Math Chapter Wise

EnglishUP PCS (Pre) 1995

Q141.The force 2i 3j 4k F displaces the point P (-1,2,3) to the point Q (1,2,3). The work done by the force is:

A2 Unit B3 Unit C4 Unit D6 Unit

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EnglishUP PCS (Pre) 1995

Q142.If a.b are two unit vectors inclined at an angle θ then:

Aa b a.b 0 × + = B( )/2 C( )/2 DNone of the above

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EnglishUP PCS (Pre) 1999

Q143.If ˆ ˆ ˆ i, j, k are unit vectors along the axes respectively, then the angle between the vectors ˆ ˆ i + j and ˆ k̂ + i is:

A3/π B2/π C4/π D6/π

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EnglishUP PCS (Pre) 1999

Q144.The value of the sealer λ for which the vector ˆ ˆ ˆ ˆ ˆ ˆ i, j+ k, i + j+ λk is coplanar, is:

A–2 B–1 C0 D1

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EnglishUP PCS (Pre) 1999

Q145.The value of λ for which λ ≠ 1 the vectors ˆ ˆ ˆ ˆ ˆ ˆ λi + j+ k. i + λj+ k and ˆ ˆ ˆ i + j+ λk are linearly dependent is:

A2 B0 C–1 D–2

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EnglishUP PCS (Pre) 1999

Q146.Where a, b, c are the inverse vectors of the non zero vectors a, b, c respectively, then the value of a + b is:

A1 B2 C3 D0

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EnglishUP PCS (Pre) 1999

Q147.If the vectors ˆ ˆ ˆ 2i + pj+ k and ˆ ˆ ˆ - 5i + 3j+ qk are collinear, then the values of p and q are:

A6 -5 -, 5 2 B3 -5, 2 2 − C3, - 2 2 − D6 5, 5 2 −

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EnglishUP TGT-2016 (08-03-2019)

Q148.If c a,b, are three non-coplanar vectors, such that a b c,c a, b 2 a,b,c × × × = × × × = × × × = × × × = then the value of a,b,c is equal to

A0 B1 C2 D4

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EnglishUP TGT-2016 (08-03-2019)

Q149.Which one of the following is not true?

Aa b a b = ⇒ = B() () () 2 2 2 a b a b a.b × = − C() a b.c × is not defined DIf the adjacent sides of a parallelogram are represented by the vectors a and b respectively, then its area is a b ×

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EnglishUP TGT-2016 (08-03-2019)

Q150.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, is

A1 B–2 C4 D–4

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EnglishUP TGT-2016 (08-03-2019)

Q151.Two forces 1 ˆ ˆ ˆ F i j k = − + = − + = − + = − + and 2 ˆ ˆ ˆ F 4i 2j 3k = + + = + + = + + = + + act on a particle and displace it from the point (0, 1, 2) to (1, –2, 3), then the total work done is

A2unit B6unit C4unit D8unit

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EnglishUP TGT-2016 (08-03-2019)

Q152.The moment of the force ˆ ˆ ˆ 3i 4j 5k + − + − acting through the point ˆ ˆ i 2j − − about the point ˆ ˆ ˆ i j k − + is

Aˆ ˆ ˆ 6i 2j 5k + − Bˆ ˆ ˆ 8i 2j k + − Cˆ ˆ ˆ 9i 3j 8k + − Dˆ ˆ ˆ 9i 3j 3k − +

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EnglishUP TGT-2016 (08-03-2019)

Q153.If ˆ â, b and ĉ are unit vectors and 2 2 2 ˆ ˆ ˆ ˆ ˆ ˆ a b b c c a 8, + = + = + = + = + = + = + = + = + = + = + = + = then ˆ ˆ ˆ 2a b c + + is equal to

A2 B4 C6 Dnone of the above

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EnglishNVS PGT 10-06-2019

Q154.The points with the position vectors 60 i 3 j, ∧ ∧ + 40 i 8 j, ∧ ∧ − − ai 52j, − − are collinear if the value of 'a' equals;

A–20 B40 C20 D–40

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EnglishNVS PGT 10-06-2019 PUPCS (pre)- 2008

Q155.If a b c 0, + + = + + = + + = + + = a 3, b 5, = and c 7 = then the angle between a and b is:

A6/π B3/π C2 3 π D3 2 π

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EnglishKVS PGT 23-12-2018

Q156.If a,b and c are three non-coplanar vectors, then the value of (((()))) (()) (()) (((()))) (((()))) (((()))) a. b c c. b a b. c a b. c a c. a b a. b c × × × + + × × × × × × is:

A–3 B–2 C1 D–1

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EnglishKVS PGT 23-12-2018

Q157.Let a,b,c be three non zero vectors such that c is a unit vector perpendicular to both a and b. If the angle between a and b be 6 π then 2 a b c is:

A2/a b B2 1 a b 2 C2 1 a b 4 D2/2 a b

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EnglishKVS PGT 23-12-2018

Q158.If a and b are unit vectors and θ is angle between them, then a b 2 − is:

Asinθ Bsin2θ Csin 2 θ Dsin2/θ

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EnglishKVS PGT 23-12-2018

Q159.If the volume of parallelepiped formed by the vectors ˆ ˆ ˆ ˆ ˆ i aj k, j ak + + + + + + + + + + + + and ˆ ˆ ai k + + is minimum then value of a will be:

A3 B2 C1/3 D3

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EnglishUP PGT-2016 (02-02-2019)

Q160.If a b c + = + = and a b c + = + = then angle between a and b is

A00 B450 C900 D1800

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