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... View Article
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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.... 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 =... 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... 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... 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... 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... 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 =... 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... 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 +... View Article
If α and β are the roots of the equation x2 – px + r = 0 and α/2, 2β are the roots of the equation x2 – qx + r = 0. Then, the value of r is
1) 2/9 (p – q) (2q – p) 2) 2/9 (q- p) (2p – q) 3) 2/9 (q – 2p)... View Article
If α and β are the roots of the equation x2 + ax + b = 0, then (1 / α2) + (1 / β2) =
1) [a2 – 2b] / b2 2) [b2 – 2a] / b2 3) [a2 + 2b] / b2 4) [b2... View Article
If α and β are the roots of the equation ax2 + bx + c = 0, αβ = 3, and a, b, c are in AP, then α + β is equal to
1) – 4 2) 1 3) 4 4) – 2 Solution: (4) – 2 (α + β) = – b... View Article
If α, β and γ are the roots of the equation x3 – 6x2 + 11 x + 6 = 0, then ∑α2β + ∑αβ2 is equal to
1) 80 2) 168 3) 90 4) – 84 Solution: (2) 168 Since ∑ɑ = 6 ∑αβ = 11 and... View Article
If α and β are the roots of the quadratic equation ax2 + bx + c = 0, observe the lists given below
1) A = 5 B = 2 C = 4 D = 6 2) A = 5 B = 2... View Article
The cubic equation, whose roots are thrice to each of the roots of x3 + 2x2 – 4x + 1 = 0, is
1) x3 – 6x2 + 36x + 27 = 0 2) x3 + 6x2 + 36x + 27 = 0... View Article
If α, β and γ are the roots of the equation x3 – 8 x + 8 = 0, then ∑α2 and ∑ 1/αβ are respectively
1) 0 and – 16 2) 16 and 18 3) – 16 and 0 4) 16 and 0 Solution: (4)... View Article
If α and β are the roots of the equation ax2 + bx + c = 0, then α / [ɑβ + b] + β / [aɑ + b] =
1) 2/a 2) 2/b 3) 2/c 4) – (2/a) Solution: (4) – (2 / a) It is given that α... View Article
If α and β are the roots of x2 – 2x cos ∅ + 1 = 0, then the equation, whose roots are αn + βn
1) x2 – 2 xcos n∅ – 1 = 0 2) x2 – 2 xcos n∅ + 1 = 0... View Article
If two persons A and B solve the equation x2 + ax + b = 0, while solving, A commits a mistake the coefficient of x was taken as 15 in place of -9 and finds the roots as – 7 and – 2 Then, the equation is
1) x2 + 9x + 14 = 0 2) x2 – 9x + 14 = 0 3) x2 + 9x... View Article
