Math Chapter Wise

English(GIC) Lecturer Exam 2015

Q161.The angle between the lines x = 1, y = 2 and y = –1, z = 0 is–

A300 B600 C900 D00

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English(GIC) Lecturer Exam 2015

Q162.The equation of the plane through the line 2x y 0 y 3z and perpendicular to 4x 5y 3z 8

A8x y 9z 0 B2x 6y 15z 0 C10x 6y 3z 0 D28x 17y 9z 0

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English(GIC) Lecturer Exam 2015 UP PCS 2007

Q163.The shortest distance between the two lines x 3 y 6 z 4 3 2 and x 2 y z 7 4 1 1 is–

A81 B9 C3 D1

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English

Q164.The line joining the point (1, 1, –1) and (2, 3, 1) is will be the direction cosine.

A1 2 1,, 3 3 3 B1 1 1,, 3 3 3 C1 2 2,, 3 3 3 D1 1 2,, 3 3 3

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EnglishUP PCS (Pre) 1997

Q165.Equation of the plane containing the lines x 1 y 1 z 1 1 2 1 + − − + − − + − − + − − = − and 2x–3y+3z–5=0= 4x–y+5z–7 is:

Ax–y+z=1 Bx+y+z=1 Cx+y–z=1 Dx+y+z=0

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EnglishUP PCS (Pre) 1997

Q166.The tangent plane of the surface x2 +2ya2 +3z2 =12 at the point (1,2,–1) is:

Ax+4y+3z=12 Bx+4y–3z=12 Cx–4y+3z=6 Dx+2y+3z=0

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EnglishUP PCS (Pre) 1997

Q167.The shortest distance between the z-axis and the line x+y +2z–3=0, 2x+3y+4z–4=0 is:

A0 B1 C2 D3

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EnglishUP PCS (Pre) 1997

Q168.The equation to the plane passing through three points (1,1,0), (1,2,1) and (–2,2,–1) is:

A2x+3y+3z=5 B2x–3y+3z = 5 C2x+3y–3z=5 DNone of these

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EnglishTGT 2010

Q169.Angle between the line r (i 2j k) (i j k) = + − + λ − + = + − + λ − + = + − + λ − + = + − + λ − + and the normal to the plane r.(2i j k) − + − + =4 is

A1 2 2 sin 3 − B1 4 cos 3 2 − C1 2 2 tan 3 − D1 2 2 cot 3 −

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EnglishTGT 2010

Q170.If line 1 1 1 x x y y z z m n − − − − − − − − − − − − = ℓ is parallel to the plane ax + by + cz+d=0, then

Aa b c l m n = Bal + bm + cn =0 C0 + + = a b c l m n DNone of these

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EnglishTGT 2010

Q171.A line which makes angle 30°, 45°, 60° with the positive direction of x-axis and y-axis and z-axis respectively, then the direction cosines of this line are

A1 3 1,, 2 2 2 B3 1 1,, 2 2 2 C3 1 1,, 2 2 3 DNone of these

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EnglishTGT 2009

Q172.Let L, is the common line to planes 2x + 3y + z = 1 and x + 3y + 2 z = 2. If the Line L make an angle α with the positive x-axis, the which of the following be the value of cosα?

A1/3 B1/2 C1 D1/2

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EnglishTGT 2005

Q173.The projection of the line joining the points (3,4,5) and (4,6,3) on to the line joining the points (– 1,2,4) and (1,0,5) is:

A−4/3 B2/3 C8/3 D1/3

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EnglishTGT 2005

Q174.If three line are drawn from O whose direction ratios are 1, 1,k, 2, 3,0 − − and 1,0,3 respectively, then they are all coplanar. then the value of K will be:

A1 B0 CThe value of K does not exist DNone of these

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EnglishTGT 2005

Q175.If the plane x–2y+3z=0 is rotated by an angle of 90º with respect to the line of Intersection which also includes the plane 2x+3y–4z–5=0 then what will be the equation of the plane when It new position.

A28x–17y+9z=0 B22x+5y–4z–35=0 C25x+17y+52z-25=0 DNone of these

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EnglishTGT 2005

Q176.Line x 1 y 2 z 3 2 1 3 − − − − − − − − − − − − = of plane x+y+z–1=0 what will be the interpolation on:

Ax+y+z-1=0= 2x-y-z+3 Bx+y-z-1=0 =x+2y-z-3 C2x-y+32-1=0=x+y+z+1 Dx+2y-3z=0=x+y+z+1

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