Math Chapter Wise

EnglishTGT 1999

Q81.If ˆ ˆ ˆ OA i j k = − + = − + = − + = − + and ˆ ˆ OB j k = + = + then the area of triangle ABC will be:

A6 B6 2 1 C3 2 1 D2

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EnglishTGT 1999

Q82.If â is a unit vector and (((()))) (((()))). 3 ˆ ˆ x x a a → → − + = − + = − + = − + = then the value of x → → is:

A4 B2 C5 D6

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EnglishPGT 2013

Q83.The value of (((()))) (((()))). + × + + × + + × + + × + A B C C A will be:

A(). × A B C B(). × B C A C() 2. × A B C D() 2. × A A B

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EnglishPGT 2013

Q84.If,, a b c are three unit vectors such that (((()))) × × a b c 1 2 = b then the angle subtended by a with c is:

A2/π B3/π C6/π D4/π

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EnglishPGT 2013

Q85.A force 5 3 4 + + i j k acts through the point 2 3 + + i j k. What will be the moment of force about the point ˆ 2 + − i j k?

A() 8 2 2 i j k − + B() 8 2 2 i j k + − C() 8 2 2 i j k − + + D() 8 2i k +

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EnglishPGT 2013

Q86.The vector b which is collinear to the vector (),, 2 1 1 a = − and satisfies the condition. 3 a b = will be:

A2 1 1,, 3 3 3 − B1 1 1,, 2 4 4 − C1 1 1,, 2 2 − D1 1 1,, 2 2 −

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EnglishPGT 2010

Q87.The volume of the parallelepiped determined by the vectors u i 2j k, v 2i 3k, w 7j 4k = + − = − + = − = + − = − + = − = + − = − + = − = + − = − + = − is

A23 cube unit B33 cube unit C–31 cube unit D21 cube unit

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EnglishPGT 2010

Q88.Vectors ˆ ˆ ˆ ˆ ˆ ˆ 2i j 4k,i 3j 5k − − − − − − − − − − − − − − − − and ˆ ˆ ˆ 3i 4j 4k − − are the sides of a triangle. Which one of the following is the angle between any two of them?

A2 1 6 cos 41 − B1 6 cos 41 − C6 1 6 cos 41 − DNone of these

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EnglishPGT 2010

Q89.a =(1,1,1) and c =(0,1,–1) are two given vectors. What will be vector b such that a b c × = and. a b 10 =.

A(4,3,3) B(3,3,3) C(3,2,2) D(2,2,2)

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EnglishPGT 2010

Q90.The equation of the plane passing through three points ˆ ˆ ˆ ˆ ˆ ˆ 2i 6j 6k, 3i 10j 9k − + − − + − − + − − + − − + − − + − − + − − + − and ˆ ˆ − − 5i 6k is

A() ˆ ˆ ˆ r. 2i j 2k 8 − − = B() ˆ ˆ ˆ r. 2i j 2k 2 − − = C() ˆ ˆ ˆ r. 2i j 2k 72 − − = D() ˆ ˆ ˆ r. 2i j 2k 18 − − =

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EnglishPGT 2009

Q91.A unit vector perpendicular to the plane of vectors ˆ ˆ ˆ 2 6 3 a i j k = − − = − − = − − = − − and ˆ ˆ ˆ 4 3 b i j k = + − = + − = + − = + − is

Aˆ ˆ ˆ 15 10 30 − + i j k Bˆ ˆ ˆ 5 2 3 − + i j k C3 2 6 ˆ ˆ ˆ 7 7 7 − + i j k D3 2 6 i j k − + ⌢ ⌢ ⌢

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EnglishPGT 2009

Q92.The value of scalar p such that vectors 2 2 3 ˆ ˆ ˆ ˆ ˆ ˆ, i j k i j k − + + − − + + − − + + − − + + − and 3 5 ˆ ˆ ˆ i pj k + + + + are coplanar, is

A3 B–3 C–4 D4

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EnglishPGT 2009

Q93.If r be position vector of a particle of mass m relative to a point 0 then the vector sum H r mv mr v = Σ × = Σ × = Σ × = Σ × = Σ × = Σ × = Σ × = Σ × is called

Amomentum Blinear momentum Cangular momentum Dangular potential energy

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EnglishPGT 2005

Q94.If a unit vector in xy-plane makes an angle of 45o with the vector ˆ ˆ i j + and an angle of 600 with vector ˆ ˆ 3i 4j, − the vector will be

Aî Bˆ ˆ i j 2 + Cˆ ˆ i j 2 − DNone of these

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EnglishPGT 2004

Q95.If | | | | a b a b + = + + = + + = + + = + where a and b are any vectors, then this equality

Aalways holds Bnever holds Chold only when (0) a kb k = ≥ or one of a and b is zero Dholds only a = b = 0

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EnglishPGT 2004

Q96.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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EnglishPGT 2004

Q97.If the vectors, a b and c form the sides BC, CA and AB respectively of a triangle ABC, then

A... 0 a b b c c a + + = Ba b b c c a × = × = × C... a b b c c a = Da b b c c a × + × = ×

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EnglishPGT 2004

Q98.If, a b and c are three coplanar unit vector, then the scalar triple product 2, 2, 2 − − − − − − − − − − − − a b b c c a will be

A0 B1 C3 D3

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EnglishPGT 2004

Q99.If a and b are two unit vectors such that 2 a b + + and 5 4 a b − − are perpendicular to each other, then the angle between a and b is

A450 B600 C1 1 cos 3 − D1 2 cos 7 −

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EnglishPGT 2004

Q100.If a and b are unit vectors such that. cos a b = θ = θ = θ then the value of | | a b + + is

A2sin 2 θ B2sinθ C2cos 2 θ D2cosθ

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