∞) (C) (–∞, 0) (D) (– ∞,∞) 4 2 x sinx + cos x⎛ x cos x x sin x cos x ⎞ 8. If l = e ⎜ − + ⎟ ∫ dx 2 2 x cos x ⎝ ⎠ then l equals - (A) e x s in x ⎛ sec x ⎞ + cos x ⎜x − ⎟ + C ⎝ x ⎠ (B) e x s in x ⎛ cosx ⎞ + cos x ⎜x sin x − ⎟ ⎝ x ⎠ (C) e x s in x ⎛ + cos x ⎜ ⎝ (D) xe x sin x+cos x – ∫ x tan x e secx ⎞ − ⎟ + C x ⎠ x sinx + cos x ⎛ cos x − x sin x ⎞ ⎜1− ⎟ dx 2 2 ⎝ x cos x ⎠ XtraEdge for IIT-JEE 61 DECEMBER 2009
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Volume-5 Issue-6 December, 2009 (Mo
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