Math Chapter Wise

EnglishUP PCS (Pre) 1996

Q121.Equation of the plane, which touches the cone 2 2 2 x 2y 3z 2yz 5zx 3xy 0 along the generator, whose direction rations are (1, 1,1) is–

Ay z By x = Cx y 1 0 DNone of these

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EnglishUP PCS (Pre) 1996

Q122.The equation of a plane through (1,2,3) and parallel to the plane 3x+4y-5z = 0, is–

A3x 4y 5z 4 0 B3x 4y 5z 4 0 C3x 4y 5z 4 0 D3x 4y 5z 0

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EnglishUP PCS (Pre) 1996

Q123.The distance of the point (1,2,0) from the plane 4x + 3y + 12z + 16 = 0 is–

A1 B2 C3 D4

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EnglishUP PCS (Pre) 1996 GIC 2015

Q124.The angle between the pair of planes 2 2 2 2x 6y 12z 18yz 2zx xy 0 is–

A1 185 cos 16 B1 185 cos 21 C1 116 cos 21 D1 16 cos 21

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EnglishUP PCS (Pre) 1996

Q125.The point of intersection of the lines x 1 y 2 z 3 2 3 4 and 4x 3y 1 0, 5x 3z 2 0 is–

A(1,1,1) B(1, 1,1) C(1, 1, 1) D(1, 1, 1)

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EnglishUP PCS (Pre) 1996

Q126.A plane passes through a point (a,b,c) and meets the axes in A,B,C then the locus of the locus of the centre of the sphere OABC is–

A2 2 2/ax by cz 2 B1 1 1/a x b y c z 2 C1 1 1/ax by cz 2 DNone of these

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EnglishUP PCS (Pre) 1996

Q127.The planes ax by cz d 0 and a x b y c z d 0 are parallel to each other, if:

Aa b c/a b c Ba b d/a b d Caa bb cc 0 Daa bb cc dd 0

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EnglishUP PCS (Pre) 2000

Q128.The equation of the plane through the points (2, 3, –4) and (1, –1, 3) and parallel to the x-axis is:

A7y + 4z – 5 = 0 B7y + 4z + 5 = 0 C4y – 7z – 5 = 0 D7y + 4z + 5 = 0

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EnglishUP PCS (Pre) 2000

Q129.The distance of the origin from the plane 2x + 6y – 3z + 7 = 0 is:

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2001

Q130.The plane containing the straight lines: x – 3 y – 2 z –1 = 1 0 1 and x – 3 y – 2 z –1 = 1 1 0 is:

Ax+y–z = 4 Bx–y+z = 2 Cx–y–z = 6 Dy+z–x = 0

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EnglishUP PCS (Pre) 2002 & 2001

Q131.The shortest distance between the lines: 1 1 1 y – x – z – 3 2 4 = 1 2 3 and 3y –1 4z –1 = 3 4 2x –1 = 2 is

A4/5 3 B4/5 C4/3 DNone of the above

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EnglishUP PCS (Pre) 2002

Q132.The shortest distance between the Z–axis and the line x + y + 2z – 3 = 0, 2x +3y + 4z – 4 = 0 is:

A2 B1/2 C0 D1

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EnglishUP PCS (Pre) 2003

Q133.If the co-ordinates of the points A,B,C and D are (3,4,5), (4,6,3), (–1,0,4) and (1,2,5) respectively: the projection of CD on AB is–

A4/3 B3/4 C3/2 D1/2

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EnglishUP PCS (Pre) 2003

Q134.The distance between the planes 2x–2y+z+1=0 and 4x–4y+2z+3=0 is–

A1/2 B1/3 C1/6 D0

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EnglishUP PCS (Pre) 2003

Q135.The plane x 2y z 0 cuts the cone xy yz zx 0 in mutually perpendicular generators is is equal to –

A3/2 B2/3 C–2 D–3

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EnglishUP PCS (Pre) 2004

Q136.If S ax by cz d and 1 1 1 1 1 S a x b y c z d, then the equation 1 S S 0 represents a plane passing through the line of intersection of the planes S 0 and 1 S 0,for–

A1 only B1only C0 only Devery real number

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EnglishUP PCS (Pre) 2004 & 2005

Q137.The shortest distance between the lines x + 3 y – 6 z x + 2 y z – 7 = and =, – 4 3 2 – 4 1 1 is:

A21 B9 C27 Dnone of the above

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EnglishUP PCS (Pre) 2005 & 2007

Q138.If the line x – 4 y – 2 z – k =, 1 1 2 lies on the plane 2x – 4y+z = 7 then the value of k is:

A7 B–7 C5 D–5

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EnglishUP PCS (Pre) 2005

Q139.The angle between the straight lines x +1 y – 2 z + 3 = 2 5 4 and x –1 y + 2 z – 3 = 1 2 –3 is:

A45° B30° C60° D90°

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EnglishUP PCS (Pre) 2005

Q140.The system of equations –2x+y+z = a, x–2y+z = b, x+y–2z = c, is consistent if:

Aa+b–c = 0 Ba–b+c = 0 Ca+b–c ≠ 0 Da+b+c = 0

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