JEE Mains 12 January 2019 Question Paper Shift 2 | JEE Main & Advanced Previous Year Papers PDF Download

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JEE (Main) Examination–2019/Evening Session/12-01-2019
E 1
1. Let Z be the set of integers. If
( )( ) { }
2
A xZ:2x2x 5x6 = Î + -+ =1 and
{ } BxZ:32x19 =Î-<-< , then the number of
subsets of the set A × B, is :
(1)  2
18
(2) 2
10
(3) 2
15
(4) 2
12
Ans (3)
Sol. A = {x Î z : 
2
(x 2)(x –5x 6)
2
++
 = 1}
2
(x 2)(x –5x 6)
2
++
 = 2
0
 Þ x = –2, 2, 3
A = {–2, 2, 3}
B = {x Î Z : –3 < 2x – 1 < 9}
B = {0, 1, 2, 3, 4}
A × B has is 15 elements so number of subsets
of A × B is 2
15
.
2. If 
44
sin 4cos 2 4 2 sin cos a+ b+= ab ;
a, [0,] bÎp , then cos(a + b) – cos(a – b) is
equal to :
(1) 0 (2) 
2 -
(3) –1 (4) 
2
Ans (2)
Sol. A.M. ³ G.M.
1
44
44
4
sin 4cos 11
(sin .4cos .1.1)
4
a+ b++
³ ab
sin
4
 a + 4 cos
2
b + 2 ³ 4
2
sin a cos b
given that sin
4
 a + 4 cos
4
 b + 2 = 4
2
 sina cosb
Þ A.M. = G.M. Þ sin
4
 a = 1 = 4 cos
4
 b
sin a = 1, cos b = ± 
1
2
Þ sin b = 
1
2
 as b Î [0, p]
cos (a + b) – cos (a – b) = –2 sin a sin b
= –
2
MATHEMATICS
TEST PAPER OF JEE(MAIN) EXAMINATION – 2019
(Held On SATURDAY 12
th
 JANUARY ., 2019) TIME : 02 : 30 PM To 05 : 30 PM
3. If an angle between the line,
x 1 y 2 z3
2 12
+ --
==
-
and the plane, x – 2y – kz = 3 is 
–1
22
cos
3
æö
ç÷
ç÷
èø
,
then a value of k is:
(1) 
5
3
-
(2) 
3
5
(3) 
5
3
(4) 
3
5
-
Ans (3)
Sol. DR's of line are 2, 1, –2
normal vector of plane is 
ˆ ˆˆ
i – 2j– kk
sin a = 
2
ˆˆ ˆ ˆ ˆˆ
(2i j– 2k).(i – 2j– kk)
31 4k
+
++
sin a = 
2
2k
3k5 +
.......(1)
cos a = 
22
3
.......(2)
(1)
2
 + (2)
2
 = 1 Þ k
2
 = 
5
3
4. If a straight line passing thourgh the point
P(–3, 4) is such that its intercepted portion between
the coordinate axes is bisected at P, then its
equation   is :
(1) x – y + 7 = 0
(2)  3x – 4y + 25 = 0
(3) 4x + 3y = 0
(4) 4x – 3y + 24 = 0
Ans (4)