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A second-degree homogeneous equation in x and y always represents

1) A pair of straight lines 2) A circle 3) A conic section 4) None of the above Solution: A... View Article

The equation (x – 5)² + (x – 5)(y – 6) – 2(y – 6)² = 0 represents

1) A circle 2) Two straight lines passing through the origin 3) Two straight lines passing through the point (5,... View Article

The values of h for which the equation 3x² + 2hxy – 3y² – 40x + 30y – 75 = 0 represents a pair of straight lines, are

1) 4, 4 2) 4, 6 3) 4, –4 4) 0, 4 Solution: Given 3x2 + 2hxy – 3y2 –... View Article

If the equation hxy + gx + fy + c = 0 represents a pair of straight lines, then

1) fh = cg 2) fg = ch 3) h2 = gf 4) fgh = c Solution: Given hxy +... View Article

Two lines represented by equation x² + xy + y² = 0 are

1) Coincident 2) Parallel 3) Mutually perpendicular 4) Imaginary Solution: Given x2 + xy + y2 = 0 Divide by... View Article

The equation (x + y)² – (x²+ y²) = 0 represents

1) A circle 2) Two lines 3) Two parallel lines 4) Two mutually perpendicular lines Solution: Given (x + y)2... View Article

The point of intersection of the lines represented by equation 2(x + 2)² + 3(x + 2) (y – 2) – 2(y – 2)² = 0 is

1) (2, 2) 2) (–2, –2) 3) (–2, 2) 4) (2, –2) Solution: Given 2(x + 2)2 + 3(x +... View Article

The point of intersection of the lines represented by the equation 2x² + 3y² + 7xy + 8x + 14y + 8 = 0 is

1) (0, 2) 2) (1, 2) 3) (–2, 0) 4) (–2, 1) Solution: Given 2x2 + 3y2 + 7xy +... View Article

One bisector of the angle between the lines given by a(x – 1)² + 2h(x – 1)y + by² = 0 is 2x + y – 2 = 0.The other bisector is

1) x – 2y + 1 = 0 2) 2x + y – 1 = 0 3) x + 2y... View Article

The equation of the bisectors of the angles between the lines represented by x² + 2xy cot θ + y² = 0 , is

1) x2 – y2 = 0 2) x2 – y2 = xy 3) (x2 – y2 ) cot θ =... View Article

The combined equation of the bisectors of the angle between the lines represented by (x² + y²)√3 = 4xy is

1) y2 – x2 = 0 2) xy = 0 3) x2 + y2 = 2xy 4) none of these... View Article

The equation of the bisectors of the angle between the lines represented by the equation x² – y² = 0 is

1) x = 0 2) y = 0 3) xy = 0 4) None of these Solution: Given x2 –... View Article

The equation x² – 3xy + λy² + 3x – 5y + 2 = 0 when λ is a real number, represents a pair of straight lines. If θ is the angle between the lines, then cosec² θ is equal to

1) 3 2) 9 3) 10 4) 100 Solution: Given x2 – 3xy + λy2 + 3x – 5y +... View Article

The pair of lines represented by 3ax² + 5xy + (a² – 2)y² = 0 are perpendicular to each other for

1) Two values of a 2) for all a 3) For one value of a 4) For no value of... View Article

If the pair of straight lines x² – 2pxy – y² = 0 and x² – 2qxy – y² = 0, be such that each pair bisects the angle between the other pair, then

1) pq + 1 = 0 2) pq – 1 = 0 3) p + q = 0 4) p... View Article

18 Mar 2021: UPSC Exam Comprehensive News Analysis

CNA 18 March 2021:- Download PDF Here TABLE OF CONTENTS A. GS 1 Related B. GS 2 Related POLITY AND... View Article

If the pair of straight lines given by Ax² + 2Hxy + By² = 0, (H² > AB) forms an equilateral triangle with line ax + by + c = 0, then (A + 3B) (3A + B) is

1) H2 2) -H2 3) 2H2 4) 4H2 Solution: We know that angle between pair of straight lines ax2+2hxy +... View Article

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