If the roots of the quadratic equation x2 + px + q = 0 are tan 30 and tan 15 respectively, then the value of 2 + q – p is
1) 3 2) 0 3) 1 4) 2 Solution: (1) 3 tan 300 and tan 150 are the roots of... View Article
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If α, β and γ are the roots of the equation x3 – 7x + 7 = 0, then (1 / α4) + (1 / β4) + (1 / ɣ4) =
1) 7/3 2) 3/7 3) 4/7 4) 7/4 Solution: (2) 3/7 Since ∑α = 0, αβ = – 7 αβɣ... View Article
If the difference between the roots of x2 + ax – b = 0 is equal to the difference between the roots of x2 – px + q = 0, then a2 – p2 in terms of b and q is equal
1) – 4 (b + q) 2) 4 (b + q) 3) 4 (b – q) 4) 4 (q –... View Article
If α and β are the roots of the equation ax2 + bx + c = 0, then the equation, whose roots are 2α + 3β and 3α + 2β, is
1) acx2 + (a + c)bx- (a + c)2 = 0 2) acx2 – (a + c)bx- (a + c)2... View Article
If α, β and γ are the roots of x3 – 2x2 + 3x – 4 = 0, then the value of α2β2 + β2 γ2 + γ2 α2
1) – 7 2) – 5 3) – 3 4) 0 Solution: (1) – 7 x3 – 2x2 + 3x... View Article
If α and β are the roots of the equation ax2 + bx + c = 0 and px2 + qx + r = 0 has roots [1 – ɑ] / ɑ and [1 – β] / β, then r =
1) a + 2b 2) a + b + c 3) ab + bc + ca 4) abc Solution: (2)... View Article
If one root is square of the other root of the equation x2 + px + q = 0, then the relation bewteen p and q is
1) p3 – (3p – 1)q + q2 = 0 2) p3 – q(3p + 1) + q2 = 0... View Article
If sin α and cos α are the roots of the equation px2 + qx + r = 0, then
1) p2 + q2 – 2pr = 0 2) p2 – q2 + 2pr = 0 3) p2 – q2... View Article
If α and β are the roots of the equation lx2 + mx + n = 0, then the equation, whose roots are α3β and αβ3, is
1) l4x2 – nl (m2 – 2nl)x + n4 = 0 2) l4x2 + nl(m2 – 2nl)x + n4 =... View Article
Let A (1, k), B(1, 1) and C (2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of value which k can take is given by
1) {1, 3} 2) {0, 2} 3) {–1,3} 4) {–3, –2} Solution: Given A (1, k), B(1, 1) and C... View Article
If the coordinates of the vertices of the triangle ABC be (-1, 6), (-3, -9), and (5, -8) respectively, then the equation of the median through C is
1) 13x – 14y – 47 = 0 2) 13x – 14y + 47 = 0 3) 13x + 14y... View Article
If the middle points of the sides, BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and (-5, 7) respectively then the equation of the side AB is
1) x – y – 2 = 0 2) x – y + 12 = 0 3) x + y... View Article
The equation of the line passing through the point (x’ , y’) and perpendicular to the line yy’ = 2a(x + x’) is
1) xy’ + 2ay + 2ay’ – x’ y’ = 0 2) xy’ + 2ay – 2ay’ – x’ y’... View Article
If the coordinates of the points A, B, C be (-1, 5), (0, 0) and (2, 2) respectively and D be the middle point of BC, then the equation of the perpendicular drawn from B to the line AD is
1) x + 2y = 0 2) 2x + y = 0 3) x – 2y = 0 4) 2x... View Article
If the coordinates of A and B be (1, 1) and (5, 7), then the equation of the perpendicular bisector of the line segment AB is
1) 2x + 3y = 18 2) 2x – 3y + 18 = 0 3) 2x + 3y – 1... View Article
A line L is perpendicular to the line 5x – y = 1 and the area of the triangle formed by the line L and coordinate axes is 5. The equation of the line L is
1) x + 5y = 5 2) x + 5y = ±5√2 3) x – 5y = 5 4) x... View Article
The equations of the lines which cuts off an intercept -1 from y-axis and equally inclined to the axes are
1) x – y + 1 = 0, x + y + 1 = 0 2) x – y –... View Article
The line (3x – y + 5) + λ(2x – 3y – 4) = 0 will be parallel to y-axis, if λ =
1) ⅓ 2) -3/2 3) -⅓ 4) 3/2 Solution: Given (3x – y + 5) + λ(2x – 3y –... View Article
If the line 2x + 3y = 5 and y = mx + c be parallel, then
1) m = ⅔, c =5 2) m = -⅔, c = 5 3) m = -⅔, c = any... View Article
If the angle 2θ is acute, then the acute angle between x2 (cos θ – sin θ) + 2xy cos θ + y2 (cos θ + sin θ) = 0 is
1) 2θ 2) θ/3 3) θ 4) θ/2 Solution: Given x2 (cos θ – sin θ) + 2xy cos θ... View Article
