Math Chapter Wise

EnglishDSSSB PGT 2021

Q21.There are two orthogonal vectors A,B in R3, each of length 1 unit. Let P be a vector satisfying the equation P×B = A P − −, then-

AP is orthogonal to B BP is not orthogonal to B CP is orthogonal to A DP is not orthogonal to A

Show answer

EnglishDSSSB PGT 2021

Q22.The work done in a moving particle in the force field along the straight line from (0, 0, 0) to (2, 1, 3) is–

A22 units B14 units C16 units D42 units

Show answer

EnglishDSSSB PGT 2021

Q23.The unit vector perpendicular to each of the vectors u = 2i 2j +k, v = i + j k − − − − is–

Ai 3j + 4k 26 − − Bi + 3j + 4k/26 Ci 3j 4k 26 − − Di +3j 4k 26 − −

Show answer

EnglishKVS TGT 2017

Q24.If the vectors i 3j 2k,2i j 4k and 3i 2j xk are coplanar, then the value of x is–

A1 B3 C–2 D2

Show answer

EnglishKVS TGT 2017

Q25.Given that a and b are unit vectors. If the vectors p 3a 5b and q a b are mutually perpendicular then–

Aa and b are also mutually perpendicular. Ba, b have opposite directions Ca and b make an angle of 3 Da and b make an angle of 4

Show answer

EnglishKVS TGT 2017

Q26.The projection of the vector i 2j k on the vector 4i 4j 7k is–

A5 5/19 B19/9 C9/19 D6/19

Show answer

EnglishKVS TGT 2017

Q27.Let a,b,c be there vectors such that a.(b c) b.(c a) c(a b) 0 and a 1, b 4 and c 8 then a b c equals–

A13 B81 C9 D5

Show answer

EnglishUP PGT 2021

Q28.Let a ∧ and b ∧ be two unit vectors and θ be the angle between them. Which of the following will be value of cos 2 θ.

Aa b 4 ∧ ∧ + Ba– b 4 ∧ ∧ Ca b 2 ∧ ∧ + Da b 2 ∧ ∧ −

Show answer

EnglishUP PGT 2021

Q29.If the vectors i– 3 j 7 k ∧ ∧ ∧ + x and i– y j– z k ∧ ∧ ∧ are collinear then the value of 2 xy z is equal to –

A9/7 B6/7 C−6/7 Dnone of the above

Show answer

EnglishUP PGT 2021

Q30.If A and B are vectors such that B 5 = A and B 4i– 3k ∧ ∧ × = A then A.B is equal to –

A5 6 B5 2 C10 2 D10 6

Show answer

EnglishUPPSC GIC 2021

Q31.If () () () = + + θ ˆ ˆ ˆ r asint i acost j at tan k then the value of 2 × dr d r dt dt is-

Aa2/cos θ Ba2/sin θ Ca2/tan θ Da2/sec θ

Show answer

EnglishUP TGT 2011 UPPSC GIC 2021 UPPSC Ashram Paddhati 2021 JDD-75-PGT-TIER-II-X-15. 28.06.2015

Q32.The value of () () () ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ i. j k j. k i k. i j × + × + × is-

A0 B1 C2 D3

Show answer

EnglishUP TGT 2021

Q33.If a,b and c are three vectors in such a way that a + b + c = 0 and a = 1, b = 4, c = 2, then the value of () 2 a.b +b.c + c.a is equal to

A21 B–21 C19 D21 – 2

Show answer

EnglishUP TGT 2021

Q34.If A and B are two vectors, then angle between vectors A + B and A×B is

A0º B60º C90º D120º

Show answer

EnglishUP TGT 2021

Q35.If â and b̂ are unit vectors such that ˆ â + 2b and ˆ ˆ 5a – 4b are perpendicular to each other, then the angle between â and b̂ is

A4/π B–1 1 cos 3 C–1 2 cos 7 D3/π

Show answer

EnglishUP TGT 2021

Q36.Find the value of 'a' such that the vectors ˆ ˆ ˆ ˆ ˆ ˆ 2i – j+ k,i + 2j – 3k and ˆ ˆ ˆ 3i + aj+ 5k are coplanar.

A1 B2 C4 D–4

Show answer

EnglishUP TGT 2021

Q37.The points with position vectors ˆ ˆ ˆ ˆ ˆ ˆ 60i + 3j,40i – 8j,ai – 52j are collinear if a is equal to

A–40 B40 C20 D25

Show answer

EnglishUP TGT 2021

Q38.The position vectors of the points A, B, C and D are ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ 3i – 2j – k,2i + 3j – 4k,–i + j+ 2k and ˆ ˆ ˆ 4i + 5j+ λk respectively. If the points A, B, C and D lie on a plane, the value of λ is

A–146/17 B–73/17 C7 D13

Show answer

EnglishUP TGT 2021 UKPSC GIC 2018

Q39.If () () () ˆ ˆ ˆ ˆ ˆ ˆ u = i × a×i + j× a× j +k × a×k then u is equal to

A0 Ba C2a D3a

Show answer

EnglishUPPSC Ashram Paddhati 2021 UP PGT 2013 UKPSC GIC 2018

Q40.If a, b, c are three unit vectors such that 1 a×(b× c) = b 2, then the angle which a makes with c is

A30° B45° C60° D90°

Show answer