Math Chapter Wise

EnglishEMRS PGT-2023

Q01.If the vectors a, b and c form the sides BC, CA and AB respectively of a ∆ ∆ ∆ABC, then:

Aa×b = b×c = c×a Ba b = b c = c a = 0 ⋅ ⋅ ⋅ Ca×a + a×c + a×b = 0 Da b = b c = c a = 0 ⋅ ⋅ ⋅

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EnglishEMRS PGT-2023

Q02.Let ˆ ˆ ˆ a = 3i + 2j+ 2k and ˆ ˆ ˆ b = i + 2j- 2k be two vectors. If a vector perpendicular to both the vectors a + b and a - b has the magnitude 12, then one such vector is:

A() ˆ ˆ ˆ 4 2i - 2j- k B() ˆ ˆ ˆ 4 2i + 2j- k C() ˆ ˆ ˆ 4 -2i - 2j+ k D() ˆ ˆ ˆ 4 2i + 2j+ k

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EnglishEMRS PGT-2023

Q03.If a unit vector â makes angles π 3 with î, π 4 with ĵ and () θ 0, π ∈ with k̂, then value of θ is:

A4/π B5 12 π C2 3 π D5 6 π

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EnglishBihar (TRE 2.0)-2023

Q04.The value of () () a -b × a + b is

A2 ( )/a×b B(a2 - b2) C( )/a×b DMore than one of the above ENone of the above

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EnglishBihar (TRE 2.0)-2023

Q05.Time period is a

Avector quantity Bscalar quantity CNeither scalar nor vector quantity DMore than one of the above ENone of the above

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EnglishNVS PGT 2022

Q06.If a,b,c are unit vectors, then 2 2 2 ˆ ˆ ˆ ˆ ˆ ˆ a b b c c a − + − + − does not exceed:

A4 B9 C8 D6

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EnglishRPSC PGT 2022

Q07.If a and b are unit vector, then correct statement is-

Aa + b will never be a unit vector Ba + b is unit vector, if a is parallel to b Ca + b is unit vector, if a is perpendicular to b Da + b is unit vector, if angle between a and b is 2 3 π

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EnglishKVS PGT 2023

Q08.If a, b and c are unit vectors such that a + b + c = 0, then the value of a. b + b. c + c.a is:

A1 B3/2 C- 3 2 D0

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EnglishKVS PGT 2023

Q09.The value of () i j k j k i k i j × + + × + + × + is equal to:

A() 2 i j k + + B0 C1 Di j k/+ +

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EnglishKVS PGT 2023

Q10.For any vector a, the value of () () () 2 2 2 ˆ ˆ a i a j a k × + × + × is:

A2/3a B2/a C2/2a D2/4a

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EnglishNVS PGT 2022

Q11.If () () () ˆ ˆ ˆ ˆ ˆ ˆ i i a j j a k k a m.a, × × + × × + × × = then m is equal to:

A0 B–2 C2 D1

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EnglishNVS PGT 2022

Q12.If a b c + = and a b c, + = then angle between a and b is:

A0° B45° C90° D180°

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EnglishKVS PGT 2022

Q13.If | a | 4 | b | 5 and a. b 10 = then the value | a b | × is:

A10 2 B5 C10 3 D10

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EnglishKVS PGT 2022

Q14.Vectors a i 2j 3k, b 2i 3j k, = − + = − + and c 3i j 2k, = − − are given. The value of a b c is:

A14 B28 C24 D20

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EnglishRPSC PGT 2022

Q15.Let a = (2 î – ĵ + k̂), b = (î + 2 ĵ – k̂) and c = (î + ĵ–2 k̂) be three vector. A vector in the plane of b and c whose projection on a is zero, will be

A– 2 î – ĵ + 5 k̂ Bĵ + k̂ Cĵ – k̂ Dî + ĵ – k̂

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EnglishRPSC PGT 2022

Q16.A,BandC are unit vectors. A is perpendicular to both B and C and angle between B and C is 30º. Then vector A is -

A(B C)/± × B1 (B C) 2 ± × C2(B C)/± × D1 (B C) 3 ± ×

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EnglishRPSC PGT 2022

Q17.a;b;c are unit vectors b and c are non collinear vector. If a × (2b ×c) =b, then angle between a and b is -

A90º B60º C45º D0º

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EnglishRPSC PGT 2022

Q18.The midpoints of sides AB and AC of a triangle ABC are points D and E, respectively, then resultant of forces represented by BE and DC in magnitude and direction is represented by -

A1 BC 2 B2 BC 3 C3 BA 2 D3 BC 2

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EnglishRPSC PGT 2022

Q19.If additive inverse vector of vector of vector pi + 2j – 3k is the vector (ab i + b j + pk), then which of the following is true (a>0)?

Ap = 9, b = 4, a = 3/2 Bp = 9, b = 4, a = 81/4 Cp = 3, b = 4, a = 81/2 Dp = 9, b = 4, a = 9/2

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EnglishDSSSB PGT 2021

Q20.Let − x = 2i + j 2k and y = i + j.If z is a vector such that x.z = z, z x = 2 2 − − and the angle between x×y and z is 30° ° °, then the magnitude of the vector ()× x×y z is _________

A3/2 B3/2 C1/2 D3 2/2

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