Math Chapter Wise

EnglishUP PCS (Pre) 2006

Q141.The point of intersection of the line x 1 y 1 z 1 1 2 3 − − − − − − − − − − − − = and x 4 y 6 z 7 2 3 3 − − − − − − − − − − − − = is:

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

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EnglishUP PCS (Pre) 2006

Q142.The family of planes 2x y z 2 3 2 0 − λ + µ + λ − µ − = − λ + µ + λ − µ − = − λ + µ + λ − µ − = − λ + µ + λ − µ − = always passes through a fixed point whose co-ordinates are:

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

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EnglishUP PCS (Pre) 2006

Q143.Which of the following represents a straight line in three dimensions:

Ax=1 Bx+y=1 Cx+y+z=1, z=0 DNone of the above

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EnglishUP PCS (Pre) 2006

Q144.If the planes 1 1 1 1 a x b y c z d 0 + + + = + + + = + + + = + + + = and 2 2 2 2 a x b y c z d 0 + + + = + + + = + + + = + + + = are perpendicular to each other, then

A1 2 1 2 1 2 1 2 a a b b c c d d + + = B1 2 1 2 1 2 1 2 a a b b c c d d 0 + + + = C1 2 1 2 1 2 a a b b c c 0 + + = D1 1 1 1 2 2 2 2 a b c d a b c d + + =

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EnglishUP PCS (Pre) 2007

Q145.The plane αx + βy + γz = 0 cuts the cone yz zx xy 0 In perpendicular generators if–

A0 B0 αβ +βγ + αγ = C0 D2 2 2/0

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EnglishUP PCS (Pre) 2007

Q146.The pole of the plane 2x + 3y – 4z = 6 with respect to the sphere x2 + y2 + z2 –2x – 5 = 0 is–

A3 2,, 2 2 B2,3, 2 C2, 2,2 Dnone of the above

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EnglishUP PCS (Pre) 2007

Q147.The equation of the cone whose generators pass through the point (α, β, γ) and whose directions cosines l, m, n satisfy the relation al2 + bm2 + cn2 = 0 is–

A2 2 2/ax by cz 0 B2 2 2/(x a) (y b) (z c) 0 C2 2 2/a(x ) b(y ) c(z ) 0 Dnone of the above

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EnglishUP PCS (Pre) 2007

Q148.The image of the point (–3, 8, 4) in the plane 6x – 3y – 2z + 1 = 0 is the point.

A(3, 8, 4) B(6,16,8) C(9,2,0) D(0,2,4)

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EnglishUP PCS (Pre) 2007

Q149.The equation of Plane x + 2y + 2z + d = 0 through P = (1,2,2) and normal to OP meets the co-ordinate axes OX, OY, OZ at A, B, C, respectively, The area of the triangle ABC is–

A30 B243 2/8 C243/4 D243/8

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EnglishUP PCS (Pre) 2007

Q150.If the cone 2x2 + λy2 – 5z2 = 0 has three mutually perpendicular tangent planes, then λ is equal to –

A10/3 B3 C5 D10

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EnglishUP PCS (Pre) 2007

Q151.The angle between the line– x 1 y 1 z 2 3 4 2 and the plane 2x – 3y + z + 4 = 0 is–

A1 4 cos 406 B1 4 sin 406 C1 4 sin 406 D1 4 cos 406

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EnglishUP PCS (Pre) 2008

Q152.The equation of the plane passing through the intersection of the planes x + y + z = 6 and 2x + 3y + 4z + 5 = 0 and the point (1, 1, 1), is

A5x+6y+8z–20=0 B10x+15y+3z+28=0 C20x+23y+26z–69=0 Dx–2y+3z–10=0

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EnglishUP PCS (Pre) 2008

Q153.The lines x –1 y – 2 z + 9 = and –2 2k –5 x +1 y + 2 z – 9 = are 3k –2 –2 perpendicular with each other for k =?

Ak = 2 Bk = 1 Ck = –1 Dk = –2

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English

Q154.The shortest distance between the x-axis and the line x –1 y – 2 z – 3 = is 0 1 1

A1/2 B1 C2 D2

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English

Q155.The equation of the line parallel to x y z = 1 2 3, and passing through the point (2, 3, 4) is

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

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English(GIC) Lecturer Exam 2015

Q156.The coordinate of the image of the point (1, 3, 4) with respect to the plane 2x–y+z+3 = 0 is

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

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English(GIC) Lecturer Exam 2015

Q157.The perpendicular line is drawn from (2, 4, 1) to x–axis. The co-ordinates of the foot of perpendicular

A(0, 4, –1) B(2, 0, 0) C(0, 4, 0) D(0, 0, –1)

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English(GIC) Lecturer Exam 2015

Q158.The distance of the point (3, 4, 5) from the y- axis is

A5 B34 C41 D50

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English(GIC) Lecturer Exam 2015

Q159.If (–2, 6) is the image of the point (4, 2) with respect to straight line L, then equation of L is given by

A3x–2y+5 = 0 B3x+2y–5 = 0 C3x–2y–5 = 0 D3x+2y–5 = 0

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English(GIC) Lecturer Exam 2015

Q160.The line x y z 1 2 3 and the plane 2x 4y 2z 3 meet in–

AOnly one point BNo point CInfinitely many points DNone of the above

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