1. Xtra Edge February 2012 - Career Point

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Passage # 1 (Ques. 14 to 16) It is given that A = (tan –1 x) 3 + (cot –1 x) 3 , where x > 0 & B = (cos –1 t) 2 + (sin –1 t) 2 , where ⎡ 1 ⎤ t∈ ⎢0 , ⎥ & sin ⎣ 2 ⎦ –1 x + cos –1 π x = for –1 ≤ x ≤ 1 & 2 π ∀ x∈R tan –1 x + cot –1 x = 2 14. The interval in which A lie is ⎡ 3 3 π π ⎞ ⎡ 3 3 (A) ⎢ , ⎟ π π ⎞ ⎛ 3 3 ⎞ ⎢ ⎟ (B) ⎢ , ⎟ ⎣ 8 2 ⎟ (C) ⎜ π π ⎟ ⎠ ⎢⎣ 32 8 ⎜ , ⎟ (D) None ⎠ ⎝ 10 5 ⎠ 15. Maximum value of B is 2 π (A) 8 2 π (B) 16 2 π (C) 4 (D) None 16. If least value of A is λ & max. value of B is µ then cot –1 ⎛ ⎛ λ − µπ ⎞⎞ ⎜ ⎟ ⎜ cot ⎜ ⎟ ⎟ = ⎝ ⎝ µ ⎠⎠ π − π 7π −7π (A) (B) (C) (D) 8 8 8 8 Passage # 2 (Ques. 17 to 19) Consider lines x − 2 y − 3 z 4 L1 : = = 1 1 − k − , L2 : 2 x − 1 y − 4 z − 5 = = 2 1 17. A vector perpendicular to L1 &L2 and of length 3 2 is- (When k = 1) (A) 3 î –3 j ˆ (B) 2(3 î +2 j ˆ – kˆ ) (C) –3 î +4 j ˆ + 2 kˆ (D) 3 î + 4 kˆ 18. Value of 'k' so that lines L1 and L2 are coplanar, is - (A) –1 (B) –1/2 (C) –2 (D) 2 19. Equation of plane containing these lines is (A) x – y – 2 = 0 (B) 2x – y + 2 = 0 (C) x – y + 7 = 0 (D) None of these This section contains 3 questions (Questions 20 to 22). 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) 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, B-Q, B-R, C-P, C-Q and D-S, then the correctly bubbled 4 × 4 matrix should be as follows : P Q R S A B C D P Q R S P Q R S P Q R S P Q R S Mark your response in OMR sheet against the question number of that question in section-II. + 6 marks will be given for complete correct answer and No Negative marks for wrong answer. However, 1 mark will be given for a correctly marked answer in any row. 20. Match the following Consider a plane P = 0 on whom foot of perpendicular from point (1, 1, 1) is (2, 3, 4). Column-I Column-II (A) sum of intercepts of P = 0 on coordinate axis is (P) 52/7 (B) perpendicular distance of (Q) 110/3 (0, 0, 0) from plane is λ then λ 2 is (C) A line through (0, 0, 0) and (R) 120 perpendicular to plane is x y z = = then a + b+ c may be a b c (D) Radius of circle obtained by (S) 200/7 plane 'P' and sphere x 2 + y 2 + z 2 = 36 is 'r' then r 2 21. is equal to Match the Column : Column-I Column-II (A) Distance of 3x + 4y – 5 = 0 from (1, 1) is (P)1 (B) Area of ∆ formed by x + y = with co-ordinate axis is 2 (Q) 4/3 (C) Circumcentre of ∆ formed by 3x + 4y – 7 = 0 and axis is (h, k) then h + k is (R) 2/5 (D) Two sides of ∆ are x + y = 1 (S) 49/24 and 2x + y + 4 = 0. If circumcentre is (2, 1) then slope of third side is 22. Match the Column : Column-I Column-II (A) Find the number of 6 digit (P) 1 natural numbers, where each digit appears at least twice (B) In how many ways can five (Q) 677 different books be tied up in three bundles (C) How many non-empty (R) 11754 collections are possible by using 5P's and 6 Q's (D) How many students do you (S) 25 need in a school to guarantee that there are atleast 2 students, who have the same 1st two initials in their 1st names XtraEdge for IIT-JEE 66 FEBRUARY 2012
XtraEdge for IIT-JEE 67 FEBRUARY 2012
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Volume - 7 Issue - 8 February, 2012
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25% increase in number of girls fro
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Dr Amitabha Ghosh was the only Asia
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Sol. (i) The capacitor A with diele
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Sol. (i) Let m be the mass of elect
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Step 5. 1 gram equivalent acid neut
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= 2π ∫ π 2 / 3 2 t sec dt 2 t 1
Page 17 and 18: (A) (C) A 2B0πqR 3 B 0 PR 3 2 ×
Page 19 and 20: PHYSICS 1. AB and CD are two ideal
Page 21 and 22: 4. In a Young's experiment, the upp
Page 23 and 24: Matter Waves : Planck's quantum the
Page 25 and 26: The intercept of V0 versus ν graph
Page 27 and 28: PHYSICS FUNDAMENTAL FOR IIT-JEE The
Page 29 and 30: etween total mass and number of mol
Page 31 and 32: KEY CONCEPT Organic Chemistry Funda
Page 33 and 34: KEY CONCEPT Inorganic Chemistry Fun
Page 35 and 36: 1. It is possible to supercool wate
Page 37 and 38: z 1 K2 = = y( 0. 48M − z) 1. 26×
Page 39 and 40: MATHEMATICAL CHALLENGES 1. as φ (a
Page 41 and 42: 9. Point P (x, 1/2) under the given
Page 43 and 44: 10. 11 ∴ n(E) = 10 + 9 + 8 + ...
Page 45 and 46: dx (ii) ∫ 2 ax + bx + c This can
Page 47 and 48: MATHS Functions with their Periods
Page 49 and 50: a PHYSICS Questions 1 to 9 are mult
Page 51 and 52: R P ⊗ B O ω0 14. Magnitude of cu
Page 53 and 54: XtraEdge for IIT-JEE 51 FEBRUARY 20
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Page 61 and 62: 21. Column-I Column-II (A) If y = 2
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Page 65 and 66: 2. In the reaction 3 Cu + 8 HNO3
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Page 79 and 80: Use : It can be used to accelerate
Page 81 and 82: 10. (i) (ii) Benzene H CH3 - C = O
Page 83 and 84: NH3 NH3 NH3 Co +3 NH3 NH3 NH3 No un
Page 85 and 86: 7. f(A) = A 2 - 5A + 7 I2 ⎡ 3 1
Page 87 and 88: y 2 = - (2 - x) 2 + 9 This is the e
Page 89 and 90: (0, 4) ( 2 3, 2) (4, 0) ⎡ 2 4 2
Page 91 and 92: 15. X = ? Y = 20 Ω l1 = 40 cm l -
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