IIT-JEE 2010 - Career Point

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18. Solve for x : x < 1. 19. If A = ⎡4 ⎢ ⎢ 1 ⎢⎣ 2 tan − 5 − 3 3 ⎛ x −1 ⎞ ⎜ ⎟ + tan ⎝ x − 2 ⎠ ⎛ x + 1 ⎞ ⎜ ⎟ = ; ⎝ x + 2 ⎠ 4 −1 −1 π −11⎤ 1 ⎥ ⎥ find A –1 − 7 ⎥⎦ or Using the properties of determinates prove that - a + x y z x x a + y y 2 z = a (a + x + y + z) a + z 20. Find the distance of the point (2, 3, 4) from the plane 3x + 2y + 2z + 5 = 0, measured parallel to the line x + 3 y − 2 z = = 3 6 2 21. If → a and → b are unit vectors and θ is the angle between them, then prove that cos θ 1 = 2 2 → + → 22. A football match may be either won, drawn or lost by the host country team. So there are three ways of forecasting the result of any one match, one correct and two incorrect. Find the probability of forecasting at least three correct results for four matches. or A candidate has to reach the examination centre in time. Probabilities of him going by bus or scooter or 3 1 3 by other means of transport are , , 10 10 5 respectively. The probability that he will be late is 1 1 and respectively, if he travels by bus or scooter. 4 3 But he reaches in time if he uses any other mode of transport. He reached late at the center. Find the probability that he traveled by bus. π/ 2 Section C cos x 23. Evaluate : ∫ dx (1 + sin x)(2 + sin x) 0 a b 24. Using integration, find the area of the circle x 2 +y 2 = 16, which is exterior to the parabola y 2 = 6x. or Find the area of the smaller region bounded by the 2 2 x y x y ellipse + = 1 and the line + = 1. 2 2 a b a b 25. Show that a right circular cylinder which is open at the top, and has a given surface area, will have the greatest volume if its height is equal to the radius of its base. ⎡1 −1 1 ⎤ 26. For A = ⎢ ⎥ ⎢ 2 1 − 3 ⎥ , find A –1 and hence solve the ⎢⎣ 1 1 1 ⎥⎦ system of equations. x + 2y + z = 4 – x + y + z = 0 x – 3y + z = 2 27. A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope just two consecutive letters TA are visible. What is the probability that the letter has come from- (i) TataNagar (ii) Calcutta or Find the probability distribution of the number of white balls drawn in a random draw of 3 balls without replacement from a bag containing 4 white and 6 red balls. Also find mean and variance of the distribution. 28. Find the distance of the point (3, 4, 5) from the plane x + y + z = 2 measured parallel to the line 2x = y = z. 29. Every gram of wheat provides 0.1 gm of proteins and 0.25 gm of carbohydrates. The corresponding values for rice are 0.05 gm and 0.5 gm respectively. Wheat costs Rs. 4 per kg and rice Rs. 6 per kg. The minimum daily requirements of protein and carbohydrates for an average child are 50 gms and 200 gms respectively. In what quantities should wheat and rice be mixed in the daily diet to provide minimum daily requirements of proteins and carbohydrates at minimum cost. Frame an L.P.P. and solve it graphically. XtraEdge for IIT-JEE 74 DECEMBER 2009
XtraEdge Test Series ANSWER KEY IIT- JEE 2010 (December issue) PHYSICS Ques 1 2 3 4 5 6 7 8 9 Ans B A B C A,B C,D A,B,D B,C A,B,C,D Ques 10 A → P,Q,R,S B → Q,P,Q,R C → P,Q,R,S D → P,Q,R,S Ques 11 A → Q B → R C → P D → S Ques 12 13 14 15 16 17 18 19 Ans 3 2 5 2 6 2 1 1 CHEMISTRY Ques 1 2 3 4 5 6 7 8 9 Ans D D D C D A,B,C B A,B,D B,C,D Ques 10 A → R B → Q,T C → P D → S Ques 11 A → Q,S B → R,S C → P,Q,T D → R,S Ques 12 13 14 15 16 17 18 19 Ans 1 2 2 0 2 9 0 6 MATHEMATICS Ques 1 2 3 4 5 6 7 8 9 Ans B C C C A,B,D A,C A,B,C,D A,D D Ques 10 A → Q B → R C → P D → S Ques 11 A → Q B → S C → P D → R Ques 12 13 14 15 16 17 18 19 Ans 1 4 6 4 1 3 3 3 IIT- JEE 2011 (December issue) PHYSICS Ques 1 2 3 4 5 6 7 8 9 Ans D B C D A,B,C,D A,C A,C,D A,B,C,D A,B,C,D Ques 10 A → Q B → S C → R D → P Ques 11 A → R B → P C → S D → Q Ques 12 13 14 15 16 17 18 19 Ans 2 3 3 5 2 3 0 1 CHEMISTRY Ques 1 2 3 4 5 6 7 8 9 Ans A B D C A,C,D A,B,D A,B,D C D Ques 10 A → R B → P,S,T C → Q D → P,T Ques 11 A → S B → R C → P D → Q Ques 12 13 14 15 16 17 18 19 Ans 1 7 2 7 8 1 9 1 MATHEMATICS Ques 1 2 3 4 5 6 7 8 9 Ans B C A C A,B,C,D A,B,C B,D A,B A,C Ques 10 A → S B → P C → Q D → R Ques 11 A → S B → R C → Q D → P Ques 12 13 14 15 16 17 18 19 Ans 2 5 3 6 1 2 0 4 XtraEdge for IIT-JEE 75 DECEMBER 2009
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Volume - 5 Issue - 6 December, 2009
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Volume-5 Issue-6 December, 2009 (Mo
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vehicle is equipped with high end s
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XtraEdge for IIT-JEE 9 DECEMBER 200
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(a) Find the number of moles of the
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