JEE(MAIN) – 2015 TEST PAPER WITH ANSWER (HELD (HEL D ON SATURDAY SATURDAY 04th APRIL, 2015)
31 .
Let a , b and c be three non-zero vectors such that no two of them are collinear and
a, b c
35 .
1 b c a . If is the angle 3
between vectors b and c , then a value of sin is :
Ans. 36 .
2 (1) 3 (3) Ans. 32 .
Ans. 33 .
2 2 3
Ans. 34 .
Ans.
(2)
(4)
2 3 3
2 3
(3) Let O be the vertex and Q be any point on the parabola, x2 = 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :(1 ) y2 = 2x (2) x2 = 2y (3) x2 = y (4) y2 = x (2) If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB : BC, is : (1) 1 : 3 (3) 3 : 1
The equation of the plane containing the line 2x – 5y + z = 3 ; x + y + 4z = 5, and parallel to the plane, x + 3y + 6z = 1, is : (1) x + 3y + 6z = 7 (2) 2x + 6y + 12z = – 13 (3) 2x + 6y + 12z = 13 (4) x + 3y + 6z = – 7 (1) Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is : (1) 275 (2) 510 (3) 219 (4) 256 (3) Locus of the image of the point (2, 3) in the line (2x – 3y + 4) + k (x – 2y + 3) = 0, k R, is a
Ans. 37 .
(1) circle circle of rad radius ius
(2) circle of radius
Ans. 38 .
Ans.
(4)
39 .
3: 2
(3) The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0) is : (1 ) 8 2 0 (2 ) 78 0 (3 ) 9 0 1 (4 ) 86 1 (2)
Ans.
3
(3) straight line parallel to x-axis (4) straight line parallel to y-axis (1)
(1 cos 2x) (3 cos x) is equal to : x 0 xtan4x lim
(1) 2
(2) 2 : 3
2
(2)
1 2
(3) 4 (4) 3 (1) The distance of the point (1, 0, 2) from the point of intersection of the line x 2 y 1 z 2 and the plane 3 4 12 x – y + z = 16, is : (1) 3 21
(2) 13
(3) 2 14 (2)
(4) 8
40 .
The sum of coefficients of integral powers of
44 .
50
x in the binomial expansion of 1 2 x
numbers such that
is : 1 50 3 1 (1) 2
(3) Ans. 41 .
1 50 3 1 2
(4)
1 50 3 2
(3) The sum of first 9 terms of the series 13 13 23 13 23 33 .... is : 1 1 3 1 3 5
Ans. 42 .
15 64
Ans. 45 .
(2)
Ans. 46 .
9 32
Ans.
(3)
7 32
(4)
5 64
Ans.
(2)
43 .
The set of all values of for which the system
47 .
of linear equations :
2x1 – 2x2 + x3 = x1
Ans.
2x1 – 3x2 + 2x3 = x2 –x1 + 2x2 = x3
has a non-trivial solution
48 .
(1) con contain tainss two eleme elements nts (2) contains more than two elements (3) is an empty set (4) is a singleton Ans.
(1)
(2) circle of radius 2 (3) straight line parallel to x-axis (4) straight line parallel to y-axis (1) The number of common tangents to the circle x2 + y2 – 4x – 6y – 12 = 0 and x2 + y 2 + 6x + 18y + 26 = 0, is : (1) 3 (2) 4 (3) 1 (4) 2 (1) The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is : (1) 120 (2) 72 (3) 216 (4) 192 (4) Let y(x) be the solution of the differential equation dy (x log x) + y = 2x log x, (x 1). dx Then y(e) is equal to : (1) 2 (2) 2e (3) e (4) 0 (1)
(1) 142 (2) 192 (3) 71 (4) 96 (4) The area (in sq. units) of the region described by {(x, y) : y2 2x and y 4x – 1} is : (1)
z1 2z 2 is unimodular and 2 z1z2
z2 is not unimodular. Then the point z 1 lies on a: (1) circl circlee of radiu radiuss 2
1 50 2 1 (2) 2
A complex number z is said to be unimodular if |z| = 1. Suppose z 1 and z 2 are complex
Ans.
1 2 2 2 1 2 is a matrix satisfying the If A = a 2 b
equation equation AA A AT = 9I, where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to : (1) (2 (2, 1) (2) (–2, –1) (3) (2 (2, –1) (4) (–2, 1) (2)
49 .
If m is the A.M. of two distinct real numbers l and n(l, n > 1) and G1, G2 and G3 are three geometric means between l and n , then
54 .
k x 1 , 0 x g(x) = mx 2 , 3 x 5
G14 2G 42 G34 equals.
Ans. 50 .
(1) 4 lmn 2 (3) 4 l2mn (4)
Ans.
(3) s ~ r
(4) s r ~ s
55 .
The integral
x (x ( x 1) 2
(1) x 4 1 c 1 4
x 1 (3) 4 c x
Ans. 53 .
Ans.
4
3 4
equals :
1 4
x 1 c x4
(2)
4
Ans.
1 4
(4) x 4 1 c
(2) The normal to the curve, x 2 + 2xy – 3y 2 = 0, at (1, 1) : (1) meets the curve again in the third quadrant (2) meets the curve again in the fourth quadrant (3) does not meet the curve again (4) meets the curve again in the second quadrant (2) Let 2x , tan–1 y = tan–1 x + tan–1 1 x2 1 where | x | < . Then a value of y is : 3 3x x 3 3x x 3 (1) (2) 1 3x 2 1 3x 2 3x x 3 (3) 1 3x 2
(2) 4
(4)
16 5
(3) The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is : (1 ) 1 5 . 8 (2 ) 1 4 . 0 (3 ) 1 6 . 8 (4 ) 1 6 . 0 (2) The integral
dx
1 4
4
10 3
(3 ) 2
(2) s r
51 .
52 .
(1)
(1) s r ~ s (2)
Ans.
is differentiable, then value of k + m is -
(2) 4 l2m2n2 (4) 4 lm 2n
The negation of ~ s ~ r s is equivalent to :
Ans.
If the function.
56 .
4
logx 2 dx log x 2 log(36 12x x 2 ) 2
Ans. 57 .
is equal to : (1 ) 1 (2) 6 (3 ) 2 (4 ) 4 (1) Let and be the roots of equation x2 – 6x – 2 = 0. If an = n – n, for n 1, then a10 2a 8 the value of 2a 9 is equal to :
Ans. 58 .
3x x 3 (4) 1 3x 2
(1 ) 3 (2 ) – 3 (3 ) 6 (4 ) – 6 (1) Let f (x) be a polynomial of degree four having extreme values at x = 1 and x = 2.
If lxim0 1
(3) Ans.
(1 ) 0 (1)
(x) = 3, then f (2) (2) is equal to : x 2
(2) 4
(3 ) – 8
(4 ) – 4
59 .
The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the
60 .
x2 y2 1 is : latera recta to the ellipse 9 5
(1)
(3) Ans.
(2)
27 2
(2) 27
27 4
(4) 18
If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is : 12
1 (1) 220 3
11
55 2 (3) 3 3 Ans.
11
1 (2) 22 3
10
2 (4) 55 3
(Bonus)
