JEE-MAIN 2017 (PAPER-2 ) TEST PAPER WITH ANSWER (HELD ON SUNDAY 02 nd APRIL, 2017) PART I APTITUDE TEST

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1 Directions : (For Q. No. 1 and 4). The problem figure shows the top view of objects. Looking in the direction of the arrow, identify the correct elevation, from amongst the answer figures. CODE-X JEE-MAIN 017 (PAPER- ) TEST PAPER WITH ANSWER (HELD ON SUNDAY 0 nd APRIL, 017) PART I APTITUDE TEST. Problem Figure : 1. Problem Figure : (). Problem Figure : 4. Problem Figure : Directions : (For Q. No. 5 and 6). Which one of the answer figures will complete the sequence of the three problem figures? 5. Problem Figure :? 1

2 JEE(MAIN) Problem Figure :? 9. Problem Figure : Directions : (For Q. No. 7 and 10). The D figure shows the view of an object. Identify the correct top view from amongst the answer figures. 7. Problem Figure : 8. Problem Figure : 10. Problem Figure : Direction : (For Q. No. 11 and 1) The problem figure shows the elevation of an object. Identify the correct top view from amongst the answer figures. 11. Problem Figure :

3 14. Problems figure CODE-X 1. Problem Figure : Direction : (For Q. No. 1 to 15). The problem figure shows the top view of an object. Identify the correct elevation from amongst the answer figures looking in the direction of the arrow. 1. Problem Figure : 15. Problem figure Directions : (For Q.No. 16). One of the following answer figures is hidden in the problem figure in the sane size and direction. Select the correct one. 16. Problem figure

4 JEE(MAIN)-017 Directions : (For Q. No. 17 to 19) The D problem figure shows a view of an object. Identify the correct front view from amongst the answer figures, looking in the direction of arrow. 17. Problem figure 19. Problem figure 18. Profblem figure Directions : (For Q.No. 0 to ). Identify the correct D figure from amongst the answer figures, which has the same elevation, as given in the problem figuree on the left. 0. Problem figure 1. Problem figure 4

5 . Problem figure CODE-X 4. Ans. Directions : (For Q. No. and 5). Which one of the answer figures shows the correct view of the -D problem figure after the problem figure is opened up?. 5. 5

6 JEE(MAIN)-017 Directions : (For Q. No. 6 and 7). Find the odd figure out of the problem figures given below Ans. 7. Directions : (For Q. No. 8 and 1). Which one of the answer figures is the correct mirror image of the problem figure with respect to X-X? 8. () 6

7 CODE-X () () Ans. 7

8 JEE(MAIN)-017 Directions : (Q. No. to 4). The D problem figure shows a view of an object. Identify the correct front view, from amongst the answer figures, looking in the direction of arrow () 8

9 6. Which type of roof will provide maximum protection from heat radiation in a building? Concrete slab, water proofed and covered with a roof garden Painted aluminium sheeting () Concrete slab with plaster Concrete slab with mud and brick tiles Ans. 7. What is Venice famous for? Springs Canals () Mountains Valleys 8. Gol Gumbaj of Bijapur is :- A Mosque A Fort () A Mausoleum A Palace 9. Solar energy is converted to electrical energy by:- Rain water Photovoltaic cells () Electro magnets Bio technology 40. Buland Darwaza is located in :- Golconda Fatehpur Sikri () Red Fort Agra Fort 41. Ellora temples are :- Built in wood Made in marble () Built in sandstone Cut out of rock 4. Salim Chisti mosque is located in :- Delhi Gwalior () Fatehpur Sikri Hyderabad 4. IGBC stands for :- Indian Government Biological Center International Great Beautiful City () Indian Green Building Council Indian Great Building Center CODE-X 44. Big Ben is a : Temple Clock Tower () Palace Mosque 45. Pyramids are located in : Ethiopia Rome () Egypt Greece 46. Vertical sun protectors over wall openings help in cutting off summer sun rays on : On all sides South side () West side North side 47. Temperature of the Earth due to the 'Greenhouse Effect' : Keeps increasing / decreasing Increases () Decreases Remains constant 48. Which one of the following is not a load bearing component in a building? Concrete floor slab Column () Beam Partition wall 49. Which color is obtained by mixing red and yellow colors? Brown Purple () Pink Orange 50. The ruins of Hampi are located in which State? Tamil Nadu Karnataka () Andhra Pradesh Kerala 9

10 JEE(MAIN) If A and B be two finite sets such that in total number of subsets of A is 960 more than the total number of subsets of B, then n(a) n(b) (where n(x) denotes the number of elements in set X) is equal to : 6 () 4 5. The order and the degree of the differential equation of all ellipses with centre at the origin, major axis along x-axis and eccentricity respectively : are,, 1, 1 (), 1 1, 5. If A and B are two independent events such that P(A) = 10 and P(A B) = 4, then P(A B) 5 is equal to : () Let S be the set of all real values of 'a' for which the following system of linear equations ax + y + 5z = 1 x + y + z = 1 y + 7z = 1 is consistent. Then the set S is : an empty set equal to R () equal to R {1} equal to {1} PART II MATHEMATICS 56. If the shortest distance between the lines x + = y = 1z, x = y + 4 = 6z 1 is 4 units, then a value of is : () 57. If the digits at ten's and hundred's places in (11) 016 are x and y respectively, then the ordered pair (x, y) is equal to :- (1, 8) (1, 6) () (6, 1) (8, 1) 58. Which one of the following points does not lie on the normal to the hyperbola, drawn at the point 8,? 10, 1 1, () 1 1, 11, x y Ans. 59. An urn contains 5 red, 4 black and white marbles. Then the number of ways in which 4 marbles can be drawn from it so that at most of them are red, is : () If (x + iy) = 7 + 4i, then a value of 55. If an equilateral triangle, having centroid at the origin, has a side along the line, x + y =, then the area (in sq. units) of this triangle is : 6 6 () 6 9 Ans is :- 6i i () i 6 10

11 61. The equation of the circle, which is the mirror image of the circle, x + y x = 0, in the line, y = x is :- x + y 6x 4y + 1 = 0 x + y 6x 8y + 4 = 0 () x + y 8x 6y + 4 = 0 x + y 4x 6y + 1 = 0 Ans. log(sin 7x cos 7x) 6. lim x 0 sin x equals :- () CODE-X 1 Ans. 66. Two numbers are selected at random (without replacement) from the first six positive integers. If X denotes the smaller of the two numbers, then the expectation of X, is : 1 log 7 () If the line, y = mx, bisects the area of the region {(x,y) : 0 x, 0 y 1 + 4x x }, then m equals : () The product of the perpendiculars drawn from x y the foci of the ellipse, 1 upon the 9 5 tangent to it at the point 5, is : 1 9 () An observer standing at a point P on the top of a hill near the sea shore notices that the angle of depression of a ship moving towards the hill in a straight line at a constant speed is 0. After 45 minutes, this angle becomes 45. If T (in minutes) is the total time taken by the ship to move to a point in the sea where the angle of depression from P of the ship is 60, then T is equal to : 5 14 () The perpendicular distance from the point (,1,1) on the plane passing through the point (1,,) and containing the line, r ˆi ˆj (i ˆ ˆj 4k) ˆ is 11 () x The integral dx is equal to (x x ) x 1 () 1 x cot x 1 1 C 1 x tan (x 1) 1 x tan (x 1) 1 x cot x 1 1 C C C 1 11 (Where C is a constant of integration) 11

12 JEE(MAIN) The value of cos85 sin 55 is () Let a 1, a, a, a 4, a 5 be a G.P. of positive real numbers such that the A.M., of a and a 4 is 117 and the G.M. of a and a 4 is 108. Then the A.M. of a 1 and a 5 is () Ans. 71. The integral dx is equal to 1 tan x 4 () 1 7. Three vectors a, b and c 6 are such that a 1, b, c 4 and a b c 0. Then the value of 4a b b c c a is equal to : 7 68 () For all real numbers x, y and z, the determinant x xy xz y x z 1 xy xz yz z 1 y x 1 xy xz 1 y is equal to : (y xz) (z x) zero () (x y) (y z) (z x) (x yz) (y z) 74. If and are the two values of such that the roots and of the quadratic equation, x x x 5 0 satisfy 1 1 is equal to : () Ans. 4 0, then If the sum of the first 15 terms of the series is 15 k, then k is equal to : 16 1 () Water is running into an underground right circular conical reservoir, which is 10 m deep and radius of its base is 5 m. If the rate of change in the volume of water in the reservoir is m / min., then the rate (in m / min) at which water rises in it, when the water level is 4 m, is : 8 () A bag contains three coins, one of which has head on both sides, another is a biased coin that shows up heads 90% of the time and the third one is an unbiased coin. A coin is taken out from the bag at random and tossed. If it shows up a head, then the probability that it is the unbiased coin, is : () If the functiuon f : R R, defined by ax, x f(x) = is differentiable, ax bx, x then the value of f '( ) + f '() is equal to : 0 () Which one of the following statements is a tautology? p (p q) (p q) q () p (p q) p (q p) 80. The sum of the abscissae of the points where the curves, y = kx + (5k + )x + 6k + 5, (k R), touch the x-axis, is equal to : 4 19 ()