Math Chapter Wise

EnglishRajasthan TGT 2011

Q121.if vectors ˆ ˆ ˆ a i j k, = − + = − + = − + = − + ˆ ˆ ˆ b i 2j k = + − = + − = + − = + − and ˆ ˆ ˆ c 3i j 5k = + α + = + α + = + α + = + α + are coplanar, then the value of α is

A2 B6 C–2 D–6

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EnglishKVS TGT DEC 2017

Q122.If the vectors i 3j 2k,2i j 4k and 3i 2j xk are coplanar, then the value of x is–

A1 B3 C–2 D2

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EnglishKVS TGT DEC 2017

Q123.Given that a and b are unit vectors. If the vectors p 3a 5b and q a b are mutually perpendicular. then–

Aa and b are also mutually perpendicular. Ba, b have opposite directions Ca and b make an angle of 3 Da and b make an angle of 4

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EnglishKVS TGT DEC 2017

Q124.Let a,b,c be there vectors such that a.(b c) b.(c a) c(a b) 0 and a 1, b 4 and c 8 then a b c equals–

A13 B81 C9 D5

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EnglishKVS TGT DEC 2017

Q125.Given two vectors 15 x 3 9 and 15 y 9 k. For x and y to be orthogonal, value of k is–

A22 B–22 C17.75 D–17.75

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EnglishKVS TGT DEC 2017

Q126.To write the vector 26 x 12 2 in the linear combination form 1 2 3 C C C of the vectors 1 1 C 1, 1 2 1 C 1, 0 and 3 0 C 0, 1 the values of,, are in that order.

A7, 9, 19 B9, 7, 19 C19, 9, 7 D7, 19, 9

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EnglishTGT 2013

Q127.If the vectors ˆ ˆ ˆ a 2i 3j k = − − = − − = − − = − − and ˆ ˆ ˆ b i 4j 2k = + − = + − = + − = + − represent two sides of a triangle then what will be the area of the triangle?

A1 232 2 B232 C234 D1 230 2

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EnglishTGT 2011

Q128.Find the value of the moment acted by the force ˆ ˆ ˆ F 3i 2j k = + + = + + = + + = + + and F − − at the points ˆ ˆ ˆ i j k − + − + and ˆ ˆ ˆ 2i 3j k − − − − respectively.

A2 5 B3 5 C4 5 D5 5

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EnglishTGT 2011

Q129.The vectors a and b are such that a b a b + = − + = − + = − + = − then the angle between the two vectors will be:

A4/π B8/π C2/π DNone of these

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EnglishTGT 2011

Q130.The vectors ˆ ˆ ˆ ˆ ˆ ˆ i j 2k, i j k λ + + + λ − λ + + + λ − λ + + + λ − λ + + + λ − and ˆ ˆ ˆ 2i j k − + λ − + λ − + λ − + λ are coplanar then the value of is:

A–2 B0 C1 D–1

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EnglishTGT 2011

Q131.If two unit vectors a and b makes an angle of 300 and 1200 respectively with the x-axis, then the value of a b + + will be:

A2/3 B2 C3 D2

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EnglishTGT 2011

Q132.If the vectors ˆ ˆ ˆ ˆ ˆ ˆ i 2j 3k, i 4j 7k, + + λ + + + + λ + + + + λ + + + + λ + + ˆ ˆ ˆ 3i 2j 5k − − − − − − − − − − − − are collinear then the value of -- will be:

A3 B4 C5 D6

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EnglishTGT 2011

Q133.The work done by the force ˆ ˆ ˆ F 2i j k = − − = − − = − − = − − on an object moving with respect to the vector ˆ ˆ ˆ a 3i 2j 5k = + − = + − = + − = + − work down.

A12 unit B11 unit C10 unit D9 unit

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EnglishTGT 2011

Q134.The moment produced by the force (((()))) ˆ ˆ ˆ i 2j 3k + + + + acting about the point (((()))) ˆ ˆ ˆ 2i 3j k − + + − + + − + + − + + and at the point ˆ ˆ ˆ i j k + + + + is:

Aˆ ˆ ˆ 3i j 4k − − Bˆ ˆ ˆ 3i j 4k + − Cˆ ˆ ˆ 3i j 4k + + DNone of these

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EnglishUP PCS (Pre) 1998

Q135.The position vector of the point at which the plane (((()))) ˆ ˆ ˆ r i j k 2 − − = − − = − − = − − = meets the line (((()))) ˆ ˆ ˆ r t 2i 3j k = + + = + + = + + = + + is:

A() ˆ ˆ ˆ 2i 3j k + + B() ˆ ˆ ˆ 2i 3j k − + + Cˆ ˆ ˆ i 3j 2k + + D() ˆ ˆ ˆ i 3j 2k − + +

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EnglishUP PCS (Pre) 1994

Q136.The value of the product. a (b a) is (a 0,b 0)

Anull vector Bnon-null vector Czero scalar Dnon-zero scalar

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EnglishUP PCS (Pre) 1994

Q137.The point of application of a force F (0,6,8) is changed from P(1, 1,2) to Q(1,1,2). The work done is–

A6 units B8 units C10 units D12 units

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EnglishUP PCS (Pre) 1994

Q138.If A 2i 2j k, = + − = + − = + − = + − B 6i 3j 2k = + − = + − = + − = + − then the angle between A and B is –

A300 B600 C1 20 cos 21 − D1 5 cos 21

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EnglishUP PCS (Pre) 1994

Q139.The area of the a triangle ABC whose vertices are A(1, 2,3), B(3,1,2), C(2,3, 1) is–

A0 B4 3 C2 3 D7 3 2

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EnglishUP PCS (Pre) 1995

Q140.If A i 2j 3k, B i 2j k, = − + + = − + + = − + + = − + + C 3i j then A tB + + is perpendicular to C if have value of scalar t is–

A2 B6 C4 D5

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