Math Chapter Wise

EnglishRajasthan TGT 2013

Q101.A straight line r =a+λb meets the plane r. n =0 at the point P. The position vector of P

Aa.n a b b.n Bb.n b a a.n Cb.n b b a.n − Da.n a b b.n −

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EnglishRajasthan TGT 2011

Q102.The equation of the plane passing through the points (2, 3, 1) and (-4, 5, 3) and parallel to x- axis is

Ax y z 2 − + = B3x 4z 1 − = Cy 4z 7 0 + − = Dy z 2 0 − − =

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EnglishJharkhand TGT 2017

Q103.If (l1, m1, n1), (l 2, m2, n2) are direction cosines of two lines and θ is the angle between them, then cosθ=

A() 1 1 1 2 2 2 m n + + l B1 2 1 2 m m + l l C() () () 1 2 1 2 1 2 2 2 2 2 2 2 1 1 1 2 2 2 m m n n m n m n + + + + + + l l D1 2 1 2 1 2 m m n n + + l l

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EnglishJharkhand TGT 2017

Q104.The angle between the planes 2x–y+z=13 and x+y+2z=9 is

A2/π B4/π C3/π D2 3 π

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EnglishJharkhand TGT 2017

Q105.The Z- intercept of the plane whose equation is x–3y+2z=9 is

A9 B–3 C9/2 D2/9

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EnglishKVS TGT DEC 2017

Q106.If the pair of straight lines xy–x–y+1 = 0 and the line ax+2y–3 = 0 are concurrent, then a =

A–1 B0 C3 D1

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EnglishKVS TGT DEC 2017

Q107.The foot of perpendicular from (0,2,3) to the line x 3 y 1 z 4 5 2 3 is–

A(–2, 3, 4) B(2, –1, 3) C(2, 3, –1) D(3, 2, –1)

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EnglishTGT 2005

Q108.The foot of perpendicular from (α,β,γ α,β,γ α,β,γ α,β,γ) on y- axis is:

A(α, 0, 0) B(0, β, 0) C(0, 0, γ) D(0, 0, 0)

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EnglishTGT 2005

Q109.The equation of the plane passing through the point (–2, –2, 2) and containing the line joining the points (1,1,1) and (1, –1, 2) is:

Ax + 2y – 3z + 4 = 0 ] B3x – 4y + 1 = 0 C5x + 2y – 3z – 17 = 0 Dx – 3y – 6z + 8 = 0

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EnglishTGT 2011

Q110.The plane 2x-2y+z+12=0 and the sphere x2 +y2 +z2 –2x–4y+2z–3= 0 at for point will touch-

A(1,–4,–2) B(–1,4,–2) C(–1,4,2) D(1,4,–2)

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EnglishUP PCS (Pre) 1998

Q111.The equation of the plane passing through the points (1, 1, 1) and (2, 3, 0) and parallel to the z-axis is:

A2x – y = 1 Bx – y + z + 1 = 0 Cx – 2y + 1 = 0 D4x – 3y + 1 = 0

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EnglishUP PCS (Pre) 1998, 2009

Q112.The shortest distance between the lines x 1 y z 0 1 0 − = and x 2 y z 0 0 1 − = is:

A3 B2 C1 D0

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EnglishUP PCS (Pre) 1998

Q113.The angle between the planes 3x + 4y – 5z = 9 and 2x + 6y + 6z = 7 is:

A6/π B4/π C3/π D2/π

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EnglishUP PCS (Pre) 1998

Q114.A system of equations for the line of intersection of the planes 4x + 4y – 5z = 12 and 8x + 12y – 13z = 32 is:

Ax 1 y 2 z 2 3 4 − − = Bx 1 y 2 z 2 3 4 + − = Cx 1 y 2 z 2 3 4 − + = Dx 1 y 2 z 2 3 4 + + =

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EnglishUP PCS (Pre) 1995

Q115.The general equation of the plane which is parallel to x–axis is–

Aby cz d 0,b0,c0 + + = Bax by cz d 0,a0,b0 c0 + + + = Cax cz d 0,a0,c0 + + = Dax by cz d 0,a0,b0

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EnglishUP PCS (Pre) 1995

Q116.A plane meets the coordinate axes in points A,B,C such that the centroid of ABC is (2,3,4). The equation of the plane is–

A4x 3y 6z 18 B4x 3y 3z 18 − + = C6x 4y 3z 18 D6x 4y 3z 36

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EnglishUP PCS (Pre) 1995

Q117.The equation of the plane passing through the points (2, 2, 1) and (9, 3, 6) and perpendicular to the plane 2x 6y 6z 9 is–

A3x 4y 5z 9 B3x 4y 5z 9 C3x 4y 5z 8 D3x 4y 5z 8

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EnglishUP PCS (Pre) 1995

Q118.The equations of the straight line through (1,2,3) and perpendicular to the plane x 2y 5z 9 0 are–

Ax 1 y 2 z 3/1 2 5 Bx 1 y 2 z 3/1 2 3 Cx 1 y 2 z 3/1 2 5 DNone of these

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EnglishUP PCS (Pre) 1995

Q119.The value of for which the equation 2 2 2 x y z yz 0 represents a pair of planes is–

A0 B1 C–1 D2

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EnglishUP PCS (Pre) 1995, 1999

Q120.The shortest distance between the two straight lines– 4 6 3 x y z 3 5 2 2 3 4 and 5y 6 2z 3 3x 4 8 9 5 is–

A23 B3 C0 D6 10

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