Math Chapter Wise

EnglishUP PCS (Pre) 2009

Q201.Moment of the force, represented by ˆ ˆ (3i + k) and passing through the point ˆ ˆ ˆ (i - j+ 3k), about the point ˆ ˆ ˆ (i + 2j-k) is

Aˆ ˆ ˆ/i -3j-4k Bˆ ˆ ˆ/i -5j-3k Cˆ ˆ ˆ/3i -12j-9k Dˆ ˆ ˆ/3i -12j+9k

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EnglishUP PCS (Pre) 2009

Q202.Two non-zero vectors are linearly dependent, if and only if, their vector product is

Aa unit vector Ba constant vector Cnull vector DNone of the above

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English

Q203.If a.b a.c = and a b a c × = × × = × × = × × = × then

Aa c/− is parallel to a Bb c − is perpendicular to a Cb is parallel to c Db c 0 − =

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English

Q204.Let ˆ ˆ ˆ ˆ ˆ ˆ a i 2j 3k, b i 3j 2k = + + = − + = + + = − + = + + = − + = + + = − + and ˆ ˆ c j k = − What is x equal to which is orthogonal to a and satisfies the equation x b b c × = × × = × × = × × = ×?

A−ˆ ˆ/3i k Bˆ ˆ 3i k − + Cˆ ˆ ˆ i 2j k − + − Dˆ ˆ ˆ i 2j k − +

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English

Q205.The volume of the parallelopiped with coterminous edges ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ a = 3i - 2j+ 5k,b = i + j+ k and c = 2i + 4j-k, is

A11 units B14 units C15 units D12 units

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English(GIC) Lecturer exam, 2015

Q206.If () () × × = × × a b c a b c, then

A() a c b 0 × × = B() c a b 0 × × = C() c a b 0 × × = DNone of the above

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English(GIC) Lecturer exam, 2015

Q207.The moment of a force represented by ˆ ˆ 3i + k acting through the point ˆ ˆ ˆ 2i - j+ 3k about the point is ˆ ˆ ˆ i + 2j-k

Aˆ ˆ ˆ 3i 11j 9k − + − Bˆ ˆ ˆ 3i 11j 9k − + Cˆ ˆ ˆ 3i 11j 9k − − Dˆ ˆ ˆ 3i 11j 9k − + +

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English(GIC) Lecturer exam, 2015

Q208.If ˆ ˆ ˆ a, b, c are any three vectors such that () () a + b. c = a - b. c = 0 then () × × a b c is equal to

A0 Ba Cb Dc

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English(GIC) Lecturer exam, 2015

Q209.() () () ˆ ˆ ˆ ˆ ˆ ˆ a - i i + a - j j+ a + k k is equal to

Aˆ ˆ ˆ i j k + + B() ˆ ˆ ˆ 3 i j k + + Ca D3a

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English(GIC) Lecturer exam, 2015

Q210.If ˆ ˆ ˆ ê = ai +bj+ ck is a unit vector, then maximum value of ab+bc+ca is equal to

A–3/2 B0 C1 D3

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English(GIC) Lecturer exam, 2015

Q211.The volume of the parallelopiped determined by ˆ ˆ ˆ ˆ ˆ ˆ A = i + 2j-k, B = -2i + 3k and ˆ ˆ C = 7j-4k is

A21 B22 C23 D24

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English(GIC) Lecturer exam, 2015

Q212.If ˆ ˆ ˆ ˆ ˆ a.i = a.(i + j) = a.(i + j+k) =1,then a is equal to

Aî Bĵ Ck̂ Dˆ ˆ/j+ k

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English(GIC) Lecturer exam, 2015

Q213.The triangle ABC with position vector of A is ˆ ˆ ˆ 2i - j+ k, of B is ˆ ˆ ˆ i - 3j – 5k, and C is ˆ ˆ ˆ 3i - 4j- 4k,

Aequilateral Bisosceles Cright angled DNone of the above

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English(GIC) Lecturer exam, 2015

Q214.The projection of the vector ˆ ˆ ˆ a = 2i + 3j+ 2k on the vector ˆ ˆ ˆ b = i + 2j+k is given by

A7 6/3 B4 6/3 C5 6/3 D2 6/3

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English(GIC) Lecturer exam, 2015

Q215.Given three vectors ˆ ˆ ˆ A i j 2k, = + − = + − = + − = + − ˆ ˆ ˆ B 2i j k, = − + = − + = − + = − + ˆ ˆ ˆ C pi 3j k For what value of p, vector A B will be perpendicular to vector C?

A–10 B–11 C–12 D0

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English(GIC) Lecturer exam, 2015

Q216.Volume of a parallelepiped whose co-terminous edges are given by ˆ ˆ a 2i 3j, ˆ ˆ ˆ b i j k and ˆ ˆ c 3i k is–

A2 B5 C10 D4

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English(GIC) Lecturer exam, 2015

Q217.The area of parallelogram determined by vectors ˆ ˆ 3i 2j and ˆ ˆ 2j 4k is–

A2 B4 C2 61 D61

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English(GIC) Lecturer exam, 2015

Q218.If a,b,c are any three vectors, then b c,c a,a b, is equal to–

A2 a,b,c B2 a,b,c C2 2 2/a b c DNone of the above

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English(GIC) Lecturer exam, 2015

Q219.Distance between the planes ˆ r.(i 2j 2k) 5 0 and ˆ r.(i 2j 2k) 8 0 is given by–

A13/3 B3/13 C3/11 D3/13

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EnglishTGT 2013

Q220.If OA a = and OB b = then what will be the value of BA?

Aa b/+ Ba Cb Da b

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