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Equation of angle bisectors between x and y-axes are

1) y = ± x 2) y = ± 2x 3) y = ± (½)x 4) y = ± 3x Solution: We know the equation of the x-axis is y = 0 Equation of y-axis is x = 0 X-axis... View Article

If vertices of parallelogram are respectively (0,0), (1,0), (2,2) and (1,2), then angle between diagonals is

(1) π/3 (2) π/2 (3) 3π/2 (4) π/4 Solution: Given vertices of the parallelogram are (0,0), (1,0), (2,2) and (1,2) Slope of first diagonal,... View Article

The angle between the straight lines x – y√3 = 5 and x√3 + y = 7 is

1) 600 2) 900 3) 750 4) 300 Solution: Given lines x - y√3 = 5 …(i) => y = x/√3 - 5 Slope, m1 = 1/√3 x√3 + y = 7 …(ii) => y = -x√3 + 7... View Article

The inclination of the straight line passing through the point (-3, 6) and the midpoint of the line joining the (4, -5) and (-2, 9) is

(1) π/4 (2) π/6 (3) π/3 (4) 3π/4 Solution: Midpoint of line joining (4, -5) and (-2, 9) = ((4 - 2)/2, (-5 + 9)/2) = (1, 2) The inclination... View Article

If the lines y = (2 + √3)x + 4 and y = kx + 6 are inclined at an angle 60⁰ to each other, then the value of k will be

1) 1 2) 2 3) -1 4) -2 Solution: Given y = (2 + √3)x + 4 …(i) Slope, m1 = (2 + √3) y = kx + 6 …(ii) Slope, m2 = k Given angle between them is... View Article

The line passes through (1, 0) and (-2, √3) makes an angle of ___ with the x-axis.

1) 60o 2) 120o 3) 150o 4) 135o Solution: Given line passes through (1, 0) and (-2, √3). Slope, m = (y2 - y1)/(x2 - x1) = (√3 - 0)/(-2 - 1) =... View Article

The angle between the lines x + 2y = 11 and 2x – y = 9 is

1) 60o 2) 30o 3) 90o 4) 45o Solution: Given x + 2y = 11 …(i) => y = -½ x + 11 Slope, m1 = -½ 2x - y = 9 …(ii) => y = 2x - 9 Slope, m2... View Article

The angle between the two lines y – 2x = 9 and x + 2y = 7, is

1) 60o 2) 30o 3) 90o 4) 45o Solution: Given y - 2x = 9 ..(i) => y = 2x + 9 Slope, m1 = 2 x + 2y = 7…(ii) => y = -½ x + 7 Slope, m2 =... View Article

The angle between the lines x cos 30^o + y sin 30^o = 3 and x cos 60^o + y sin 60^o= 5 is

1) 90o 2) 30o 3) 60o 4) None of these Solution: x cos 30o + y sin 30o = 3 …(i) => y = -cot 300 x + 3/sin 300 => y = -√3 x + 6 Slope,... View Article

The angle between the lines y = (2 – √3)x + 5 and y = (2 + √3)x – 7 is

(1) 300 (2) 600 (3) 450 (4) 900 Solution: Given y = (2 - √3)x + 5 …(i) Slope, m1 = (2 - √3)x y = (2 + √3)x - 7 ..(ii) Slope, m2 = (2 +... View Article

Three straight lines 2x + 11y – 5 = 0, 24x + 7y – 20 = 0 and 4x – 3y – 2 = 0

1) form a triangle 2) are only concurrent 3) are concurrent with one line bisecting the angle between the other two 4) None of the above... View Article

The position of reflection of the point (4, 1) about the line y = x -1 is

1) (1, 2) 2) (3, 4) 3) (-1, 0) 4) (2, 3) Solution: Let Q be the image of P. Join PQ and it cuts the line mirror y = x-1 at point R. Let R... View Article

The equation of bisectors of the angles between the lines |x| = |y| are

1) y = ± x and x = 0 2) x = 1/2 and y = 1/2 3) y = 0 and x = 0 4) None of these Solution: Given |x| = |y| => |y| = ± x => y = x or y... View Article

If one of the lines of my² + (1 – m²)xy – mx² = 0 is a bisector of the angle between the lines xy = 0, then m is/are

1) - 1/2 2) - 2 3) ± 1 4) 2 Solution: Given xy = 0 => x = 0 or y = 0 ie y axis or x axis. So the coordinate axis is bisected by the line... View Article

The vertices of a triangle are A (3, 7), B (3, 4) and C (5, 4). The equation of the bisector of ∠ABC is

1) y = x + 1 2) y = x - 1 3) y = 3x - 5 4) y = x Solution: Given A (3, 7), B (3, 4), and C (5, 4) are the vertices of the triangle ABC.... View Article

If α and α², are the roots of x² + x + 1 = 0, then the equation, whose roots are α³¹ and α⁶², is

1) x2 - x + 1 = 0 2) x2 + x - 1 = 0 3) x2 + x + 1 = 0 4) x60 + x30 + 1 = 0 Solution: (3) x2 + x + 1 = 0 Given α and α2 are the roots of the... View Article

If α and β are the roots of the equation x² + px + q = 0 and the sum (α + β) – x – (α² + β²) / 2 (x²) + (α³ + β³) / 3 (x³) – ….. exists, then it is =

1) log(x2 + px + q) 2) log(x2 - px + q) 3) log(1 + px + qx2) 4) log(1 - px + qx2) 5) log (x2 qx + q) Solution: (4) log(1 - px + qx2) The... View Article

If sec α and cosec α are the roots of the equation x² + px + q = 0

1) p2 = p + 2q 2) q2 = p + 2q 3) p2 = q(q +2) 4) q2 = p (p + 2) 5) p2 = q (q - 2) Solution: (3) p2 = q (q +2) Since sec α + cosec α = p and... View Article

If α and β are the roots of x² + 5x + 4 = 0, then the equation, whose roots are (α+ 2)/3 and (β+2)/3, is

1) 9x2 + 3x + 2 = 0 2) 9x2 - 3x - 2 = 0 3) 9x2 + 3x - 2 = 0 4) 9x2 - 3x + 2 = 0 Solution: (4) 9x2 - 3x + 2 = 0 α + β = - 5, αβ = 4 The roots... View Article

If one root of the quadratic equation ax² + bx + c = 0 is equal to nth power of the other root, then the value of (aⁿc)^1/(n+1) + (acⁿ)^1/(n+1) is equal to

1) b 2) - b 3) 1/ (bxn+1) 4) - (1/bxn+1) Solution: (1) b The given equation is ax2 + bx + c = 0. Let α and αn be the roots of the equation,... View Article

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