Math Chapter Wise

EnglishUP PCS (Pre) 2007

Q321.The conic, whose focus is pole and directrix is 2 π θ = θ = is a–

Apair of straight lines Bparabola Cellipse Dhyperbola

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EnglishUP PCS (Pre) 2007

Q322.The radius of the circle passing through the point (6,2) two of whose diameters are x + y = 6 and x + 2y = 4, is–

A10 B6 C2 5 D4 5

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EnglishUP PCS (Pre) 2007

Q323.The eccentricity of an ellipse whose pair of conjugate diameters are y = x and 3y = –2x is–

A1/5 B1/3 C1/2 D1/2

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EnglishUP PCS (Pre) 2007

Q324.The angle between the tangents drawn from the point (–2, 0) to the parabola y2 = 4 (x + 1) is–

A0 B4 C3 D2

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EnglishUP PCS (Pre) 2007

Q325.The locus of the point of intersection of perpendicular tangents to a parabola is a–

Astraight line Bcircle Cparabola Dhyperbola

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EnglishUP PCS (Pre) 2007

Q326.A square is formed by the two pairs of straight lines 2 x 8x 12 0, 2 y 14y 45 0 circle is inscribed in it. The centre of the circle is–

A(7,4) B(4,7) C(3,7) D3,4 8

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EnglishUP PCS (Pre) 2008 (G.I.C.) Lecturer Exam, 2015

Q327.The maximum number of normal that can be drawn from any point to a parabola is

Aone Btwo Cthree Dfour

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EnglishUP PCS (Pre) 2008

Q328.If the normal at one end of a latusrectum of an ellipse passes through one extremity of the minor axis, then that eccentricity e is given by the equation

Ae4 +e2 -1= 0 Be4 +3e2 +1= 0 Ce4 -e2 -1= 0 De2 +e2 -1= 0

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EnglishUP PCS (Pre) 2008

Q329.If h2 = ab then the angle between the lines ax2 +2 hxy+by2 = 0 is

A90° B0° C45° D60°

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EnglishUP PCS (Pre) 2009

Q330.If 60° ° ° be the angle between the asymptotes of a hyperbola, then its eccentricity is

A4/3 B2/3 C3 D3

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EnglishUP PCS (Pre) 2009

Q331.If the sum of the distances of a point from two perpendicular lines in a plane is 1, then the locus of the point is

Aa square Ba circle Ca straight line Dtwo interescting lines

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EnglishUP PCS (Pre) 2009

Q332.The intersection of x = t2, y = t2 (t real) and x2 +y2 = 8, is

A(2, 2) B(–2, –2) C(–2, +2) D(2, –2)

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EnglishUP PCS (Pre) 2009

Q333.The normal at the point (1, 1) on the curve 2y = 3–x2 is

Ax + y = 0 Bx + y = –1 Cx – y = –1 Dx – y = 0

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English

Q334.The figure formed by all the asymptotes of the curve x2 y2 = c2 (x2 + y2) is a

Atriangle Bparallelogram Crectangle Dsquare

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English

Q335.The curve (x – 2)2 = y (y – 1)2 at the point (2, 1) has

Aan isolated point Ba cusp Ca node Dnone of the above

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English(GIC) Lecturer Exam, 2015

Q336.Angle between the lines represented by x2 –xy–

Atan–1/(–2) Btan–1/(1) Ctan–1/(–3) Dtan–1/(–1)

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English(GIC) Lecturer Exam, 2015

Q337.The lines 3x–4y+4=0 and 6x–8y–7=0 are tangents to the same circle. The radius of the circle is

A11/10 B11/5 C3/2 D3/4

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English(GIC) Lecturer Exam, 2015

Q338.The number of values of m for which the line y–1=m(x–1) cuts the circle x2 +y2 =4 at two real points, is

A1 B2 CInfinite DNone of the above

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English(GIC) Lecturer Exam, 2015

Q339.The number of common tangents that can be drawn to the circles x2 +y2 –4x–6y–3 = 0 and x2 +y2 –2x–2y+1 = 0 is equal to

A1 B2 C3 D4

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English(GIC) Lecturer Exam, 2015

Q340.The angle made by the double ordinate of length 8 at the vertex of the parabola y2 =4x is equal to

Aπ/3 Bπ/2 Cπ/4 Dπ/6

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