UPSEE - Mathematics -2003 Unsolved Paper

• 1. UPSEEPAST PAPERMATHEMATICS- UNSOLVED PAPER - 2003

2. SECTION I Single Correct Answer Type There are five parts in this question. Four choices are given for each part and one of them iscorrect. Indicate you choice of the correct answer for each part in your answer-book bywriting the letter (a), (b), (c) or (d) whichever is appropriate 3. 01 Problem 1 attains minimum value at : x21 x2 a. x = 0 b. x = 4 c. x = 1 d. x = 3 4. 02 Problem a b x cb a x c If a, b, c are the non-coplanar vectors, then the value of is : cxa b c a x b a. 1 b. 2 c. 0 d. none of these 5. 03 Problem If x 2y = 4, the minimum value of xy is : a. - 2 b. 0 c. 0 d. -3 6. 04 Problem If z = x + iy and 1 iz1, the locus of z is :z i a. x-axis b. y-axis c. circle with unity radius d. none of the above 7. 05 Problem The vertex of an equilateral triangle is (2, -1) and the equation of its base is x + 2y = 1, the length of its sides is :2 a. 154 b.3 3 c. 154 d. 15 8. 06 Problem The resultant of two forces P and Q is R. If the direction of P is reversed keeping the direction Q same, the resultant remains unaltered. The angle between P and Q is : a. 900 b. 600 c. 450 d. 300 9. 07 Problem The distance s (in cm) traveled by a particle in t seconds is given by, s = t3 + 2t2 + t. The speed of the particle after 1 s will be : a. 2 cm/s b. 8 cm/s c. 6 cm/s d. none of these 10. 08 Problem The roots of | x 2|2 + | x - 2| - 6 = 0 are : a. 4, 2 b. 0, 4 c. -1, 3 d. 5, 1 11. 09 Problem The height of a tower is 7848 cm. A particle is thrown from the top of the tower with the horizontal velocity of 1784 cm/s. The time taken by the particle to reach the ground is (g = 981 cm/s2) ? a. 8 s b. 2 s c. 4 s d. 8 s 12. 10 Problem The directrix of the hyperbola is :6 a. y136x b. 139 c. y139x d. 13 13. 211 Problem55 The value of cos 1 cossin 1 cosis : 3310 a. 3 b. 0 c. 25 d. 3 14. 12 Problem1 x 2x If f x log , then fwill be equal to :1 x1 x2 2f(x2) f(x2) 2f(2x) 2f(x) 15. 13 Problem If (1+ x 2x2)6 = 1 + a1x + a2x2++ a12x12 then the value of a2 + a4 + .+ a12, is : a. 31 b. 32 c. 64 d. 1024 16. 14 Problem 2x3 6x + 5 is an increasing function, if : a. 0 < x < 1 b. -1 < x < 1 c. x < - 1 or x > 1 1 d. -1 < x < - 2 17. 15 Problem Two trains are 2 km apart. Their lengths are 200 m and 300 m. They are approaching towards each other with speed of 20 m/s and 30 m/s respectively. They will cross each other after : a. 150 s b. 100 s c. 50 s25 d.3 s 18. 16 Problem d 3y d 2y =1, has degree and order as :2 1 dx 3 dx 2 a. 3, 1 b. 3, 2 c. 1, 3 d. 2, 3 19. 17 Problem1 1 The value of I x x dx is :0 2 a. 141 b.21 c.8 d. none of these 20. 18 Problem4 2 If A = 3 4, | adj A| is equal to : a. 6 b. 16 c. 10 d. none of these 21. 19 Problem ab c x a b c is equal to a. [a b c ] b. 3 [a b c ] c. 0 d. 2 [a b c ] 22. 20 Problem A block weighing w, is supported on an inclined surface with the help of a horizontal force P. The same block can be supported with the help of another force Q acting parallel to the inclined surface, then the value of is : a. w sin b. 1Q c. 11 d. Q2 23. 21 Problem2|x 1| dx is equal to : 0 a. 0 b. c. 1 d. 2 24. 22 Problem For a pack of cards two are accidently dropped. Probability that they are of opposite shade is :13 a.51 1 b. 52 x 5126 c. 51 d. none of these 25. 23 Problem If a particle is displaced from the point A (5, -5, -7) to the point B(6, 2, -2) under the influence of the forces P110 i j 11k , P2ij4 5 6k , P3 2 i 9k , j then the work done is : a. 87 b. 85 c. 81 d. none of these 26. 24 Problem1 If sin x + cos x = , then tan 2x is :5 a. 251724 b. 7 c. 72525 d. 7 27. 25 Problem In a ABC, Band C . If D divides BC internally in ratio 1 : 3, then the3 4sin BAD value of sin CADis :1 a.31 b. 62 c. 31 d. 3 28. 26 Problem If | a x b | | a b | , then the angle between is : a. b.2 /3 c. /4 d. /2 29. 27 Problem Let A, B and C are the angles of a triangle and A 1 B 2 C tan , tan . Then, tan 2 3 2 3 2 is equal to :1 a.32 b.32 c.97 d. 9 30. 28 Problem The value of : lim 1 x tan xx 1 23 a. 42 b. 32 c. d. 4 31. 29 Problem x 1 If f(x) = , then the maximum value of f(x) is : x a. e b. (e)1/e e1 c. e d. none of these 32. 30 Problem The volume of the solid formed by rotating the area enclosed between the curve y = x2 and the line y = 1 about y =1 is (in cubic unit) :9 a.54 b. 38 c.37 d.5 33. 31 Problem15 dx is equal to :8x 3 x 11 5 a. log2 3 1 5 b.log 3 3 1 3 c.log 5 5 1 3 d.log 2 5 34. 32 Problem Area of the square formed by |x| + |y| = 1 (in square unit) is : a. 0 b. 1 c. 2 d. 4 35. 33 Problem if x = 3 + i, then x3 3x2 8x + 15 is equal to : a. 45 b. -15 c. 10 d. 6 36. 34 Problem The function f(x) = log (x + x2 1 ) is : a. Even function b. Odd function c. Neither even nor odd d. Periodic function 37. 35 Problem The perpendicular PL, PM are drawn from any point P on the rectangular hyperbola xy = 25 to the asymptotes. The locus of the mid point of OP is curve with eccentricity : a. An ellipse with e = 2 b. Hyperbola with e =21 c. parabola with e =2 d. none of the above 38. 36 Problem | a| | b| |c | 1 and a b c 0, then the value of a b Ifb c c a is : a. 0 b. -13 c. 2 d. 3 39. 37 Problem If x = logb a, y = logc b, z = loga c, then xyz is : a. 0 b. 1 c. 3 d. none of these 40. 38 Problem1 cos cos The value of the determinant is :cos 1 coscos cos1 a. 0 b. 12 2 c.2 2 d. 41. 39 Problem If P(A) = P(B) = x and , then x is equal to :1 a. 21 b. 41 c. 31 d.6 42. 40 Problem If p and q are the roots of the equation x2 + px + q = 0, then : a. p = 1 or 0 b. p = -2 or 0 c. p = -2 d. p = 1 43. 41 Problem If a dice is thrown twice, the probability of occurrence of 4 at least once is :11 a. 3635 b. 36 7 c. 26 d. none of these 44. 42 Problem8 The value of |x 5 |dx is0 a. 9 b. 12 c. 17 d. 18 45. 43 Problem The value of | sin3 |d is :0 a. 0 b. c. 4/3 d. 3/8 46. 44 Problem A ball weighting 2 kg and speed 6 m/s collides with another ball of 4 kg moving in opposite direction with speed of 3 m/s. They combine after the collision. The speed of this combined mass (in m/s) is : a. 4 b. 2 c. 0 d. 3 47. 45 Problem If , , are the roots of the equation x3 + 4x +1 = 0, then1 1 1is equal to : a. 2 b. 3 c. 4 d. 5 48. 46 Problem If cos + cos 2 + cos 3 = 0, the general value of is : a.2m 4 n 2 b. m13 n c.m 1 3 d. 2m3 49. 47 Problem Three like parallel forces P, Q and R are acting on the vertices of a ABC whose resultant passed through its centroid, then :P Q R a. b a cP Q R b. tan A tan B tan C c. P = Q = R d. None of the above 50. 48 Problem A person observes the angle of elevation of a building as 300. The person proceeds towards the building with a speed of 25( 3 -1) m/h. After two hours, he observes the angel of elevation as 450. the height of the building (in m) is : a. 50 ( 3 - 1) b. 50(3 + 1) c. 50 d. 100 51. 49 Problemx 2 The value of lim x 3 is :x x 1 a. 0 b. 1 c. e2 d. e4 52. 50 Problem If A + B + C = , then cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C is equal to : a. 0 b. 1 c. 2 d. 3 53. FOR SOLUTIONS VISIT WWW.VASISTA.NET