JEE Mains 2020 Total Marks
80
Chapter wise Tests
o
1. If the resultant of two forces of magnitudes P and Q acting at a point at an angle of 60 is 7Q, then P/Q is
3
(a) 1 (b) 2 (c) 2 (d) 4
2 2, 5 BC, CA
2. ABC is an isosceles triangle right angled at A. Forces of magnitude and 6 act along and AB respectively. The
magnitude of their resultant force is
(a) 4 (b) 5 (c) 11 + 2 2 (d) 30
3. The unit vector parallel to the resultant vector of 2i + 4 j − 5 k and i + 2 j + 3 k is
1 i + j+k
(3 i + 6 j − 2 k)
(a) 7 (b) 3
i + j + 2k 1
(−i − j + 8 k)
(c) 6 (d) 69
4. If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then AD + BE + CF is
(a) A zero vector (b) A unit vector
(c) 0 (d) None of these
5. If position vectors of a point A is a + 2b and a divides AB in the ratio 2 : 3 , then the position vector of B is
(a) 2a - b (b) b - 2a
(c) a - 3b (d) b
o a . b = − 8,
6. If the moduli of a and b are equal and angle between them is 120 and then | a | is equal to
(a) - 5 (b) - 4 (c) 4 (d) 5
8. For any three non-zero vectors r1 , r2 and r3 ,
r1 . r1 r1 . r2 r1 . r3
r2 . r1 r2 . r2 r2 . r3 = 0
r3 . r1 r3 . r2 r3 . r3
.
Then which of the following is false
(a) All the three vectors are parallel to one and the same plane
(b) All the three vectors are linearly dependent
(c) This system of equation has a non-trivial solution
(d) All the three vectors are perpendicular to each other
9. If a and b are unit vectors such that a b is also a unit vector, then the angle between a and b is
(a) 0 (b) 3 (c) 2 (d)
10. (a − b) (a + b) =
(a) 2( a b) (b) a b
(c) a − b
2 2
(d) None of these
11. A unit vector which is perpendicular to i + 2 j − 2k and −i + 2 j + 2k is
1 1
(2i − k) (−2i + k)
(a) 5 (b) 5
1 1
(2i + j + k) (2i + k)
(c) 5 (d) 5
12. The unit vector perpendicular to 3i + 2 j − k and 12i + 5 j − 5 k, is
5i − 3 j + 9 k 5i + 3 j − 9 k
(a) 115 (b) 115
−5 i + 3 j − 9 k 5i + 3 j + 9 k
(c) 115 (d) 115
P (1, − 1, 2), Q (2, 0, − 1) R (0, 2, 1)
13. A unit vector perpendicular to the plane determined by the points and is
IN ASSOCIATION WITH JEEMAIN.GURU
JEE Mains 2020 Total Marks
80
Chapter wise Tests
2i − j + k 2i + j + k
(a) 6 (b) 6
−2i + j + k 2i + j − k
(c) 6 (d) 6
14. If a, b, c are vectors such that [a b c ] = 4 , then [a b b c c a] =
(a) 16 (b) 64 (c) 4 (d) 8
[i k j] + [k j i] + [j k i]
15.
(a) 1 (b) 3 (c) - 3 (d) - 1
16. If a = 3i − j + 2k, b = 2i + j − k and c = i − 2 j + 2k, then
(a b) c is equal to
(a) 24 i + 7 j − 5 k (b) 7 i − 24 j + 5 k
(c) 12i + 3 j − 5 k (d) i + j − 7 k
17. Angle between the line r = (i + 2 j − k) + (i − j + k) and the normal to the plane r . (2i − j + k) = 4 is
2 2 2 2
sin−1 cos −1
3 3
(a) (b)
2 2 2 2
tan −1 cot −1
3 3
(c) (d)
r 2 + 2 u 1 . r + 2 d1 = 0 r 2 + 2 u 2 . r + 2d 2 = 0
18. The spheres and cut orthogonally, if
u1 . u 2 = 0
(a)
(b) u 1 + u 2 = 0
u 1 . u 2 = d1 + d 2
(c)
(d) (u1 − u 2 ).(u1 + u 2 ) = d1 + d 2
2 2
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19. A vector n of magnitude 8 units is inclined to x-axis at 45 , y-axis at 60 and an acute angle with z axis. If a plane
( 2 , − 1, 1)
passes through a point and is normal to n , then its equation in vector form is
(a) r.( 2 i + j + k) = 4 (b) r.( 2 i + j + k) = 2
(c) r.(i + j + k) = 4 (d) None of these
20. The vector equation of the plane through the point (2, 1, -1) and passing through the line of intersection of the plane
r.(i + 3 j − k) = 0 and r.( j + 2k) = 0 is
(a) r.(i + 9 j + 11k) = 0 (b) r.(i + 9 j + 11k) = 6
(c) r.(i − 3 j − 13k) = 0 (d) None of these
IN ASSOCIATION WITH JEEMAIN.GURU
