If the roots of x2 – ax + b = 0 are two consecutive odd integers, then a2 – 4b is equal to
1) 3 2) 4 3) 5 4) 6 5) 7 Solution: (2) 4 Let α, β are the roots of... View Article
Latest Posts
If α and β are the roots of x2 – ax + b2 = 0, then α2 + β2 is equal to
1) a2 + 2b2 2) a2 – 2b2 3) a2 – 2b 4) a2 + 2b 5) a2 – b2... View Article
The value of a, so that the sum of squares of the root of the equations x2 – (a – 2) x – a + 1 = 0 assume the least value, is
1) 2 2) 0 3) 3 4) 1 Solution: (4) 1 x2 – (a – 2) x – a +... View Article
If a ϵ R and the equation -3(x)- [x])2 + 2(x – [x]) + a2 = 0 (where, [x]denotes the greatest integer ≤ x] has no integral solution, then all possible values lie in the interval )
1) (-1, 0) ∪ (0,1) 2) (1,2) 3) (-2, -1) 4) (- ∞,- 2) ∪ (2, ∞) Solution: (1) (-1,... View Article
If x, y, z are in GP and ax = by = cz, then
1) loga c = logb a 2) logb a = logc b 3) logc b = loga c 4) None... View Article
Equation of the bisector of the acute angle between lines 3x – 4y + 7 = 0 and 12x + 5y – 2 = 0 is
1) 21x – 77y + 100 = 0 2) 99x – 27y + 81 = 0 3) 99x + 27y... View Article
If two pairs of lines x2 – 2mxy – y2 = 0 and x2 – 2nxy – y2 = 0 are such that one of them represents the bisector of the angles between the other, then
1) mn = 1 2) m + n = mn 3) mn = – 1 4) m – n =... View Article
Let P = (- 1, 0), Q = (0, 0) and R = (3, 3√3) be three points. Then, the equation of the bisector of the ∠PQR is
1) y = √3x 2) √3y = x 3) y = – √3x 4) √3y = -x Solution: Given P... View Article
The angle between the pair of straight lines y2 sin2 θ – xy sin2 θ + x2 (cos2 θ – 1) = 0 is
1) π/3 2) π/4 3) π/6 4) π/2 Solution: Given y2 sin2 θ – xy sin2 θ + x2 (cos2... View Article
The angle between the lines in x2 – xy – 6y2 – 7x + 31y – 18 = 0 is
1) 90o 2) 60o 3) 45o 4) 30o Solution: Given x2 – xy – 6y2 – 7x + 31y –... View Article
The angle between the lines √3x – y – 2 = 0 and x – √3y + 1 = 0 is
1) 90o 2) 60o 3) 45o 4) 30o Solution: Given lines are √3x – y – 2 = 0 …(i)... View Article
If (a, a2) falls inside the angle made by the lines y = x/2, x > 0 and y = 3x, x > 0, then a belongs to
1) (3, ∞) 2) (1/2, 3) 3) (-3, – (1/2)) 4) (0, 1/2) Solution: The given lines are y =... View Article
The angle between the lines represented by the equation 2x2 + 3xy – 5y2 = 0, is
1) π/3 2) π/2 3) tan-1 |12/5| 4) tan-1 (7/3) Solution: Given 2x2 + 3xy – 5y2 = 0 Comparing... View Article
The angle between the pair of lines (x2 + y2) sin2 α = (x cos θ – y sin θ)2 is
1) θ 2) 2θ 3) α 4) 2α Solution: Given (x2 + y2) sin2 α = (x cos θ –... View Article
The angle between the pair of straight lines formed by joining the points of intersection of x2 + y2 = 4 and y = 3x + c to the origin is a right angle. Then, c2 is equal to
1) 20 2) 13 3) 1/5 4) 5 Solution: Given x2 + y2 = 4 …(i) Also y = 3x... View Article
A line passes through the point of intersection of the lines 100x + 50y – 1 = 0 and 75x + 25y + 3 = 0 and makes an equal intercept on the axes. Its equation is
1) 25x + 25y – 1 = 0 2) 5x – 5y + 3 = 0 3) 25x + 25y... View Article
The lines (a + 2b)x + (a – 3b)y = a – b for different values of a and b pass through the fixed point, whose coordinates are
1) (2/5, 3/5) 2) (3/5, 3/5) 3) (1/5, 1/5) 4) (3/5, 2/5) Solution: Given equation of line is (a +... View Article
A line passes through point (2, 2) and perpendicular to the line 3x + y = 3. Then, y – intercept is
1) 2 2) 5/3 3) 4/3 4) 3/4 Solution: Given line is 3x + y = 3 => y =... View Article
The pair of lines joining origin to the points of intersection of the two curves ax2 + 2hxy + by2 + 2gx = 0 and a’x2 + 2h’xy + b’y2 + 2g’x = 0 will be at right angles, if
1) (a’ + b’ ) g’ = (a + b) g 2) (a + b ) g’ = (a’ +... View Article
If θ is the angle between the lines ax2 + 2bxy + by2 = 0, then angle between x2 + 2xy sec θ + y2 = 0 is
1) θ 2) 2θ 3) θ/2 4) 3θ Solution: Given equation of lines is x2 + 2xy sec θ +... View Article
