Transcript
JEE Main 2015
[1]
Mathematics 61.
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 hree elemnts is: (1) 219 (2) 256 (3) 275 (4) 510 Sol. [1]
66.
A complex number z is said to be unimodular if z 1 .
67.
62.
The number of integers greater than 6,00 than can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is (1) 216 (2) 192 (3) 120 (4) 72 Sol. [2]
e
binomial expansion of 1 2 x
Suppose z1 and z2 are complex numbers such that
z1 2 z2 2 z1z2 is unimodular and z2 is not unimodular. Then the point z1 lies on a: (1) straight line parallel to x-axis. (2) straight line parallel to y-axis. (3) circle of radius 2. (4) circle of radius
68.
2
If an
n
, for n 1, then the value of
a10 2a8 is equal tyo 2a9 (1) 6 (3) 3 Sol. [3]
64.
LM1 If A M2 MNa
69.
OP PP Q
2 2 1 2 is a matrix satsfying the equation 2 b
AAT 9 I , where I is 3 × 3 identity matrix, then the ordered pair (a, b) is equal to : (1) (2, –1) (2) (–2, 1)
b g
b
g
(4) 2, 1
Sol. [4] 65.
1 50 3 1 2
j
(2)
1 50 3 2
(3)
1 50 3 1 2
(4)
1 50 2 1 2
e e
j
e j e
j
If m is the A.M. of two distinct real numbers l and n
bl, n 1g and
G1 , G2 and G3 are three geometric
(1) 4 l 2 mn
(2) 4 lm2 n
(3) 4 lmn2
(4) 4 l 2 m2 n 2
2 x1 2 x2 x3 x1 2 x1 3x2 2 x3 x2 x3
has a non-trivial solution, (1) is an empty set (2) is a singleton. (3) contains two elements (4) contains more than two elements Sol. [2]
The sum of first 9 terms of the series
13 13 2 3 33 .... is 1 1 3 5 (1) 71 (2) 96 (3) 142 (4) 192 Sol. [2] 70.
lim
x0
b1 cos 2 xgb3 cos xg is equal to : x tan 4 x
(1) 4 (3) 2 Sol. [3] 71.
The sets of all values of for which the system of linear equations:
x1 2 x2
(1)
Sol. [2] (2) – 6 (4) – 3
(3) 2, 1
is
means between l and n, then G14 2G24 G34 equals.
Let and be the roots of equation x 2 6x 2 0 n
50
j
Sol. [1]
Sol. [3] 63.
The sum of coefficients of integral powers of x in the
(2) 3 (4) 1/2
If the function.
g( x)
R|Sk x 1, |T mx 2,
0 x 3 3 x
is differentiable, then the value of k m is (1) 2 (3) Sol. [1]
13 3
(2)
16 5
(4) 4
JEE Main 2015
[2]
72.
b g
The normal to the curve, x 2 2 xy 3y 2 0 at 1, 1
(1) does not meet the curve again. (2) meets the curve again in the second quadrant (3) meets the curve again in the third quadrant (4) meets the curve again in the fourth quadrant Sol. [4] 73.
Let f ( x) be a polynomial of degree four having ex-
78.
b gb g
(1) 901 (3) 820 Sol. [3] 79.
(2) 4
(3) 0 Sol. [2] 74.
(4) 4
z
The integral
F x 1I GH x JK 4
(1)
e
j
(3) x 1
e
j
x2 x4 1
3/ 2
1/ 4
80.
2.
(4) circle of radius
3.
The number of common tangents to the circles
x 2 y 2 6x 18y 26 0 , is
e
j
1/ 4
c
(2) x 4 1
c
F x 1I (4) G H x JK 4
4
c 1/ 4
c
(1) 1 (3) 3 Sol. [3] 81.
2
log x 2
e
2
log x log 36 12 x x
(1) 2 (3) 1 Sol. [3]
2
j
dx
(2) 4 (4) 6
o( x, y) : y (3)
82.
15 64
t
5 (2) 64 (4)
9 32
Sol. [4] Let y( x) be the solution of the differential equation
b x log xg dydx 2 x log x, bx 1g They y(e) is equal to : (1) e (3) 2 Sol. [2]
(1)
27 4
(2) 18
(3)
27 2
(4) 27
(2) 0 (4) 2e
Let O be the vertex and Q be any point on the parabola,
x 2 8y. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is
2 x and y 4 x 1 is
7 (1) 32
x2 y2 1 , is 9 5
Sol. [4]
The area (in sq. units) of the region described by 2
(2) 2 (4) 4
The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the
The integral
z
77.
(3) circle of raidus
ellipse
4
76.
b2x 3y 4g kbx 2y 3g 0 , k R , is a :
x 2 y 2 4x 6y 12 0 and
Sol. [4] 75.
Locus of the image of the point (2, 3) in the line
Sol. [3]
equals:
1/ 4
4
4
dx
(2) 861 (4) 780
(1) straight line parallel to x-axis. (2) straight line parallel to y-axis.
2
then f (2) is equal to : (1) 8
b g
vertices 0, 0 0, 41 and 41, 0 is :
L f (x) OP 3 treme values at x 1 and x 2 . If limM1 N x Q x0
The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with
(1) x 2 y
(2) y 2 x
(3) y 2 2x
(4) x 2 2y
Sol. [4] 83.
The distance of the point (1, 0, 2) from the point of intersection of the line
x 2 y 1 z 2 and the 3 4 12
plane x y z 16, is (1) 2 14
(2) 8
(3) 3 21
(4) 13
Sol. [4]
JEE Main 2015
[3]
84.
The equation of the plane containing the line 2 x 5 y z 3 ; x y 4z 5 , and parallel to the
88.
plane, x 3 y 6z 1, is
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 30o, 45o and 60o respectively, then the ratio, AB : BC, is
(1) 2 x 6 y 12 z 13
(1)
(2) x 3 y 6z 7
(3) 1 : 3
(3) x 3 y 6z 7 Sol. [3]
89.
Let a, b and c be three non-zero vectors such that no
(4) 2 : 3
1 1 1 Let tan y tan x tan
where x
1 two of them are collinear and a b c b c a . 3 If is the angle between vectors b and c, then a
e j
(1)
value of sin is (3)
(1)
2 2 3
(2)
2 3
S o l. [1]
(3)
2 3
(4)
2 3 3
90.
1 3
(2)
1 3x 2 3x x 3
(4)
1 3x 2
b
(3) s r ~ s
FG IJ HK F 1I (3) 220G J H 3K
11
12
FG 2 IJ H 3K F 1I (4) 22G J H 3K (2) 55
10
11
Sol. [1] 87.
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) 16.8 (2) 16.0 (3) 15.8 (4) 14.0 Sol. [4]
3x x 3 1 3x 2 3x x 3 1 3x 2
g
b
86.
55 2 3 3
2
The negation of ~ s r s is equivalent to (1) s ~ r
If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains excatly 3 balls is
FG 2x IJ , H 1 x K
. Then a value of y is
3x x 3
Sol. [1]
(1)
3: 2
Sol. [1]
(4) 2 x 6 y 12 z 13
85.
(2)
3 :1
b
S o l. [3]
g
(2) s r ~ s
g
(4) s r
