If √9x2 + 6x + 1 < (2 - x), then
1) x ∈ (- 3 / 2, 1 / 4) 2) x ∈ (- 3 / 2, – 1 /... View Article
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The solution set of inequality loge [x – 2] / [x – 3] is
1) (2, ∞) 2) (-∞, 2) 3) (-∞, ∞) 4) (4, ∞) Solution: (2) (-∞, 2) loge [x – 2]... View Article
If one root of the equation x2 + (1 – 3i)x – 2(1 + i) = 0 is – 1 + i, then the other root is
1) -1 – i 2) (-1 – i)/2 3) i 4) 2i Solution: (4) 2i Let the other root be... View Article
The point (t2 + 2t + 5, 2t2 + t – 2) lies on the line x + y = 2 for
1) all real values of t 2) some real values of t 3) t = (-3±√3)/6 4) No real values... View Article
Equation to the straight line cutting off an intercept 2 from the negative direction of the axis of y and inclined at 30o to the positive direction of axis of x, is
1) y + x – √3 = 0 2) y – x + 2 = 0 3) y – √3x... View Article
The equation of straight line passing through point of intersection of the straight line 3x – y + 2 = 0 and 5x – 2y + 7 = 0 and having infinite slope is
1) x = 2 2) x + y = 3 3) x = 3 4) x = 4 Solution: Given... View Article
A line AB makes zero intercepts on x-axis and y-axis and it is perpendicular to another line CD, 3x + 4y + 6 = 0. The equation of line AB is
1) y = 4 2) 4x – 3y + 8 = 0 3) 4x – 3y = 0 4) 4x... View Article
The equation of the straight line joining the origin to the point of intersection of y – x + 7 = 0 and y + 2x – 2 = 0 is
1) 3x + 4y = 0 2) 3x – 4y = 0 3) 4x – 3y = 0 4) 4x... View Article
If we reduce 3x + 3y + 7 = 0 to the form x cos α + y sin α = p, then the value of p is
1) 7/2√3 2) 7/3 3) 3√7/2 4) 7/3√2 Solution: Given 3x + 3y + 7 = 0 => -x –... View Article
If the intercept made by the line between the axis is bisected at the point (5, 2), then its equation is
1) 5x + 2y = 20 2) 2x + 5y = 20 3) 5x – 2y = 20 4) 2x... View Article
Two points (a, 0) and (0, b) are joined by a straight line, another point on this line is
1) (3a, –2b) 2) (a2, ab) 3) (–3a, 2b) 4) (a, b) Solution: Let A(a, 0) and B(0, b) be... View Article
A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is
1) x + 2y = 5 2) x – y + 1 = 0 3) x + y – 3... View Article
A straight line makes an angle of 1350 with the x-axis and cuts y-axis at a distance -5 from the origin. The equation of the line is
1) 2x + y + 5 = 0 2) x + 2y + 3 = 0 3) x + y... View Article
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is
1) 1/3 2) 2/3 3) 1 4) 4/3 Solution: Slope of line 3x + y = 3 is m1 =... View Article
If the equation y = mx + c and x cos α + y sin α = p represents the same straight line, then
1) p = c√(1 + m2) 2) c = p√(1 + m2) 3) cp = √(1 + m2) 4) p2... View Article
The equation of the line which cuts off the intercepts 2a sec θ and 2a cosec θ on the axes is
1) x sin θ + y cos θ – 2a = 0 2) x cos θ + y sin θ... View Article
Equations of lines which pass through the points of intersection of the lines 4x – 3y – 1 = 0 and 2x – 5y + 3 = 0 and are equally inclined to the axes are
1) y ± x = 0 2) y – 1 = ±1 (x – 1) 3) x – 1 =... View Article
The equation to the straight line passing through the point (a cos3 θ, a sin3 θ) and perpendicular to the line x sec θ + y cosec θ = a, is
1) x cos θ – y sin θ = a cos 2θ 2) x cos θ + y sin θ... View Article
Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of 1200 with the x-axis, is
1) x√3 + y + 8 = 0 2) x√3 + y = 8 3) x√3 – y = 8... View Article
If (3/2, 5/2) is the midpoint of the line segment intercepted by a line between axes, then the equation of the line is
1) 5x + 3y + 15 = 0 2) 3x + 5y + 15 = 0 3) 5x + 3y... View Article
