3- Question Report (3)

ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 76. p  q  q ~ p is- 76. p  q  q ~ p  (1) equivalent to p  q (1) p  q  (2) Tautology (2)  (3) Fallacy (3)  (4) Neither tautology nor fallacy (4)  77. Minimum distance between parabola 77.  y2 = 8x x+y + 4 = 0  y2 = 8x and its image with respect to line  x + y + 4 = 0 is- (1) 2 2 (2) 3 2 (1) 2 2 (2) 3 2 (3) 4 2 (4) 5 2 (3) 4 2 (4) 5 2 78. Two numbers x and y are chosen at random 78. {1,2,3,4......15}  from the set of integers {1,2,3,4......15}. The xy(x,y) probability that point (x,y) lies on a line   (0,0)     2 2  through (0,0) having slope 3 is- 3 1 1 1 1 1 1 1 1 (1) 3 (2) 15 (3) 21 (4) 42 (1) 3 (2) 15 (3) 21 (4) 42 79. The value of 79. 1 tan   1 tan   1 tan   ..... 1 tan   1 tan   1 tan   ..... terms 4 8 8 16 16 32 4 8 8 16 16 32  is equal to- 51 31 (1)  (2)  51 31 (2)   2 2 2 (1)  41 2 (4)  21 4 21 41 (3)  (3)  (4)   2  4 2  0000CT103116004 H-31/35

ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 80. Tangent to a non linear curve y = ƒ(x), at any 80. y = ƒ(x) P point P intersects x-axis and y-axis at A and x-y- AB B respectively. If normal to the curve y=ƒ(x) P y = ƒ(x) at P intersects y-axis at C such that y-C  AC = BC, ƒ(2) = 3, then equation of curve is- AC= BC, ƒ(2) = 3  6 - x (1) y  (2) x2 + y2 = 13 (1) y  6 (2) x2 + y2 = 13 (4) 2y = 3x x (4) 2y = 3x (3) 2y2 = 9x (3) 2y2 = 9x n n pm n n pm 81. If  r3    1  80 , then possible value 81.   r3    1  80 n  r1 p1 m1 r1 r1 p1 m1 r1 of n can be- - (1) 3 (2) 4 (3) 5 (4) 6 (1) 3 (2) 4 (3) 5 (4) 6 82. If in ABC, AB = 4, BC = 6 and AC = 5, 82. ABC , AB = 4, BC = 6 AC = 5, h1,h2,h3 be the length of altitude of from A,B,C h1,h2,h3 vertices A,B,C respectively, then value of 1 1 1 h1    -  1 1 1 h2 h3      is equal to-  h1 h2 h3  7 27 47 87 (1) 7 (2) 2 7 (3) 4 7 (4) 8 7 (1) (2) (3) (4) 15 15 15 15 15 15 15 15 4  x2 6 2 4  x2 6 2 83. 6 9  x2 3 ; (x  0) is not divisible 83. 6 9  x2 3 ; (x  0)  2 3 1  x2 2 3 1  x2 by- -  (1) x (2) x3 (3) 14+ x2 (4) x5 (1) x (2) x3 (3) 14+ x2 (4) x5  H-32/35 0000CT103116004

ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 84. Two parallel towers A and B of different 84.   heights are at some distance on same level ABA 10  ground. If angle of elevation of a point P at QB 20 20m height on tower B from a point Q at P B P 10m height on tower A is  and is equal to A  50 R  half the angle of elevation of point R at 50m   height on A from point P on B, then  is- (1) 30º (2) 45º (1) 30º (2) 45º (3) 15º (4) 60º (3) 15º (4) 60º 85. Radius of circle touching y-axis at point 85. y-P(0,2)  P(0,2) and circle x2 + y2 = 16 internally- x2 + y2 = 16 - 5 3 5 (4) 2 5 3 5 (4) 2 (1) 2 (2) (3) (1) 2 (2) 2 (3) 4 2 4 86. AB,BC are diagonals of adjacent faces of a 86. AB,BC        rectangular box with its centre at the origin,  its edges parallel to the co-ordiantes axes. BOC, COA AOB If the angles BOC, COA and AOB are  and   cos + cos + cos  respectively, then cos + cos + cos is- -  (1) –1 (2) 0 (1) –1 (2) 0 3 3 (4)  (3) 2 (3) (4) data insufficient 2 x   87. Number of solutions of the equation 87. 6 t2 1 nt dt  5|x|, x  R0 x0   6 t2 1 nt dt  5|x|, x  R0 is- - 0 (1) 5 (2) 4 (3) 2 (4) 3 (1) 5 (2) 4 (3) 2 (4) 3  0000CT103116004 H-33/35

ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017 88. The shaded region in given figure is- 88. - AA BC BC (1) A  B  C (2) C   A  B (1) A  B  C (2) C  A  B (3) C  B  C (4) C   A  B (3) C  B  C (4) C  A  B 89. The number of numbers between 1 and 1010 89. 1 1010 1 which contains digit 1, is- -  (1) 1010 – 910 (2) 1010 – 910 + 1 (1) 1010 – 910 (2) 1010 – 910 + 1 (3) 109 10 (3) 109 10 (4) 10Cr 9r (4) 10Cr 9r r0 r0 90. If r  3iˆ  2ˆj  5kˆ , a  2ˆi  ˆj  kˆ ,   ˆi  3ˆj  2kˆ 90.  r  3iˆ  2ˆj  5kˆ , a  2iˆ  ˆj  kˆ ,   ˆi  3ˆj  2kˆ b b and   2ˆi  ˆj  3kˆ such that r  a    c , c  2iˆ  ˆj  3kˆ r a    c c b b then -  (1) ,  ,  are in A.P (1) ,  ,   2 2 (2) 2 are in A.P (2) 2  (3)  are in A.P (3)   (4) ,  , are in G.P (4) ,  ,  3 3  H-34/35 0000CT103116004

ALL INDIA OPEN TEST/LEADER & ENTHUSIAST COURSE/JEE (Main)/19-03-2017   0000CT103116004 H-35/35