Math Chapter Wise

EnglishUP PGT-2016 (02-02-2019)

Q161.If vectors ˆ ˆ ˆ p xi 3j 2k, = + + = + + = + + = + + ˆ ˆ ˆ a 2i 2j 3k = + + = + + = + + = + + and ˆ ˆ ˆ b 2i 3j 4k = + + = + + = + + = + + are coplanars, then value of x is

A2 B–2 C3 D–3

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EnglishUP PGT-2016 (02-02-2019)

Q162.If â and b̂ are two unit vectors inclined at an angle 300 to each other, then ˆ â b + + is equal to

A3 1 B3 1/+ C−3 1/2 D3 1 2 +

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EnglishUP PGT-2016 (02-02-2019)

Q163.If ˆ ˆ ˆ A i j k,A.B 2 = + + = + + = + + = + + = and ˆ ˆ A B j k × = − × = − × = − × = − then 3B is equal to

A2 2 B3 2 C2 3 D3 3

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EnglishUP PGT-2016 (02-02-2019)

Q164.If (((()))) (((()))) 2 2 A B A.B 81 × + = × + = × + = × + = and B 3, = then A is equal to

A9 B3 C27 D1

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EnglishUP PGT-2016 (02-02-2019)

Q165.Value of ˆ ˆ ˆ ˆ ˆ ˆ i j, j k,k j − − − − − − − − − − − − is

A1 B2 C3 D0

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EnglishUP PGT-2016 (02-02-2019)

Q166.Two constant forces ˆ ˆ ˆ P 2i 5j 6k = − + = − + = − + = − + and ˆ ˆ ˆ Q i 2j k = − + − = − + − = − + − = − + − act on a particle at the point A(4,–3,–2). Moment of the resultant force about O(0,0,0) is

Aˆ ˆ ˆ 21i 22j 9k + + Bˆ ˆ ˆ 21i 22j 9k − − − Cˆ ˆ ˆ 21i 22j 9k − + Dˆ ˆ ˆ 21i 22j 9k − −

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EnglishUP PGT-2016 (02-02-2019)

Q167.If 1, ω, ω2 are the cube roots of unity, then value of the determinant 7 14 14 7 7 14 1 ω is

Aω2 Bω C1 D0

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EnglishUP PCS (Pre) 2000

Q168.If the vectors ˆ ˆ ˆ A i j ak = − + = − + = − + = − + and ˆ ˆ ˆ B 2ai j 4k = + + = + + = + + = + + are perpendicular, then a is:

A1 B−1/2 C1/6 D0

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EnglishUP PCS (Pre) 2000

Q169.The value of λ for which the vectors ˆ ˆ ˆ i j k − + λ − + λ − + λ − + λ, ˆ ˆ ˆ i j k λ + − λ + − λ + − λ + − and ˆ ˆ ˆ i j k − + λ + − + λ + − + λ + − + λ + are coplanar, is:

A0 B1 C3 D3

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EnglishUP PCS (Pre) 2000

Q170.If (((()))) (((()))) (((()))) ˆ ˆ ˆ ˆ ˆ ˆ i i a j j a k k a m.a × × + × × + × × = × × + × × + × × = × × + × × + × × = × × + × × + × × = the m is equal to:

A0 B–2 C2 D1

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EnglishUP PCS (Pre) 2000, 2002

Q171.The vectors ˆ ˆ ˆ i 2j 3k + + + +, ˆ ˆ ˆ 2i j 3k − + + − + + − + + − + + and ˆ ˆ ˆ 3i 2j k + − + − from the sides of:

Aan equilateral triangle Ban isosceles triangle Ca right angled triangle Dnone of these

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EnglishUP PCS (Pre) 2000

Q172.The vectors ˆ ˆ ai j + +, ˆ ˆ aj k + + and ˆ ak i + are linearly dependent if and only if:

Aa = 2 Ba = 1 Ca = 0 Da = –1

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EnglishUP PCS (Pre) 2001

Q173.a×b + b× c + c×a is equal to:

A0 Ba + b + c C() () c -a a - b × DNone of the above

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EnglishUP PCS (Pre) 2001

Q174.If a = 3i - j+ 5k, b = 2i + j+ k, and c = 3i + 2j+ 3k, then, abc is equal to:

A–1 B1 C5 D11

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EnglishUP PCS (Pre) 2001

Q175.The ˆ ˆ ˆ i + j+ k unit vector which is perpendicular to ˆ ˆ i + k is

Aĵ Bˆ ˆ/i - k C() 1 ˆ ˆ i - k 2 Dˆ ˆ ˆ 2i + j+ 2k 3

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EnglishUP PCS (Pre) 2001

Q176.If ˆ ˆ ˆ OA = i - j+ k and ˆ ˆ OB = j+ k then the area of the triangle OAB is:

A6 B1 6 2 C1 3 2 D2

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EnglishUP PCS (Pre) 2001

Q177.A vector perpendicular to the vectors ˆ ˆ ˆ 4i + 3j+ k and ˆ ˆ ˆ ˆ ˆ ˆ 2i - j+ 2k where (i - j+ k being unit vectors along axes of x, y, z respectively) is:

Aˆ ˆ ˆ/5i + 6j+10k Bˆ ˆ ˆ/7i -6j-10k Cˆ ˆ ˆ/2i + 4j- k Dˆ ˆ ˆ/6i + 2j-3k

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EnglishUP PCS (Pre) 2002

Q178.A force ˆ ˆ ˆ 3i + 4j+ 5k acts through a point ˆ ˆ ˆ 2i + j+ 3k Then the moment of the force about the point ˆ ˆ ˆ i + 2j+ k, in magnitude, is:

A5 2 units B5 3 units C5 units Dnone of the above

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EnglishUP PCS (Pre) 2002

Q179.If the vectors ˆ ˆ ˆ mi + 3j+ 4k, ˆ ˆ ˆ 3i + j-mk, ˆ ˆ ˆ -i + mj+ 6k are coplanar, then m is equal to:

A–1 B0 C1 D2

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EnglishUP PCS (Pre) 2002

Q180.The value of the scalar triple product [a b + c a + b + c]is:

A0 B1 Ca b + c D2 a b + c

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