Math Chapter Wise

EnglishTGT 2003

Q81.The lines lx + my + n = 0, mx + ny +l = 0 and nx + ly + m = 0 (not all equal) are concurrent if

Al2 +m2 + n2 = 1 Blm + mn + nl = 1 Clm + mn + n = 0 Dl + m + n = 0

Show answer

EnglishRajashtan TGT 2015 TGT 2003

Q82.Projection of lines on the axes is 2, 3, 6, then what will be the length of the line:

A5 B7 C9 D1

Show answer

EnglishPGT 2011

Q83.For every point P(x,y,z) on the xy–plane:

Ax=0 By=0 Cz=0 DNone of these

Show answer

EnglishPGT 2010

Q84.The equation of the plane passing through the point Po(–3, 0, 7) and perpendicular to the vector ˆ ˆ ˆ x 5i 2j k = + − = + − = + − = + − is

A5x+2y+z–22= 0 B5x+2y+2z+22= 0 C5x+2y–z+22= 0 D5x+2y–2z–22= 0

Show answer

EnglishPGT 2005

Q85.The image of the point P(1,3,4) in the plane 2x–y+z+3 = 0 is:

A(3, 5, –2) B(–3, 5, 2) C(3, 5, –2) D(–1, –2, –3)

Show answer

EnglishPGT 2005

Q86.The plane lx+my+nz = p touches the conicoid ax2 +by2 +cz2 = 1, if:

A2 2 2 2 m n p a b c + + = l B2 2 2 2 m n 1 a b c p + + = l Ca l 2 + bm2 + cn2 = p2 DNone of these

Show answer

EnglishPGT 2005

Q87.Tangent planes are drawn to the conicoid ax2 +by2 +cz2 = 1 through the point (α, β, γ). The perpendicular from the origin to them generate

A2 2 2 2 () 0 + + + α +β + γ = ax by cz x y z B2 2 2 2 () 0 + + + α +β + γ = x y z x y z a b c C2 2 2 2 () α +β + γ = + + x y z x y z a b c D2 2 2 2 () α +β + γ = + + x y z ax by cz

Show answer

EnglishPGT 2003

Q88.(3, 6, –5)and (1, 2, 3)meets the plane through the three points (1, –2, 4), (3, 0, 2)and (3, 1, 4)

A4 8 51,, 5 5 5 − − B4 8 51,, 5 5 5 − − C2 8 51,, 5 5 5 − − D2 8 51,, 5 5 5 − − −

Show answer

EnglishPGT 2002 UP PCS (Pre) 1996

Q89.The shortest distance between the two lines, one joining the points (–1,2, –3) and (–16, 6, 4) and the other line joining the points (1, –1,3) and (4,9,7) is:

A3 B5 C7 D9

Show answer

EnglishPGT 2002

Q90.If l1, m1, n1; l2, m2, n2 be the direction cosines of two perpendicular straight lines, then:

Al1l2+m1m2+n1n2 =0 Bl1l2+m1m2+n1n2 =1 C1 1 1 2 2 2 m n 0 m n + + = l D1 1 1 2 2 2 m n 1 m n + + = l

Show answer

EnglishRajasthan TGT 2016 L.T. 2018

Q91.If the lines x 2 y 3 z 4 3 4 5 − − − − − − − − − − − − = and x 1 y 2 z 3 3 4 − − − − − − − − − − − − = λ are coplanar, then λ is equal to

A2 B1 C4 D3

Show answer

EnglishRajasthan TGT 2016

Q92.The equation of the plane perpendicular to the yz-plane and passing through the points (1, –2, 4) and (3,–4,5) is

A2x+y–3z+12=0 By+2z–6=0 C3x+y–4z+15=0 Dx–2y+7=0

Show answer

EnglishRajasthan TGT 2016

Q93.The angle between the planes given by combined equation 6x2 +4y2 –10z2 +3yz+4zx–11xy=0 is equal to

A1 2 cos 3 − B2/π C3/π D1 1 cos 6 −

Show answer

EnglishRajasthan TGT 2016

Q94.The x 1 y 21 z 1 2 6 3 − − + − − + − − + − − + = − line and the plane 3x+2y+2z=19

Aare perpendicular to each other Bare parallel to each other Cline lies in the plane. Dangle between line and plane is 3 π

Show answer

EnglishRajasthan TGT 2016

Q95.The straight line x y z m 0 − α − β + γ − α − β + γ − α − β + γ − α − β + γ = l is parallel to

Ax-axis only By-axis only Cz-axis only Dx and y-axes both

Show answer

EnglishRajasthan TGT 2016

Q96.The equation of plane parallel to x-axis is

Aax+by+cz+d=0 Bax+by+d= 0 Cby+cz+d=0 Dax+cz+d=0

Show answer

EnglishRajasthan TGT 2016

Q97.The shortest distance between the lines x 1 y 2 z 3 2 3 4 − − − − − − − − − − − − = and x 2 y 4 z 5 3 4 5 − − − − − − − − − − − − = is

A1/6 B1/6 C1/3 D1/3

Show answer

EnglishRajasthan TGT 2015 L.T. 2018 Lecturer GIC 2015

Q98.Co-ordinates of the foot of the perpendicular from the point (3, 1,11) − − to the line x y 2 z 3 2 3 4 − − = is

A(2,3,4) B(2,5,7) C(2,1,1) D(1,2,3)

Show answer

EnglishRajasthan TGT 2015

Q99.The image of the point (1,2,3) with respect to the plane 2x 6z 3y 35 0 + − + = + − + = + − + = + − + = is

A(1,5, 3) − − B(3, 1,9) C(3,8, 9) − − D(3,5, 3) − −

Show answer

EnglishRajasthan TGT 2013

Q100.If 1 1 1,m,n l and 2 2 2,m,n l are direction cosines of the two lines inclined to each other at an angle θ, then the direction cosines of the external bisector of the angle between the lines are-

A1 2 1 2 1 2 m m n n,, 2cos 2cos 2cos 2 2 2 − − − θ l l B1 2 1 2 1 2 m m n n,, 2sin 2sin 2sin 2 2 2 − − − θ l l C1 2 1 2 1 2 m m n n,, 2cos 2cos 2cos 2 2 2 + + + θ l l D1 2 1 2 1 2 m m n n,, 2sin 2sin 2sin 2 2 2 + + + θ l l

Show answer