Get Previous Year KEAM Mathematics Question Papers With Answer

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If you are preparing for KEAM 2019 enterance exam then you will be searching previous year question with answer. Here you find the KEAM previous year questions papper with answer in PDF formate. Visit @ https://admission.aglasem.com/keam-2019/

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PAGE: 1 MATHEMATICS KEAM ANSWER KEY 2018 PAPER II – MATHEMATICS QUESTIONS ANSWERS 1. The value of 2cos 75 sin 75 0.2cos30 sin 30 i i + + oo oo is A 5 1 2 i + B 10 1 2 i + C 10 1 2 i - D 5 1 2 i - E 1 1 2 i + ANSWER B 2. If the conjugate of a complex number z is 1 1 i - then z is A 1 1 i - B 1 1 i + C 1 1 i - - D 1 1 i - + E 1 i ANSWER D 3. The value of 3 25 18 1 i i + Łł Łł is equal to A 1 2 i + B 22i + C 1 2 i - D 22i - E 22i - ANSWER E 4. The modulus of 11 11 ii ii +- - -+ is A 2 B 2 C 4 D 8 E 10 ANSWER A 5. If 4 /3 i ze p then 3 192 194 zz+ is equal to A –2 B –1 C –i D –2i E 0 ANSWER B KOCHI KOLLAM Puthussery Building Kaloor Sivajyothi Complex Polayathode : 0484-2531040 : 0474-2743040 M.O: Kunnumpuram Ayurveda College Jn. Trivandrum-1 : 0471-2573040 2473040 E-mail: infozephyrentrance.in Website: www.zephyrentrance.in BRANCHES KEAM ENGINEERING ANSWER KEY 2018 Aglasem Address:- 804 Park Centra Block A Sector 30 Gurgaon Haryana Pin code 122003 Website: https://admission.aglasem.com/keam-2019/ Contact Number 01244717818

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PAGE: 2 MATHEMATICS KEAM ANSWER KEY 2018 6. If a and b are real numbers and a + ib 11 1 + 3i then b + ia 11 is equal to A 3 i + B 13i + C 13i - D 0 E 3 i -- ANSWER E 7. If 22 5 3 53 a ba a bb „ - - then the equation having a b and b a as its roots is A 2 3 19 30 xx - - B 2 3 19 30 xx + - C 2 19 30 xx + + D 2 3 19 190 xx - - E 2 3 19 30 xx - + ANSWER E 8. The focus of the parabola 2 4 30 y yx - - + is A 3 2 4 Łł B 3 2 4 - Łł C 3 2 4 Łł D 3 2 4 - Łł E 3 2 4 - Łł ANSWER D 9. If : 0 fRfi¥ is an increasing function and if 2018 3 lim1 x fx fx fi then 2018 2 lim x fx fx fi is equal to A 2 3 B 3 2 C 2 D 3 E 1 ANSWER E 10. If f is differentiable at x 1 then 2 1 1 lim 1 x xf fx x fi - - is A 1 f - B 1 1 ff - C 2 1 1 ff - D 2 1 1 ff + E 1 1 ff + ANSWER C 11. Eccentricity of the ellipse 22 4 8 4 80 x y xy + - + - is A 3 2 B 3 4 C 3 2 D 3 8 E 3 16 ANSWER A 12. The focus of the parabola y + 1 2 –8x +2 is A –4 –1 B –1 –4 C 1 4 D 4 1 E –1 4 ANSWER A 13. Which of the following is the equation of a hyperbola A 2 4 16 170 x xy - + + B 22 4 4 16 4 600 x y xy + - + - C 22 2 4 2 270 x y xy + + + - D 22 3 2 430 x y xy - + - - E 2 4 6 20 x xy + + - ANSWER D

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PAGE: 3 MATHEMATICS KEAM ANSWER KEY 2018 14. Let 2 fx px qxr ++ where p q r are constants and 0 p „ . If 5 3 2 ff - and 40 f- then the other root of f is A 3 B –7 C –2 D 2 E 6 ANSWER A 15. Let : f fi RR satisfy f x fy f xy for all real numbers x and y. If 2 4 f then 1 2 f Łł A 0 B 1 4 C 1 2 D 1 E 2 ANSWER B 16. Sum of last 30 coefficients in the binomial expansion of 1 + x 59 is A 2 29 B 2 59 C 2 58 D 2 59 – 2 29 E 2 60 ANSWER C 17. 44 3 2 32 + - - A 206 B 306 C 5 10 D 406 E 106 ANSWER D 18. Three players A B and C play a game. The probability that A B and C will finish the game are respectively 11 23 and 1 4 . The probability that the game is finished is A 1 8 B 1 C 1 4 D 3 4 E 1 2 ANSWER D 19. If z 1 2 – i and z 2 1 + i then 12 12 1 zz z zi ++ -+ is A 2 B 2 C 3 D 3 E 1 ANSWER NA 20. If 2 sin cos xx fx xx - + then lim x fx fi¥ is equal to A 1 B 2 C 1 2 D 0 E ¥ ANSWER A

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PAGE: 4 MATHEMATICS KEAM ANSWER KEY 2018 21. The value of sin 31 3 p is A 3 2 B 1 2 C 3 2 - D 1 2 - E 1 2 ANSWER A 22. The sum of odd integers from 1 to 2001 is A 2 1121 B 2 1101 C 2 1001 D 2 1021 E 2 1011 ANSWER C 23. If 22 sin cos 1 cot 1 tan xx y xx + ++ then yx is equal to A 2 cos 2 x B 2 cos 3 x C –cos 2x D cos 2x E 3 cos x ANSWER C 24. The foci of the hyperbola 16x 2 – 9y 2 – 64 x + 18 y – 90 0 are A 24 5 145 1 12 – Łł B 21 5 145 1 12 – Łł C 24 5 145 1 2 – Łł D 21 5 145 1 2 – Łł E 21 5 145 1 2 – - Łł ANSWER A 25. If the sum of the coefficients in the expansions of 22 51 2 1 ax ax -+ is zero then a is equal to A 0 B 1 C –1 D –2 E 2 ANSWER B 26. The mean deviation of the data 2993694 from the mean is A 2.23 B 3.23 C 2.57 D 3.57 E 1.03 ANSWER C 27. The mean and variance of a binomial distribution are 8 and 4 respectively. What is X 1 A 8 1 2 B 12 1 2 C 6 1 2 D 4 1 2 E 5 1 2 ANSWER B 28. The number of diagonals of a polygon with 15 sides is A 90 B 45 C 60 D 70 E 10 ANSWER A

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PAGE: 5 MATHEMATICS KEAM ANSWER KEY 2018 29. In a class 40 of students study maths and science and 60 of students study maths. What is the probability of a student studying science given the student is already studying maths A 1 3 B 1 6 C 2 3 D 1 5 E 1 4 ANSWER C 30. The eccentricity of the conic 22 2 2 3 20 x y xy + - + + is A 0 B 1 2 C 1 2 D 2 E 1 ANSWER B 31. If the mean of a set of observations x 1 x 2 ……….x 10 is 20 then the mean of 1 2 3 10 4 8 12... 40 x x xx + +++ is A 34 B 32 C 42 D 38 E 40 ANSWER C 32. A letter is taken at random from the word “GTATISTICS” and another letter is taken at random from the word “ASSISTANT”. The probability that they are same letters is A 1 45 B 13 90 C 19 90 D 5 18 E 9 10 ANSWER C 33. If sin a and cos a are the roots of the equation 2 0 ax bxc + + then A 22 20 a b ac - + B 222 ac bc - + C 22 20 a b ac + - D 22 20 a b ac + + E 0 a bc + + ANSWER A 34. If the sides of a triangle are 4 5 and 6 cms. Then the area of triangle is ……..sq.cms. A 4 p B 7 4 p C 4 15 D 4 7 15 D 15 7 4 ANSWER E 35. In a group of 6 boys and 4 girls a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is A 159 B 209 C 200 D 240 E 212 ANSWER B 36. A password is set with 3 distinct letters from the word LOGARITHMS. How many such passwords can be formed A 90 B 720 C 80 D 72 E 120 ANSWER B

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PAGE: 6 MATHEMATICS KEAM ANSWER KEY 2018 37. If 5 97 is divided by 52 the remainder obtained is A 3 B 5 C 4 D 0 E 1 ANSWER B 38. A quadratic equation 2 0 ax bxc + + with distinct coefficients is formed. If a b c are chosen from the numbers 2 3 5 then the probability that the equation has real roots is A 1 3 B 2 5 C 1 4 D 1 5 E 2 3 ANSWER A 39. 32 3 3 2 79 lim 4 92 x x xx xx fi¥ + -+ +- is equal to A 2 9 B 1 2 C 9 2 - D 3 4 E 9 2 ANSWER D 40. The minimum value of max 1 2 fx xxx +- is A 1 2 B 3 2 C 1 D 0 E 2 ANSWER B 41. The equations of the asymptotes of the hyperbola 32 100 xy xy + - - are A 23 xy - - B 23 xy - C 23 xy D 43 xy E 34 xy ANSWER B 42. If fx x 6 + 6 x then f’x is equal to A 12 x B x + 4 C 6x 5 + 6 x log 6 D 6x 5 + x6 x – 1 E x 6 ANSWER C 43. The standard deviation of the data 6 5 9 13 12 8 10 is A 52 7 B 52 7 C 53 7 D 53 7 E 6 ANSWER NA 44. 0 1 cos lim 1 cos x mx nx fi - - A 2 2 m n B 2 2 n m C ¥ D –¥ E 0 ANSWER A

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PAGE: 7 MATHEMATICS KEAM ANSWER KEY 2018 45. 0 1 21 lim x x x fi +- A 0 B –1 C 1 2 D 1 E 1 2 - ANSWER D 46. Let f and g be differentiable functions such that f3 5 g3 7 f’3 13 g’3 6 f’7 2 and g’7 0. If hx fog x then h’3 A 14 B 12 C 16 D 0 E 10 ANSWER B 47. 31 sin20 cos20 oo - A 1 B 1 2 C 2 D 4 E 0 ANSWER D 48. A poison variate X satisfies PX 1 Px 2. PX 6 is equal to A 2 4 45 e - B 1 1 45 e - C 2 1 9 e - D 2 1 4 e - E 2 1 45 e - ANSWER A 49. Let a and b be 2 consecutive integers selected from the first 20 natural numbers. The probability that 2 2 22 a b ab ++ is an odd positive integer is A 9 19 B 10 19 C 13 19 D 1 E 0 ANSWER D 50. An ellipse of eccentricity 22 3 is inscribed in a circle. A point is chosen inside the circle at random. The probability that the point lies outside the ellipse is A 1 3 B 2 3 C 1 9 D 2 9 E 1 27 ANSWER B 51. If the vectors 4 11 i j mk ++ 7 26 i jk ++ and 54 i jk ++ are coplanar then m is equal to A 38 B 0 C 10 D –10 E 25 ANSWER C

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PAGE: 8 MATHEMATICS KEAM ANSWER KEY 2018 52. Let a i jk ++ r 35 b i jk ++ r and 7 9 11 c i jk ++ r . Then the area of the parallelogram with diagonals ab + rr and bc + rr is A 46 B 1 21 2 C 6 2 D 6 E 1 6 ANSWER A 53. If | | 3| | 1| |4 a bc r rr and 0 a bc ++ r rr then the value of . .. ab bc ca ++ rr rr rr is equal to A 13 B 26 C –29 D –13 E –26 ANSWER D 54. IF | | | | | |1 a b ab - r r rr then the angle between a r and b r is equal to A 3 p B 3 4 p C 2 p D 0 E p ANSWER A 55. If the vectors 2 a i jk -+ r 24 b i jk ++ r and 9 c i jk lm ++ r are mutually orthogonal then lm + is equal to A 5 B –9 C –1 D 0 E –5 ANSWER B 56. The solutions of 21 55 3 40 xx + - are A 1 1024 B –1 1024 C 1 1031 D –1024 1 E –11031 ANSWER D 57. If the equations 2 10 x ax + + and 2 0 x xa - - have a real common root b then the value of b is equal to A 0 B 1 C –1 D 2 E 3 ANSWER C 58. If sin q – cos q 1 then the value of sin 3 q – cos 3 q is equal to A 1 B –1 C 0 D 2 E –2 ANSWER A 59. Two dice of different colours are thrown at a time. The probability that the sum is either 7 or 11 is A 7 36 B 2 9 C 2 3 D 5 9 E 6 7 ANSWER B

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PAGE: 9 MATHEMATICS KEAM ANSWER KEY 2018 60. 1 1 1 11 9 37 55 73 9 + + ++ is equal to A 9 2 10 B 10 2 8 C 11 2 9 D 10 2 7 E 8 2 9 ANSWER C 61. The order and degree of the differential equation 2 3 45 " " 0 y y yy + - + is A 3 and 2 B 1 and 2 C 2 and 3 D 1 and 4 E 3 and 5 ANSWER A 62. 2 2 || x dx - is equal to A 0 B 1 C 2 D 4 E 1 2 ANSWER D 63. 0 2 1 22 dx xx - ++ is equal to A 0 B 4 p C 4 p - D 2 p E 2 p - ANSWER B 64. If 4 1 4 f x dx - and 4 2 3 7 f x dx - then 2 1 f x dx - is A 1 B 2 C 3 D 4 E 5 ANSWER E 65. 2 1 x xe dx x + A 1 x e c x + + B 1 x x e c e + + C 2 1 x x e c e + + D 1 x e c x - + + E 2 1 x e c x - + + ANSWER A 66. The remainder when 2 2000 is divided by 17 is A 1 B 2 C 8 D 12 E 4 ANSWER A

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PAGE: 10 MATHEMATICS KEAM ANSWER KEY 2018 67. The coefficient of x 5 in the expansion of x + 3 8 is A 1542 B 1512 C 2512 D 12 E 4 ANSWER B 68. The maximum value of 5 cos q + 3 cos 3 3 p q ++ Łł is A 5 B 11 C 10 D –1 E 2 ANSWER C 69. The area of the triangle in the complex plane formed by z iz and z + iz is A |z| B 2 || z C 2 1 || 2 z D 2 1 || 2 z iz + E || z iz + ANSWER C 70. Let : f fi ¡¡ be a differentiable function. If f is even then f’0 is equal to A 1 B 2 C 0 D –1 E 1 2 ANSWER C 71. The coordinate of the point dividing internally the line joining the points 4 –2 and 8 6 in the ratio 7 : 5 is A 16 18 B 18 16 C 198 33 Łł D 8 19 33 Łł E 7 3 ANSWER C 72. The area of the triangle formed by the points a b + c b c + a c a + b is a abc B a 2 + b 2 + c 2 C ab + bc + ca D 0 E aab + bc + ca ANSWER D 73. If x y is equidistant from a + b b – a and a – b a + b then A ax + by 0 B ax – by 0 C bx + ay 0 D bx – ay 0 E x y ANSWER D 74. The equation of the line passing through a b and parallel to the line 1 xy ab + is A 3 xy ab + B 2 xy ab + C 0 xy ab + D 20 xy ab + + E 4 xy ab + ANSWER B

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PAGE: 11 MATHEMATICS KEAM ANSWER KEY 2018 75. If the points 2a a a 2a and a a enclose a triangle of area 18 square units then the centroid of the triangle is equal to A 4 4 B 8 8 C –4 –4 D 4 242 E 6 6 ANSWER B 76. The area of a triangle is 5 sq. units. Two of its vertices are 2 1 and 3 –2. The third vertex lies on y x + 3. The coordinates of the third vertex can be A 33 22 -- Łł B 33 42 - Łł C 7 13 22 Łł D 11 42 - Łł E 33 22 Łł ANSWER C 77. If x 2 + y 2 + 2gx + 2fy + 1 0 represents a pair of straight lines then f 2 + g 2 is equal to A 0 B 1 C 2 D 4 E 3 ANSWER B 78. If q is the angle between the pair of straight lines x 2 – 5xy + 4y 2 + 3x – 4 0 then tan 2 q is equal to A 9 16 B 16 25 C 9 25 D 21 25 E 25 9 ANSWER C 79. If 3 2 52 32 23 i j k x i j k yi j k z i jk + - - + + + - + - +- Ł łŁ łŁł then A x 1 y 2 z 3 B x 2 y 3 z 1 C x 3 y 1 z 2 D x 1 y 3 z 2 E x 2 y 2 z 3 ANSWER C S80. sin 15 o A 31 22 - B 31 22 + C 13 22 - D 13 2 + E 1 3 22 -+ ANSWER A 81. If a r and 3 66 b i jk ++ r are collinear and . 27 ab rr then a r is equal to A 3i jk ++ Łł B 22 i jk ++ C 2 22 i jk ++ D 33 i jk ++ E 32 i jk -+ ANSWER B

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PAGE: 12 MATHEMATICS KEAM ANSWER KEY 2018 82. If | | 13 a r | |5 b r and . 30 ab rr then || ab · rr is equal to A 30 B 30 233 25 C 30 193 33 D 65 493 23 E 65 133 13 ANSWER E 83. If 56 P r + 6 : 54 P r + 3 30800 : 1 then r is equal to A 69 B 41 C 51 D 61 E 49 ANSWER B 84. Distance between two parallel lines y 2x + 4 and y 2x – 1 is A 5 B 55 C 5 D 1 5 E 3 5 ANSWER C 85. 7 C 0 + 7 C 1 + 7 C 2 + 7 C 3 + ... + 7 C 6 + 7 C 7 A 2 8 – 2 B 2 7 – 1 C 2 7 D 2 8 – 1 E 2 7 – 2 ANSWER C 86. The coefficient of x in the expansion of 1 – 3x + 7x 2 1 – x 16 is A 17 B 19 C –17 D –19 E 20 ANSWER D 87. The equation of the circle with centre 2 2 which passes through 4 5 is A x 2 + y 2 – 4x + 4y – 77 0 B x 2 + y 2 – 4x – 4y – 5 0 C x 2 + y 2 + 2x + 2y – 59 0 D x 2 + y 2 – 2x – 2y – 23 0 E x 2 + y 2 + 4x – 2y – 26 0 ANSWER B 88. The point in the xy-plane which is equidistant from 2 0 3 0 3 2 and 0 0 1 is A 1 2 3 B –3 2 0 C 3 –2 0 D 3 2 0 E 3 2 1 ANSWER D 89. Let f : fi ¥¥ be such that f1 2 and f x + y fx fy for all natural numbers x and y. If 1 n k f ak + 16 2 n – 1 then a is equal to A 3 B 4 C 5 D 6 E 7 ANSWER A 90. If n C r – 1 36 n C r 84 and n C r + 1 126 then n A 3 B 4 C 8 D 9 E 10 ANSWER D

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PAGE: 13 MATHEMATICS KEAM ANSWER KEY 2018 91. Let f : -1 1 fi -1 1 be continuous fx fx 2 for all x ˛ –1 1 and 1 0 2 f then the value of 1 4 4 f Łł is A 1 B 2 C 3 D 4 E 5 ANSWER B 92. 22 lim 11 x xx qfi +- - A –1 B 1 C 0 D 2 E 4 ANSWER C 93. If f is differentiable at x 1 and 0 1 lim 1 5 h fh h fi + then f 1 A 0 B 1 C 3 D 4 E 5 ANSWER E 94. The maximum value of the function 2x 3 – 15x 2 + 36x + 4 is attained at A 0 B 3 C 4 D 2 E 5 ANSWER D 95. If 2 1 cos 2 fx x dx fxc + then 2 f p Łł is A c B 2 c p + C c + 1 D 2p + c E c + 2 ANSWER C 96. 3 /4 /4 1 sin x dx x p p + A 21 p - B 21 p + C 2 21 p - D 2 21 p + E 21 p + ANSWER A E 97. sin 2 sin cos 0 2 22 x xx dx p + A 2 B p C 4 p D 2p E 0 ANSWER C

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PAGE: 14 MATHEMATICS KEAM ANSWER KEY 2018 98. 2 0 2 0 sin lim x x tdt x fi Łł A 2 3 B 2 9 C 1 3 D 0 E 1 6 ANSWER D 99. The area bounded by y 2 sin 2 x xx andx p is A 2 p B 4 p C 8 p D 16 p E 2p ANSWER B 100. The differential equation of the family of curves cos sin . x y e A x Bx + where A and B are arbitrary constants is A 2 20 y yy - + B 2 20 y yy + - C 2 0 y yy + + D 20 y yy + - E 2 20 y yy - - ANSWER A 101. The real part of 13 3 i - is A 2 –10 B 2 12 C 2 –12 D –2 –12 E 2 10 ANSWER NA 102. 0 2 1 lim x x xe x fi +- A 1 2 B 1 2 - C 1 D –1 E 0 ANSWER B 103. 2 sin cos 2 sin2 sin2 x xx dx x +- A sin cos sin2 xx c x + + B sin cos sin2 xx c x - + C sin sin cos x c xx + + D sin sin cos x c xx + - E sin cos sin cos xx c xx - + + ANSWER B

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PAGE: 15 MATHEMATICS KEAM ANSWER KEY 2018 104. A plane is at a distance of 5 units from the origin and perpendicular to the vector 22 i jk ++ . The equation of the plane is A .2 2 15 r i jk +- r B .2 15 r i jk + - r C .2 2 15 r i jk ++ r D . 2 15 ri jk ++ r E .2 2 15 r i jk -+ r ANSWER C 105. sin sin cos cos AB AB - + is equal to A sin 2 AB + Łł B 2 tan AB + C cot 2 AB - Łł D tan 2 AB - Łł E 2 cot AB + ANSWER D 106. If 2 2 cos4 sin4 then dx x A tBt dt + A x B –16x C 15x D 16x E –15x ANSWER B 107. The arithmetic mean of 12 ... n n nn n Co CC C is A 2 1 n n + B 2 n n C 1 2 1 n n - + D 1 2 n n - E 1 2 n n + ANSWER A 108. The variance of first 20 natural numbers is A 399 2 B 379 12 C 133 2 D 133 4 E 169 2 ANSWER D 109. If S is a set with 10 elements and A : xy xy Sxy ˛„ then the number of elements in A is A 100 B 90 C 80 D 150 E 45 ANSWER B

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PAGE: 16 MATHEMATICS KEAM ANSWER KEY 2018 110. A coin is tossed and a die is rolled. The probability that the coin shows head and the die shows 3 is A 1 6 B 1 12 C 1 9 D 11 12 E 1 11 ANSWER B 111. If A 0 12 1 23 3 11 Łł then the sum of all the diagonal entries of A –1 is A 2 B 3 C –3 D –4 E 4 ANSWER E 112. Let 37 22 76 x fxx x . If 9 x - is a root of 0 fx then the other root are A 2 and 7 B 3 and 6 C 7 and 3 D 6 and 2 E 6 and 7 ANSWER A 113. If 1 3 21 1 1 2 5 1 20 15 32 x x Ø øØø Œ œŒœ Œ œŒœ Œ œŒœ º ßºß then x can be A –2 B 2 C 14 D –14 E 0 ANSWER A D 114. If 20 x A xx Øø Œœ ºß and A –1 10 12 A Øø Œœ - ºß then x A 2 B 1 2 C 1 D 3 E 0 ANSWER B 115. If 2 4 32 2 6 6 xx xx ax bx cx dxe xx ++ ++ then 5 4 32 a b c de + + ++ is equal to A 11 B –11 C 12 D –12 E 13 ANSWER B

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PAGE: 17 MATHEMATICS KEAM ANSWER KEY 2018 116. 1 1 1 a bc b ca c ab + + + A 1 B 0 C 1 1 1 a bc - -- D a + b + c E 2 abc ++ ANSWER B 117. If 1 11 21 3 1 1 2 1 fx x xx xx x x xx - - --- then 50 f A 0 B 2 C 4 D 1 E 3 ANSWER A 118. If 1 cos 1 cos 1 sin cos 1 sin cos sin sin1 xx x x x xx xx - D + +- then /2 0 x dx p D A 1 2 - B 1 2 C 1 D –1 E 0 ANSWER A 119. The equation of the plane passing through the points 123 –1 4 2 and 3 11 is A 5 12 230 x yz + + - B 5 6 2 23 x yz + + C 5 6 2 23 x yz + + D 13 x yz + + E 2 6 57 x yz + + ANSWER B 120. In an arithmetic progression if the k th term is 5k + 1 then the sum of first 100 terms is A 50507 B 51506 C 50506 D 51507 E 52506 ANSWER A

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