Downloaded from jeemain.guru
DATE: 19-11-2019 JEE-MAIN MOCK TEST-1 XII
COURSE
NUCLEUS
TEST CODE
1 1 2 5 8
Q.No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Ans
3
4
3
2
1
4
4
1
4
1
1
1
4
2
2
Q.No.
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Ans
2
1
2
3
2
4
4
3
3
4
1
3
2
4
2
Q.No.
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
Ans
3
1
1
1
3
3
3
2
1
4
4
1
2
3
2
Q.No.
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Ans
2
2
1
4
1
2
2
2
1
1
2
4
2
3
3
PC
IOC
OC
PC
IOC
OC
PC
IOC
OC
PC
IOC
OC
PC
IOC
OC
Q.No.
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
Ans
2
2
4
4
2
4
4
3
2
3
2
2
4
2
2
PC
IOC
OC
PC
IOC
OC
PC
IOC
OC
PC
IOC
OC
PC
IOC
OC
Q.No.
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
Ans
1
2
2
3
2
3
1
3
2
1
2
3
1
4
4
HINTS & SOLUTIONS M AT H E M AT I C S Q.1
r a b c
taking dot with b c [ r b c ] = [a b c ] where a (0,1,1) ; b (1,1,1) and c ( 2,1, 0)
0 1 1 [a b c ] = 1 1 1 = 0 – (0 – 2) + 1(–1 + 2) = 3 2 1 0 and
x y z 1 1 1 = = [ r b c] 2 1 0
x(0 + 1) – y(0 – 2) + z(–1 + 2) = x + 2y + z hence equation of plane is x + 2y + z = 3;
p=
3 = 6
XII MT-1 [JEE Main]
3 Ans. ] 2
Q.2 a b V u d a [ a c d ] b (a . V ) b ( b . V ) a ( u . a ) d ( u . d ) a [ a c d ] b [ a c d ] b [ b c d ]a [ b c a ]d [ b c d ]a [ a c d ] b [ b c a ] d 0 a , b , c are coplanar ]
Q.3
Clearly minimum value of a2 + b2 + c2 O(0,0,0)
3x + 2y + z =7 P (a, b, c)
2
| (3(0) 2(0) (0) 7 | 49 7 = = = units. 2 2 2 2 (3) (2) (1) 14
(This is possible when P(a, b, c) is foot of perpendicular from O(0, 0, 0) on the plane.) Page # 1