Math Chapter Wise

EnglishUKPSC GIC 2018

Q61.If â and b̂ are unit vectors inclined at an angle θ, then the value of () ˆ 1 a - b 2 is

Asin θ/2 Bsin θ Ccosθ Dcos θ/2

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EnglishUKPSC GIC 2018

Q62.B×C,C× A,A×B is

AABC B2/ABC C3/ABC D0

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EnglishUKPSC GIC 2018

Q63.Let a 4i 5j k = + − b i 4j 5k = − + c 3i j k = + − Then a vector d which is perpendicular to both a and b and for which d. c = 21 is

A7 () i j k + − B() 7 i j k − − C() 63 i j k − − D() 3 i j k − +

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EnglishUKPSC GIC 2018

Q64.Which of the following is/ are true?

Aand BImage/formula option B (see source) CBoth DNone of these

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EnglishLT 2018

Q65.If 1, 2, 3 V V V are three non-zero vectors such that 1 2 3 2 3 1 V V V,V V V × = × = × = × = × = × = × = × = then

A1 2 V V = B2 3 V V = C1 3 V V = D2 1 3 V V V = ×

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EnglishLT 2018

Q66.If A B C D × = × × = × × = × × = × and A C B D × = × × = × × = × × = ×, then vectors A D − − and B C − − are

Aequal Bparallel Cperpendicular Dinclined at an angle of 60o

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EnglishLT 2018

Q67.The value of ((())) (((()))) c a a b × × × × × × × × × × × × is

A0̂ Bbca b Ccab c Dabc a

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EnglishLT 2018

Q68.If 2 ˆ ˆ ˆ F x yi xzj 2yzk = + + = + + = + + = + + then the value of div curl F is

A0 B1 C2 D3

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EnglishLT 2018

Q69.If 2 2 a b a.b 144 × + = × + = × + = × + = and a 4 =, then b is equal to-

A12 B8 C4 D3

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EnglishSECTION B PGT TIER-I 31.11.2014

Q70.If ˆ ˆ i, jand k are unit vectors. The value of i. j k j. i k k. i j is–

A0 B–1 C1 D3

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EnglishSECTION B PGT TIER-I 31.11.2014

Q71.If is the angle between any two vectors a and b, then a.b a b when is equal to–

A0 Bπ/4 Cπ/2 Dπ

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q72.lf a and b are two unit vectres inclined at an angle, 3 π then the value of a b + + is–

A=0 B>1 C<1 Dnone of these

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EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q73.The area of the parallelogram whose adjacent sides are ˆ ˆ i k + + and ˆ ˆ ˆ 2i j k + + + + is–

A3 B2 C4 D3

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EnglishTGT 2001

Q74.If the angle between the vectors a and b is 1200 and their magnitudes are 2 and 3 respectively, then a b ⋅ ⋅ is equal to:

A3 B3 C3 D–3

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EnglishTGT 2001

Q75.Let ˆ ˆ a i j = + = + and ˆ ˆ b 2j k = − = − then what will be point of intersection of the lines r a b a × = × × = × × = × × = × and r b a b × = × × = × × = × × = ×?

A(–1, 1, 1) B(3, –1, 1) C(3, 1, –1) D(1, 3, -1)

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EnglishTGT 2001

Q76.The magnitudes of the vectors a,b,c are 3, 4, 5 respectively. If the vectors a,b,c are respectively perpendicular to the victors b c, + c a + +, a b + + then the magnitude of a b c + + will be:

A5 2 B6 2 C7 D0

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EnglishTGT 2001

Q77.If ˆ ˆ ˆ ˆ ˆ ˆ a 2i 3j 6k,b 3i 6j 2k = + + = − + = + + = − + = + + = − + = + + = − + then a b × × is:

Aˆ ˆ ˆ i 14j 21k + − Bˆ ˆ ˆ 42i 14j 21k + + Cˆ ˆ ˆ 42i 14j 21k + − Dˆ ˆ ˆ i j k + −

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EnglishTGT 2001

Q78.Finding the angle between the vectors ˆ ˆ 3i 4j + and ˆ ˆ ˆ i j k − + − + using vector multiplication:

A74 Sin 5 3 θ = B74 Sin 3 θ = C74 Sin 5 θ = D74/5

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EnglishTGT 2001

Q79.If ˆ ˆ ˆ a,b,c are unit vectors and ˆ ˆ ˆ a b c 0 + + = + + = + + = + + = then ˆ ˆ ˆ ˆ ˆ ˆ a b b c c a ⋅ + ⋅ + ⋅ ⋅ + ⋅ + ⋅ ⋅ + ⋅ + ⋅ ⋅ + ⋅ + ⋅ is?

A−3/2 B0 C2/3 D1

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EnglishTGT 1999

Q80.If vectors a and b are unit vectors and makes an angle of 600, then:

Aa b 1/+ > Ba b 1/+ < Ca b 1/− > Da b 1/− <

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