Math Chapter Wise

EnglishPGT 2004

Q101.Moment of force ˆ ˆ ˆ 3 2 4 F i j k = + − = + − = + − = + − passing through the point (1, -1, 2) about (2, 0, 2) is

Aˆ ˆ ˆ 4 4 i j k + + Bˆ ˆ ˆ 4 4 i j k − + Cˆ ˆ ˆ 4 4 5 i j k + + Dˆ ˆ ˆ 4 4 5 i j k + −

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EnglishPGT 2003

Q102.Vector area of the triangle the position vectors of those vertices are (2, 3,–5), (3, 4, 2), (1, 1,–1)

A() 1 18, 11, 1 2 − − B() 1 18, 11, 1 4 − − C() 1 18, 11, 1 8 − − D() 1 18, 11, 1 3 − −

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EnglishPGT 2003

Q103.The volume of the tetrahedron whose vertices are given by the vectors (((()))) ˆ ˆ ˆ, i j k − + + − + + − + + − + + (((()))) ˆ ˆ ˆ, i j k − + − + (((()))) ˆ ˆ ˆ i j k + − + − with reference to the fourth vertex as origin is

A3/4 B2/3 C3/2 D1/3

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EnglishPGT 2002

Q104.If the vectors ˆ ˆ a 2i 3j = − = − and ˆ ˆ ˆ b 4i 3k = − = − are given then the expression which is not defined is:

Aa b/+ Ba b/× C( )/a.b a D() a b a ×

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EnglishPGT 2002

Q105.The vector 2i+j–k is ⊥ ⊥ ⊥ to i–4j+λk, if λ is equal to:

A0 B–1 C–2 D–3

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EnglishPGT 2002

Q106.If x and y are two unit vectors and φ is the angle between them, then 1 x y 2 − − is equal to:

A0 B2/π C1 sin 2 φ D1 cos 2 φ

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EnglishPGT 2002

Q107.The work done by the force F=2i–3j+2k in moving a particle from (3,4,5) to (1,2,3) is:

A0 B3/2 C–4 D–2

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EnglishPGT 2002

Q108.The position vectors of three points A, B and C are i+j, –i–j and li+mj+nk respectively. The points are collinear if:

Al=m=n=1 Bl= 1, m and n are any scalars Cm= l, n = 0, l is any scalar DNone of these

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EnglishPGT 2000

Q109.The projection of the vector ˆ ˆ ˆ i 2j k − + − + on the vector ˆ ˆ ˆ 4i 4j 7k − + − + is:

A6/19 B9/19 C5 6/19 D19/9

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EnglishPGT 2000

Q110.The angle between ˆ ˆ ˆ ˆ ˆ ˆ a 3i j 2k,b 2i 2j 4k = + + = − + = + + = − + = + + = − + = + + = − + is:

A1 3 cos 7 − B−2/7 C3/4 D4/7

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EnglishRajasthan TGT 2016

Q111.Vector (((()))) b b a × × × × is coplanar with

Aa only Bb only Cboth a and b Dneither a nor b

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EnglishRajasthan TGT 2016

Q112.(()) a b c a × × × = × × × = × × × = × × × =

A() () a.b. a c × B() () a.b. c a × C−( ) ( )/a.c b.c D()() a.c b a ×

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EnglishRajasthan TGT 2016

Q113.If p i 2j 3k = − + = − + = − + = − + and q 3i 3j k, = + + = + + = + + = + + then (()) 2 p q − − is equal to

Ap q Bp q/+ C−2 2/p q D() 2 p q +

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EnglishRajasthan TGT 2016

Q114.If p 5i j k, = − + − = − + − = − + − = − + − q 2i j 2k, = + + = + + = + + = + + and r 4i 2j 2k, = + − = + − = + − = + − then the volume of cubid whose coterminous edges are q r,r p + + + + and p q + + is

A42 cubic unit B84cubic unit C126 cubic unit D168 cubic unit

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EnglishRajasthan TGT 2016

Q115.a,b,c are non-zero non-coplanar vectors and b c c a a b p,q,r, [bca] [cab] [abc] × × × × × × × × × × × × = = then [abc]=

A[pqr] B[pqr]2 C[pqr]–1 D0

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EnglishRajasthan TGT 2016

Q116.The point of intersection of vector lines (((()))) (((()))) 1 ˆ ˆ ˆ ˆ ˆ ˆ 7i 10j 13k k 2i 3j 4k + + + + + + + + + + + + + + + + + + + + and (((()))) (((()))) 2 ˆ ˆ ˆ ˆ ˆ ˆ 3i 5j 7k k i 2j 3k + + + + + + + + + + + + + + + + + + + + is given by

Aˆ ˆ ˆ i j k + + Bˆ ˆ ˆ i j k − + Cˆ ˆ ˆ i j k + − DNone of these

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EnglishRajasthan TGT 2015

Q117.If a and b are non-collinear vectors and x and y are scalars such that xa yb 0, + = + = then

Ax 0,y 0 = ≠ Bx 0,y 0 = Cx 0, y 0 ≠ Dx 1, y 1 =

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EnglishRajasthan TGT 2015

Q118.If a, b, c, are three non-zero vectors then (a b).c a b c × = × = if and only if:

Aa.b 0;b.c 0 = Bb.c 0;c.a 0 = Cc.a 0;a.b 0 = Da.b 0;b.c. 0;c.a 0

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EnglishRajasthan TGT 2013

Q119.For three coplanar vectors,, a b c,, + + + a b b c c a =

A2 a b c B2/a b c C2 a b c D0

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EnglishRajasthan TGT 2011

Q120.If the sum of two unit vectors is a unit vector, then angle between then is

A3/π B4/π C3 4 π D2 3 π

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