Math Chapter Wise

EnglishUP PCS (Pre) 2003

Q181.The area of the triangle with vertices ˆ ˆ i j, ˆ ˆ i k and ˆ ˆ j k bis–

A3 B3/2 C1/3 D2/3

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EnglishUP PCS (Pre) 2003

Q182.A unit vector perpendicular to the vectors ˆ ˆ ˆ i j k and ˆ ˆ ˆ 2i 3j k + − + − is–

Aˆ ˆ ˆ/4i 3j k B1 ˆ ˆ ˆ 2i j k 6 C1 ˆ ˆ ˆ 2i j k 6 D1 ˆ ˆ ˆ 4i 3j k 26

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EnglishUP PCS (Pre) 2003

Q183.A force ˆ ˆ ˆ 5i 3j 4k acts through the point ˆ ˆ ˆ 2i j 3k, The moment of the force about the point i 2j- k + is–

Aˆ ˆ ˆ/8(2i 2j k) Bˆ ˆ ˆ/8(2i 2j k) Cˆ ˆ ˆ/8( 2i 2j k) Dnone of the above

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EnglishUP PCS (Pre) 2004

Q184.Unit vector perpendicular to the vectors ˆ i 2j 3k and ˆ i 2j k

A1 ˆ (i j k) 3 B1 ˆ (i j k) 3 C1 ˆ (i j k) 3 D1 ˆ (i j k) 3

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EnglishUP PCS (Pre) 2004

Q185.If a,b,c are non-zero vectors and (a b) c a (b c) then–

Ac is perpendicular to a and b Ba is perpendicular to b and c Cb is perpendicular to a and c Da and b are collinear

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EnglishUP PCS (Pre) 2004

Q186.If ˆ ˆ a b a.b, then

Aa is parallel to b Ba is perpendicular to b Cangle between a, and b is 450 Dangle between a, and b is 1200

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EnglishUP PCS (Pre) 2004

Q187.For there vectors ˆ a,b,c which of the following expression in not equal to any of the remaining there?

Aa.(b c) B(a b).c C(b c).a Db.(a c)

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EnglishUP PCS (Pre) 2004

Q188.If a force of magnitude 2 units act along the line joining the points ˆ i j and ˆ i k, the moment of the force above the point P(2,1,3) is–

Ai j k Bi j k Ci j k Di j k

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EnglishUP PCS (Pre) 2004

Q189.The area of the triangle whose vertices are (0,0,0) (1,2,3) and (2,3,4) is–

A1 6 2 B3 C6 D1 3 2

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EnglishUP PCS (Pre) 2005

Q190.The area of the parallelogram having diagonals ˆ ˆ ˆ ˆ ˆ ˆ a = 3i + j- 2k and b = i - 3j+ 4k is:

A10 3 B5 3 C20 D8

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EnglishUP PCS (Pre) 2006

Q191.It is angle between two vectors a and b then a.b 0 ≥ only if:

A0≤ θ≤π B0 2 π ≤ θ ≤ C2 π ≤ θ ≤ π D0 2 π < θ <

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EnglishUP PCS (Pre) 2006

Q192.If a,b,c be three non-zero vectors, then the equation a.b a.c = implies:

Ab c = Ba is orthogonal to both b and c Ceither a is orthogonal to both b and c or a is orthogonal to b c Deither b c = or a is orthogonal to b c

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EnglishUP PCS (Pre) 2007

Q193.If â and b̂ are two unit vectors such that ˆ ˆ (a 2b) (5a 4b), then the angle between â and b̂ is–

A450 B1 1 cos 3 C1 2 cos 7 D600

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EnglishUP PCS (Pre) 2007

Q194.If a 1, b 5 and c 3, then a b,b c,c a

A–1 B0 C1 D2

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EnglishUP PCS (Pre) 2007

Q195.ˆ a,b and c unit vectors such that ˆ a b c 0 then incorrect statements is–

Aˆ/a.(b c) 0 Bb̂.(c a) 0 Cˆ/c.(a b) 0 Dˆ ˆ/a.b b.c c.a 3

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EnglishUP PCS (Pre) 2008

Q196.If ˆ ˆ ˆ ˆ ˆ ˆ 2 2 i + xj+ x k,i + yj+ y k and ˆ ˆ ˆ 2 i + zj+ z k are non-coplanar vectors and 2 3 x x 1+ x y y 1+ y = 0 z z 1+ z then the value of xyz is

A2 B1 C0 D–1

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EnglishUP PCS (Pre) 2008

Q197.The triple product a + b,b+ c,c+ a is equal to:

Aabc B2/abc C3/abc Dnone of these

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EnglishUP PCS (Pre) 2008

Q198.The incorrect statement for the three vectors () () () a× b× c,b× c×a and c × a×b and is

Atheir sum is null vector Bthey are linearly dependent Cthey are linearly independent Dthey are coplanar

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EnglishUP PCS (Pre) 2009

Q199.If a×b – 3 a.b = 0 then the angle between a and b is

A2/π B3/π C4/π D6/π

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EnglishUP PCS (Pre) 2009

Q200.ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ i ×(a×i) + j×(a× j) + k(a×k) is equal to

Aa B2a C3a D4a

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