Math Chapter Wise

EnglishTGT 2013

Q221.What is the value of the cosine of the angle between the vector ˆ ˆ ˆ 2i 2j k + + and the X-axis?

A2/3 B1/3 C1/2 D1/2

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EnglishTGT 2013

Q222.If ˆ ˆ ˆ â 2i j 3k = + + and ˆ ˆ ˆ ˆ b 3i 2j k = − + are two vectors. Then teh angle between them –

A300 B450 C900 D600

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EnglishTGT 2013

Q223.If ˆ ˆ ˆ a 6i 4j 4k = + + and ˆ ˆ ˆ b 2i 4j 3k = + + then, what will be the value of b a ×?

Aˆ ˆ ˆ 4i 10j 16k + − Bˆ ˆ ˆ 4i 10j 16k + + Cˆ ˆ ˆ 4i 10j 12k + − Dˆ ˆ ˆ 4i 10j 3k + +

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EnglishTGT 2013

Q224.If two forces ˆ ˆ ˆ 4i j 3k + − + − and ˆ ˆ ˆ 3i j k + − + − are acting ona particle due to which the particle is displaced from the point ˆ ˆ ˆ i 2j 3k + + + + to ˆ ˆ ˆ 5i 4j k + + + + then the total work done by the force is:

A20 units B30 units C40 units D50 units

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EnglishTGT 2013

Q225.If a 5, a b 8 = − = and a b 10 + = then what will be the value of b?

A1 B57 C3 D42

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EnglishTGT 2013

Q226.If a b c 1 = then the value of a.b c b.c a c.a b c a.b a b.c b c.a × × × × × × × × × × × × + + × × × × × × × × × × × × is:

A1 B–1 C2 D3

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EnglishTGT 2013

Q227.If the position vectors of vectors A and B are a and b respectively, then what will be the position vector of the mid-point of AB?

Aa b/+ Ba b C() 1 a b 2 + D() 1 a b 2 −

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EnglishTGT 2013

Q228.If the vectors ˆ ˆ ˆ 2i j k + + + + and ˆ ˆ ˆ i 4j k − + λ − + λ − + λ − + λ are perpendicular to each other, then what will be the value of --?

A1 B2 C3 D4

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EnglishTGT 2013

Q229.Nodulus of the vector ˆ ˆ ˆ ĉ 4i 5j 11k = − + is:

A9 B9 2 C9 3 D10

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EnglishTGT 2013

Q230.If two vectors are a b − and a b + then heir cross product () () a b a b − × + will be:

Aa2/– b2 B() 2 a b × Ca b/× Db a/×

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EnglishUP PCS (Pre) 1997

Q231.The vectors p,q,r are coplanar, if and only if:

A() p q r 0 × × = B() p q r 0 × × = C() p q.r 0 × = D() () p q. q r 0 × × =

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EnglishUP PCS (Pre) 1997

Q232.The vectors: <1, –2, 1>, <2, 1, –1> and <7, –4, 1> of R3 are:

Alinearly dependent Blinearly independent Clinearly dependent as well as linearly independent DNone of these

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EnglishUP PCS (Pre) 1997

Q233.a b × × is:

Aa scalar quantity Ba vector quantity parallel to the plane of Ca vector quantity perpendicular to the plane containing a and b Da vector quantity parallel to a and perpendicular to b

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EnglishUP PCS (Pre) 1997

Q234.The value of ((())) ((()) 2 2 a b a.b × + × + is:

A1 B0 Ca2/b2 D2a.b

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EnglishUP PCS (Pre) 1997

Q235.If the vector ˆ ˆ ˆ ˆ ˆ ˆ ai j k,i bj k + + + + + + + + + + + + + + + + and ˆ ˆ ˆ i j ck + + (where a≠b≠c≠1) are coplanar, then the value of 1 1 1 1 a 1 b 1 c + + − − − − − − − − − − − − is;

A1 B–1 C0 DNone of these

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EnglishTGT 2010

Q236.If u and v are unit vectors and θ is acute angle between them, 2u 3v × × is a unit vector for

Aexactly two values of θ Bmore than two values of θ Cno values of θ Dexactly one value of θ

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EnglishTGT 2010

Q237.Vectors ˆ ˆ ˆ ˆ ˆ ˆ 2i j k,i 2j 3k − + + − − + + − − + + − − + + − and ˆ ˆ ˆ 3i pj 5k + + are coplaner. Then p is

A–4 B4 C2 D–2

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EnglishTGT 2010

Q238.If a and b are two unit vectors inclined at an angle θ, then sin 2 θ =

A1/2 B1/2 C−1/2 DNone of the these

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EnglishTGT 2010

Q239.The direction cosines of the vector ˆ ˆ ˆ 3i 4j 5k − + − + are

A3 4 1,, 5 5 5 − B3 4 1,, 5 2 5 2 2 − C3 4 1,, 2 2 2 − D3 4 1,, 2 5 2 5 2

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EnglishTGT 2010

Q240.Let ˆ ˆ ˆ a i j k = + + λ = + + λ = + + λ = + + λ and ˆ ˆ ˆ b i j k = + + = + + = + + = + + then a b a b + = + + = + + = + + = + holds for λ

Aλ = –1 Bλ = 1 Call real λ Dno real λ

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