Math Chapter Wise

EnglishUP PCS (Pre) 2006

Q221.For the curve x=t2 –1, y=t2 –t, the tangent is perpendicular to X-axis, where:

At= 0 B1 t 2 = Ct=∞ DNone of the above

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English

Q222.For different values of a and b, the straight line given by x (a + 2b) + y (a -3b) = a -b passes through

Athe point (1, 1) Bthe point 2 3, 5 5 Cthe origin DNone of the above

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English

Q223.One of the angles between the straight lines given by x2 – y2 – 2y – 1=0 is

A6/π B4/π C3/π D2/π

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English(GIC) Lecturer Exam 2015

Q224.The line (p+2q)x+(p–3q)y=p–q, p≠0, q≠0, for different values of p and q passes through a fixed point. The fixed point is

A3 5, 2 2 B2 2, 3 5 C3 3, 5 5 D2 3, 5 5

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English(GIC) Lecturer Exam 2015

Q225.If vertex of a triangle is (1, 1) and the mid points of two sides through this vertex are (–1, 2) and (3, 2), then the centroid of the triangle is

A1 7, 3 3 B7 1, 3 C7 1, 3 − D7 1, 3 3

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EnglishTGT 2013

Q226.If pair of St. lines represented by equation 3x2 – 8xy + ky2 = 0 is perpendicular then what will be the value of k?

A1 B–1 C–2 D–3

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EnglishTGT 2013

Q227.The condition for which the equations a'x2 + b'x + c' = 0 and ax2 + bx + c = 0 have a common solution will be:

A(ca' – ac')2 = (ab' – ba') B(ca' – ac')2 = (bc'–cb') C(ca'–ac')2 = a (bc'–cb') D(ca' – ac')2 = (ab' – ba') (bc'– cb')

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EnglishUP PCS (Pre) 1997

Q228.If the lines a1x+b1y+c1= 0 and a2x+b2y+c2=0 cut the co-ordinate axes in concyclic points, then;

A2 1 2 1 b a = Ba₁/a₂ = b₁/b₂ Ca1a2 + b1b2 = 0 DNone of these

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EnglishUP PCS (Pre) 1997 TGT 2009 / PGT 2013

Q229.The equation ((())) ((()) 2 2 x 2 y x 2 y 4 − + + + + = − + + + + = − + + + + = − + + + + = represent is:

ACircle BPair of straight lines CParabola DEllipse

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EnglishUP PCS (Pre) 1997

Q230.If the equation 2x2 + xy – y2 – 11x – 5y + λ = 0 represents a pair of lines. The value of λ

A7 B14 C28 D35

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EnglishTGT 2010

Q231.If 1 1 0 aa' bb' + = + =, then line x y 1 a b + = + = and x y 1 a' b' + = + = are

Aparallel Binclined at 30° to each other Cperpendicular to each other Dinclined at 60° to each other

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EnglishTGT 2010

Q232.If a h g h b f g f c ∆ = ∆ =, then condition of parallel line is

A∆ = 0 Bh2 = ab Ca + b = 0 DNone of these

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EnglishTGT 2009

Q233.If the equation y = mx+c and xcosα + y sinα = p represents the same straight line then,

A2 p c 1 m = + B2 c p 1 m = + C2 cp 1 m = + D2 2 2 P c m 1 + + =

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EnglishTGT 2009

Q234.It e>1, then equation 1 1 ecos r = + θ = + θ = + θ = + θ will be called as -

AParabola BHyperbola CEllipse DNone of these

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EnglishTGT 2009

Q235.The equation ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 will represent a parabola if -

Aab = h2 Ba = h Ca + b = 0 DNone of these

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EnglishTGT 2005

Q236.The extremities of a diagonal of a parallelogram are the points (3, –4) and (–6, 5). If third vertex is (–2,1), then fourth vertex is:

A(1, 0) B(–1, 0) C(1,1) DNone of these

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EnglishTGT 2005

Q237.A line meets the coordinate axes at A and B such that the centroid of the ∆ ∆ ∆OAB is (1,2). The equation of the line AB is:

Ax + y = 6 B2x + y = 6 Cx + 2y = 6 DNone to these

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EnglishTGT 2005

Q238.If the equation (a1–a2)x + (b1–b2)y + c = 0 is Equidistant from the points (a1, b1) and (a2, b2), then what will be the value of c?

A2 2 2 2 1 2 1 2 − + − a a b b B2 2 2 2 1 1 2 2 + − − a b a b C() 2 2 2 2 1 2 1 2 1 2 + + + a a b b D() 2 2 2 2 2 2 1 1 1 2 + − − a b a b

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EnglishTGT 2005

Q239.A straight line which intersects the axes 'a' and 'b'. From the inverses of the intercepts cut on the axes what will be the equation of the straight line formed:

Ax/a+y/b=1 Bax+by=1 Cax+by=ab Dax-by=1

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EnglishTGT 2004

Q240.A point R (2, –5) divides the line segment joining the point A (–3, 5) and B (4,–9), then the ratio is

A5:2 B5:1 C2:5 D3:2

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