Math Chapter Wise

EnglishUP PCS (Pre) 1997

Q361.The equation of the circle, which passes through the points (0,1), (1,0) and (2,1) is:

Ax2 +y2 –2x–2y+1=0 Bx2 +y2 +2x+2y–1=0 Cx2 +y2 –x–y=1 DNone of these

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EnglishTGT 2010

Q362.Equation ax2 + 2hxy + by2 + 2gx+2fy + c =0 represents a parabola if

Aab = h2 Ba = b Ca + b = 0 DNoen of these

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EnglishTGT 2010

Q363.If g2 + f2 = c, then the equation x2 +y2 +2gx+2fy+c = 0 will represent

Aa circle of radius g Ba circle of radius f/ Ca circle of diameter c Da circle of radius 0

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EnglishTGT 2010

Q364.The equation of the normal to the hyperbola 2 2 x y 1 16 9 − = − = at (–4,0) is

Ay = 0 By = x Cx = 0 Dx = –y

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EnglishTGT 2010

Q365.The line x cos α+ y sin α = p will touch the parabola y2 = 4a(x+a), if

Ap cos α+a = 0 Bp cos α–a = 0 Ca cos α+p = 0 Da cos α–p= 0

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EnglishTGT 2010

Q366.The equation of the normal at (3,–2) on the ellipse 4x2 + 9y2 = 72 is

A3x + 2y = 5 B3x – 2y = 5 C3x + 2y +5 = 0 DNone of these

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EnglishTGT 2009

Q367.Consider a family of circles which passes through the point (–1, 1) and touches the x– axis. If (h, k) is the coordinate of the center of the circle, then the set of values of k which lie in the following interval is.

A1 0 k 2 < < B1 k 2 ≥ C1 1 k 2 2 − ≤ D1 k 2 ≤

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EnglishTGT 2009

Q368.The equation of tangent to the parabola y2 = 8x is y = x + 2 what will be the coordinate of the point from which the tangent drawn (on the parabola) is Perpendicular to the given tangent line.

A(–1, 1) B(0, 2) C(2, 4) D(–2, 0)

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EnglishTGT 2005

Q369.A curve passes through the point (5, 3) and the point (x, y) lies on the curve. If the slope of the curve and the ordinate product of the point (x, y), the point (x, y) of the curve is equal to the equation of abscissa, then the equation of the curve will be.

Ax2 + y2 = 34 Bx2 – y2 =16 C5y – 3x=0 DNone of these

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EnglishTGT 2005

Q370.What will be the slope of tangent to the circle x2 + y2 = a2 at the point (h, k).

A0 B1 C-1 DNone of these

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EnglishTGT 2005

Q371.The polar origin of circle 2 2 x y 2 x 2 y c 0 + + λ + µ + = + + λ + µ + = + + λ + µ + = + + λ + µ + = will touch the circle 2 2 2 x y r + = + = at the point (0,0).

A() 2 2 c r = λ + µ B() 2 2 r c = λ + µ C() 2 2 2 2 c r = λ + µ D() 2 2 2 2 r c λ + µ

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EnglishTGT 2004

Q372.The point (0, 3) is closest to the curve x2 = 2y at

A(2 2, 0) B(0,0) C(2, 2) D(–2, –2)

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EnglishTGT 2004

Q373.The centre of the circle passing through the points (8, 12), (11,3) and (0, 14) is

A(2, 5) B(–2, 5) C(3, 5) D(4, 6)

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EnglishTGT 2004

Q374.The locus of the points of intersection of the perpendicular tangents to a conic is called

AAuxiliary circle BPoint circle CDirector circle DImaginary circle

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EnglishTGT 2004

Q375.When the original axes is rotated through 45° ° in the positive direction. The equation x2 –y2 = a2 is transformed to

Ax2 + y2 = 0 Bxy = a2 C2xy – a2 = 0 D2xy + a2 = 0

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