02. If (x, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) x + y = 0 (B) bx ay = 0 (C) ax by = 0 (D) bx + ay = 0 (E) ax + by =

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Rodger Eaton
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1 0. π/ sin d 0 sin + cos (A) 0 (B) π (C) 3 π / (D) π / (E) π /4 0. If (, y) is equidistant from (a + b, b a) and (a b, a + b), then (A) + y = 0 (B) b ay = 0 (C) a by = 0 (D) b + ay = 0 (E) a + by = If the points (, 0), (0, ) and (, 8) are collinear, then the value of (A) 5 (B) 6 (C) 6 (D) 7 (E) The minimum value of the function ma {, } (A) 0 (B) (C) (D) / (E) 3/ 05. Let f( + y) = f() f(y) for all and y. If f(0) =, f(3) = 3 and f(0) =, then f(3) (A) (B) (C) 33 (D) 44 (E) 55 Ans : C 06. f() 3 If f(9) = f(9) = 0, then lim 9 3 (A) 0 (B) f(0) (C) f(3) (D) f(9) (E) 07. The value of cos ( π / 4 + ) + cos ( π/ 4 ) is (A) sin (B) sin (C) cos (D) 3cos (E) cos 08. Area of the triangle with vertices (, ), (, 5) and (6, ) is (A) 5 (B) 3/5 (C) 9/ (D) 33/ (E) 35/ Ans : D 09. The equation of the line passing through ( 3, 5) and perpendicular to the line through the points (, 0) and ( 4, ) is (A) 5 + y + 0 = 0 (B) 5 y + 0 = 0 (C) 5 y 0 = 0 (D) 5 + y + 0 = 0 (E) 5y 0 = 0 0. The coefficient of 5 in the epansion of ( + ) 5 ( + ) 4 is (A) 30 (B) 60 (C) 40 (D) 0 (E) 45. The coefficient of 4 in the epansion of ( ) 5 (A) 40 (B) 30 (C) 30 (D) 3 (E) 80 KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY

2 . The equation 5 + y + y = 8 represents (A) an ellipse (B) a parabola (C) a hyperbola (D) a circle (E) a straight line 3. The centre of the ellipse 4 + y 8 + 4y 8 = 0 is (A) (0, ) (B) (, ) (C) (, ) (D) (, ) (E) (, ) 4. The area bounded by the curves y = + 3 and y = 0 is (A) 3+ (B) 3 (C) 4 3 (D) 5 3 (E) 6 3 Ans : C dy dy dy The order of the differential equation 3 d + + d d = 0 is (A) 3 (B) 4 (C) (D) 5 (E) 6 6. If f() = + 4, then f() (A) 0 (B) (C) (D) (E) 7. The area of the circle + y 0y + k = 0 is 5π. The value of k (A) (B) (C) 0 (D) (E) 3 Ans :B d (A) /4 (B) 3/ (C) 07/ (D) / (E) The solution of dy/d + y tan = sec, y (0) = 0 is (A) y sec = tan (B) y tan = sec (C) tan = y tan (D) sec = tan y (E) y cot = sec 0. If the vectors i ˆ+ j ˆ+ 6kˆ, i ˆ+λ ˆj + 6kˆ, i ˆ 3j ˆ+ kˆ are coplanar, then the value of λ is (A) 0 (B) (C) 0 (D) 0 (E). The distance between (,, 0) and + y + z + 5 = 0 is (A) 0 (B) 0/3 (C) 0/9 (D) 5 (E) Ans :B KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY

3 . The equation of the hyperbola with vertices (0, ± 5) and foci (0, ± 0) is y y y (A) = (B) = (C) = y y (D) = (E) = The value of + 4(6) + 6(36) + 4(6) + 96 (A) 9/7 (B) 7/9 (C) 6/7 (D) /9 (E) 7/7 4. The equation of the plane that passes through the points (, 0, ), (,, ), (5, 0, 3) is (A) + y 4z + 7 = 0 (B) + y 3z + 7 = 0 (C) y + 4z + 7 = 0 (D) y 4z 7 + = 0 (E) + y + 3z + 7 = 0 5. The verte of the parabola y 4y + 3 = 0 is (A) (, 3) (B) (, ) (C) (, ) (D) (3, ) (E) (, ) 6. If a,b,c are vectors such that a+ b+ c= 0 (A) π /3 (B) π /6 (C) /4 and a = 7, b = 5, c = 3 π (D) π (E) 0, then the angle between candb is 7. Let f() = 3 9a + a +, where a > 0. The minimum of f is attained at a point q and the maimum is attained at a point p. If p 3 = q, then a (A) (B) 3 (C) (D) (E) / 8. For all rest numbers and y, it is known as the real valued function f satisfies f() + f(y) = f( + y). 00 If f() = 7, then f(r) r= (A) (B) (C) (D) (E) ) 3 9. The eccentricity of the ellipse ( + y + = is 4 6 (A) / (B) / (C) / (D) /4 (E) /4 d ma{, } (A) 3/4 (B) /4 (C) / (D) (E) 0 Ans :B KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 3

4 3. If [ 0, π/ ],y [ 0, π /] and sin + cos y =, then the value of + y (A) π (B) π (C) π /4 (D) π / (E) 0 3. Let a, a + r and a + r be positive real numbers such that their product is 64. Then the minimum value of a + r (A) 4 (B) 3 (C) (D) / (E) 33. The sum S = /9! + /3!7! + /5!5! + /7!3! + /9! (A) 0 /8! (B) 9 /0! (C) 7 /0! (D) 6 /0! (E) 5 /8! Ans :B 34. If f() = , then f() (A) (B) 6 3 (C) 3 (D) 6 (E) 0 Ans : D 35. d 3 + ( ) (A) tan + c (B) /3 tan 3 + c (C) /3 tan ( 3 ) + c (D) / tan + c (E) tan 3 + c Ans : C 36. Let f n () be the nth derivative of f(). The least value of n so that f n = f n + where f() = + e is (A) 4 (B) 5 (C) (D) 3 (E) sin 765 o (A) (B) 0 (C) 3/ (D) / (D) / 38. The distance of the point (3, 5) from the line 3 4y 6 = 0 is (A) 3/7 (B) /5 (C) 7/5 (D) 3/5 (E) 39. The difference between the maimum and minimum value of the function f() = 3] is (A) 39/6 (B) 49/6 (C) 59/6 (D) 69/6 (E) 79/6 Ans : C (t t )dt + + on [, If a and b are the non zero distinct roots of + a + b = 0, then the minimum value of + a + b is (A) /3 (B) 9/4 (C) 9/4 (D) /3 (E) Ans : C KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 4

5 4. If the straight line y = 4 + c touches the ellipse 4 (A) 0 (B) ± 65 (C) 6 + y = then c ± (D) ± (E) ± 3 4. The equations λ y =, 3y = - λ and 3 y = - are consistent for (A) λ = -4 (B) λ =, 4 (C) λ =, -4 (D) λ = -, 4 (E) λ = - Ans:D 43. The set {( y, ) : + y= } in the y plane represents (A) a square (B) A circle (C) An ellipse (D) A rectangle which is not a square (E) A rhombus which is not a square Ans:A The value of cos tan 4 is (A) 4 5 (B) 3 5 (C) 3 4 (D) 5 (E) Let A (6, -), B (, 3) and C (, 8) be three points such that AB = BC. The values of are (A) 3, 5 (B) -3, 5 (C) 3, -5 (D) 4, 5 (E) -3, In an eperiment with 5 observations on, the following results were available =830 = 70 One observation that was 0, was found to be wrong and was replaced by the correct value 30. Then the corrected variance is (A) 9.3 (B) 8.3 (C) 88.6 (D) 77.3 (E) 78 Ans:E 47. The angle between the pair of lines (A) cos (D) cos 9 38 Ans:E 48. Let a be a unit vector. If ( a).( + a) y z+ 3 = = and + y 4 z 5 = = is (B) cos (C) cos (E) cos 9 38 =, then the magnitude of is (A) 8 (B) 9 (C) 0 (D) 3 (E) Ans:D 49. The area of the triangular region whose sides are y = +, y = 3 + and = 4 is (A) 5 (B) 6 (C) 7 (D) 8 (E) 9 Ans:D KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 5

6 50. If nc r = 36, nc r = 84 and nc r + = 6, then the value of r is (A) 9 (B) 3 (C) 4 (D) 5 (E) 6 5. Let f( + y) = f() f(y) and f() = + sin (3) g(), where g is differentiable. The f ( ) (A) 3f() (B) g(0) (C) f() g(0) (D) 3g() (E) 3f() g(0) Ans:E 5. The roots of the equation = 0 are (A), (B) -, (C) -, - (D), - (E), 53. If the 7 th and 8 th term of the binomial epansion (a 3b) n are equal, then a+ 3 b a 3b (A) 3 n n + (B) (C) 6 n n (D) n + 3 n 3 n 3 n (E) n 3 n 54. Standard deviation of first n odd natural numbers is (A) n (B) Ans:C ( n+ )( n+ ) 3 (C) n 3 (D) n (E) n 55. Let S = {,, 3, 0}. The number of subsets of S containing only odd numbers is (A) 5 (B) 3 (C) 63 (D) 7 (E) The area of the parallelogram with vertices (0, 0), (7, ), (5, 9) and (, ) is (A) 50 (B) 54 (C) 5 (D) 5 (E) 53 Ans:E 57. p q r p q r+ (A) q p (B) q + p (C) q (D) p (E) Let A = (A) and B = 0. If 4A + 5B C = 0, then C is (B) (C) 0 5 (D) (E) KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 6

7 59. If U =, then U - is (A) U T (B) U (C) I (D) 0 (E) U If A = 0 0, then A - is 0 0 (A) A T (B) A (C) A (D) I (E) y y 0 0 If =, then the values of, y and z are respectively + z + z (A) 0, 0, (B),, 0 (C) -, 0, 0 (D) 0, 0, 0 (E),, (A) 7 7 (B) 6 (C) 5 6 (D) 6 5 (E) If 3 5 is singular, then the value of a is 4 a (A) a = -6 (B) a = 5 (C) a = -5 (D) a = 6 (E) a = 0 Ans:D If y =, then (, y, z) 0 0 z (A) (, 6, 6) (B) (, -6, ) (C) (,, 6) (D) (6, -, ) (E) (-, 6, ) Ans:D If A =, then 0 (A) A A + I = 0 (B) A 3A + I = 0 (C) A 5A + I = 0 (D) A A + I = 0 (E) A + 3A + I = 0 KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 7

8 66. + y + y If =, then (, y, p, q) equals p q p+ q 0 0 (A) 0,, 0, 0 (B) 0, -, 0, 0 (C), 0, 0, 0 (D) 0,, 0, (E), 0,, The value of is (A) (B) (C) 4 (D) 3 (E) The value of 8 /3 6 /4 9 / is (A) - (B) - (C) -3 (D) -4 (E) Let = be a root of y = q = 0. Then y (A) ( ) (4 6) (B) ( ) (4 + 6) (C) ( ) (-4 6) (D) ( ) (-4 + 6) (D) ( ) (4 + 3) 70. If and ++ are the roots of 3 6 = 0, then (A) 50 9 (B) 40 9 (C) (D) 0 9 (E) Let and be the roots of the equation p 3 = 0. If + = 0, then the value of p is equal to (A) -4 or 4 (B) -3 or 3 (C) - or (D) - or (E) 0 Ans:C 7. If the product of roots of the equation m (m ) = 0 is -, then the value of m is (A) /3 (B) (C) 3 (D) - (E) If f() = , then (A) (B) (C) - (D) 3 (E) 4 Ans:E 74. If and y are the roots of the equation + b + = 0, then the value of + + b y+ b is (A) /b (B) b (C) /b (D) b (E) 75. The equations 5 + a + = 0 and 6 + a + = 0 have a common root. Then a (A) -4 (B) - (C) -3 (D) - (E) 0 KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 8

9 76. The roots of a + + = 0, where a 0, are in the ratio :. Then a (A) /4 (B) / (C) 3/4 (D) (E) If z 3 + z + = 0 where z is a comple number, then the value of z+ + z + z z z z equals (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Ans:C 78. Let Δ= w w, where w is a comple number such that w 3 =. Then Δ equals w 4 w (A) 3w + w (B) 3w (C) 3(w = w ) (D) -3w (E) 3w + 3i 9i 79. If 9i = + iy, then 0 9 i (A) =, y = (B) = 0, y = (C) =, y = 0 (D) = 0, y = 0 (E) = -, y = 0 Ans:D 80. π π If z = cos isin 3 3 z z + (A) 0 (B) (C) - π (D) (E) π 8. 7 π π +cos+ isin π π + cos isin (A) 0 (B) (C) (D) / (E) / 4 k 8. If A = 0 k 0 0 k k k and det (A) = 56, then k equals (A) 4 (B) 5 (C) 6 (D) 7 (E) If A = 0, then A n + ni (A) I (B) na (C) +na (D) I na (E) na I KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 9

10 84. z 5 If z = 5 and w =, then Re(w) z + 5 (A) 0 (B) /5 (C) 5 (D) (E) 85. If A =, then A 07 (A) 05 A (B) 06 A (C) 04 A (D) 07 A (E) 00 A 86. If a= e iθ, then + a a θ (A) cot (B) tan θ (C) θ i cot (D) θ i tan (E) tan θ 87. Three numbers, y, and z are in arithmetic progression. If + y + z = 3 and yz= 8, then + y + z is equal to (A) 9 (B) 0 (C) (D) 0 (E) 88. The 30 th term of the arithmetic progression 0, 7, 4 is (A) 97 (B) 87 (C) 77 (D) 67 (E) The arithmetic mean of two numbers and y is 3 and geometric mean is. Then + y (A) 30 (B) 3 (C) 3 (D) 33 (E) The solution of 3 - = 8 - is (A) /3 (B) /6 (C) 7/6 (D) 5/6 (E) /3 9. The sith term in the sequence is 3,,, is 3 (A) /7 (B) /9 (C) /8 (D) /7 (E) /7 9. Three numbers are in arithmetic progression. Their sum is and the product of the first number and the third number is 45. Then the product of these three number is (A) 35 (B) 90 (C) 80 (D) 70 (E) If a +, a +, 4a are in arithmetic progression, then the value of a is (A) (B) (C) 3 (D) 4 (E) Two numbers and y have arithmetic mean 9 and geometric mean 4. Then and y are the roots of (A) 8 6 = 0 (B) = 0 (C) = 0 (D) = 0 (E) = 0 KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 0

11 95. Three unbiased coins are tossed. The probability of getting at least tails is (A) 3/4 (B) /4 (C) / (C) /3 (D) /3 96. A single letter is selected from the word TRICKS. The probability that it is either T or R is (A) /36 (B) /4 (C) / (D) /3 (E) /3 97. From 4 red balls, white balls and 4 black balls, four balls are selected. The probability of getting red balls is (A) 7/ (B) 8/ (C) 9/ (C) 0/ (E) / Ans : C 98. In a class, 60% of the students know lesion I, 40% know lesion II and 0% know lesson I and II. A student is selected at random. The probability that the student does not know lesson I and lesson II is (A) 0 (B) 4/5 (C) 3/5 (D) /5 (E) /5 99. Two distinct numbers and y are chosen from,,3,4,5. The probability that the arithmetic mean of and y is an inter is (A) 0 (B) /5 (C) 3/5 (D) /5 (E) 4/5 00. The number of 3 3 matrices with entries or + is (A) -4 (B) 5 (C) 6 (D) 7 (E) 9 0. Let S be the set of all symmetric matrices whose entries are either zero or one. A matri X is chosen from S. The probability that the determinant of X is not zero is (A) /3 (B) / (C) 3/4 (D) /4 (E) /9 Ans :B 0. The number of words that can be formed by using all the letters of the word PROBLEM only one is (A)5! (B) 6! (C) 7! (D) 8! (E) 9! 03. The number of diagonals in a heagon is (A) 8 (B) 9 (C) 0 (D) (E) 04. The sum of odd integers from to 00 is (A) 00 (B) 000 (C) 00 (D) 003 (E) Two balls are selected from two black and two red balls. The probability that the two balls will have no black balls is (A) /7 (B) /5 (C) /4 (D) /3 (E) /6 9 9, 06. If z = i + i then z (A) 0+0i (B) +0i (C) 0+i (D) +i (E) + 3i KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY

12 07. The mean for the data 6, 7, 0,, 3, 4, 8, is (A) 9 (B) 8 (C) 7 (D) 6 (E) The set of all real numbers satisfying the inequality < is (A)(3, ) (B)[3, ) (C) [ 3, ) (D) (, 3) (E) (,3) 09. If 3 >, then 3 (A) ( 3, ) (B) (3, ) (C) (, ) (D) (, ) (E) (,3) 0. The mode of the data 8,, 9, 8,, 9, 7, 8, 7, 3, is (A) (B) 9 (C) 8 (D) 3 (E) 7. If the mean of si numbers is 4, then the sum of these numbers is (A) 46 (B) 36 (C) 6 (D) 6 (E) 06. If f() t dt = + e ( > 0), then f() 0 (A) + e (B) + e (C) 3 + e (D) e (E) d = / (A) 3/ + / +c (B) / (C) 3/ + / +c (D) 3/ + / +c (E) 3/ \ 4. In a flight 50 people speak Hindi, 0 speak English and 0 speak both English and Hindi. The number of people who speak at least one of the two languages is (A) 40 (B) 50 (C) 0 (D) 80 (E) If f( ) =, then the value of f(f() (A) (B) 0 (C) (D) (E) 6. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even? (A) 3/4 (B)/4 (C) / (D) /3 (E) / lim 0 (A) (B) (C) 0 (D) Does not eist (E) KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY

13 8. d e + e + (A) + c (B) + c e + e + (C) + c + e (D) + c e (E) + c e 9. tan tan (A) sec θ (B) sec θ (C) sec θ / (D) sin θ (E) cos θ 0. d (A) π /4 (B) π / (C) π (D) 0 (E) π Ans : NA KEAM-ENGINEERING : PAPER-II-QUESTION WITH ANSWER KEY 3

KEAM (ENGINEERING) ANSWER KEY 2017

KEAM (ENGINEERING) ANSWER KEY 2017 MTHMTICS KM KY 07 PG: KM (NGINRING) KY 07 PPR II MTHMTICS QUSTIONS & S. p q r p q r + is equal to () q p () q + p (C) q () p () 0 5 0. Let = 0 5 5 () 0 and () 0 = 0. If + 5 C = 0, then C is 0 5 5 5 5 0