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The maximum value of Z = 5x + 3y, subject to constraints 3x + 5y ≤ 15, 5x + 2y ≤ 10 and x , y ≥ 0 is

1) 235 / 19 2) 325 / 19 3) 523 / 19 4) 532 / 19 Solution: (1) 235 / 19 Z = 5x + 3y Subject to constraints 3x + 5y ≤ 15, x... View Article

If one of the lines given by 6x² – xy + 4cy² = 0 is 3x + 4y = 0 then c is equal to

1) 1 2) - 1 3) 3 4) - 3 Solution: Given 6x2 - xy + 4cy2 = 0…(i) One of the line is 3x + 4y = 0 So (3x + 4y)(2x + cy) = 0 6x2 + 8xy + 3cxy +... View Article

The straight lines 3x + 4y – 5 = 0 and 4x – 3y = 15 intersected at the point P. On these lines, the points Q and R are chosen so that PQ = PR. The slopes of the line QR passing through (1, 2) are

1) -7, 1/7 2) 7, 1/7 3) 7, (-1/7) 4) 3, -(1/3) Solution: Given lines are 3x + 4y - 5 = 0…(i) 4x = 3y + 15…(ii) Slope of (i) m1 = -¾ Slope of... View Article

The value of λ if λx² – 10xy + 12y² + 5x – 16y – 3 = 0 represents a pair of straight lines is

1) 1 2) - 1 3) 2 4) - 2 Solution: Given λx2 - 10xy + 12y2 + 5x - 16y - 3 = 0 Comparing with general equation ax2+ 2hxy + by2 + 2gx + 2fy +... View Article

If the lines x + 3y – 9 = 0, 4x + by – 2 = 0 and 2x – y – 4 = 0 are concurrent, then b is equal to

1) - 5 2) 5 3) 1 4) 0 Solution: Given x + 3y - 9 = 0 4x + by - 2 = 0 2x - y - 4 = 0 For the lines to be concurrent, determinant = 0 =>... View Article

The equation of the line bisecting perpendicularly the segment joining the points (- 4, 6) and (8, 8) is

1) 6x + y - 19 = 0 2) y = 7 3) 6x + 2y - 19 = 0 4) x + 2y - 7 = 0 Solution: Let A(- 4, 6) and B(8, 8) be the points. Slope of AB, m1 = (y2 -... View Article

The line, which is parallel to X-axis and crosses the curve y = √x at an angle 45⁰, is

1) y = 1/4 2) y = 1/2 3) y = 1 4) y = 4 Solution: Let the line parallel to x-axis be y = c The equation of the curve is y = √x Point of... View Article

If a line with y-intercept 2, is perpendicular to the line 3x – 2y = 6, then its x-intercept is

1) 1 2) 2 3) - 4 4) 3 Solution: Given 3x - 2y = 6 => y = (3/2) x - 3 Here slope m1 = 3/2 Slope of perpendicular line, m2 = -⅔ (since m1m2... View Article

A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 and makes equal intercepts with axes. Then, equation of the line is

1) 5x + 5y - 3 = 0 2) x + 5y - 3 = 0 3) 5x - y - 3 = 0 4) 5x + 5y + 3 = 0 Solution: Given 3x + y + 1 = 0 ..(i) 2x - y + 3 = 0 …(ii) Solving... View Article

The perpendicular bisector of the line segment joining P(1, 4) and Q (k, 3) has y-intercept – 4. Then, the possible value of k is

1) - 4 2) 1 3) 2 4) - 2 Solution: Given points are P(1, 4) and Q (k, 3). Slope of PQ, m1 = (y2 - y1)/(x2 - x1) = (3 - 4)/(k - 1) = -1/(k -1)... View Article

If the lines kx – 2y – 1 = 0 and 6x – 4y – m = 0 are identical (coincident) lines, then the values of k and m are

1) k = 3, m = 2 2) k = - 3, m = 2 3) k = - 3, m = - 2 4) k = 3, m = - 2 Solution: Given lines are kx - 2y - 1 = 0 …(i) 6x - 4y - m = 0 …(ii)... View Article

A line passing through origin and is perpendicular to two given lines 2x + y + 6 = 0 and 4x + 2y – 9 = 0. The ratio in which the origin divides the line, is

1) 1 : 2 2) 2 : 1 3) 4 : 2 4) 4 : 3 Solution: Given 2x + y + 6 = 0 ..(i) The equation of line perpendicular to 2x + y + 6 = 0 and pass... View Article

The pairs of straight lines x² – 3xy + 2y²= 0 and x²– 3xy + 2y²+ x – 2 = 0 form a

1) square but not rhombus 2) rhombus 3) parallelogram 4) rectangle but no a square Solution: Given x2 - 3xy + 2y2 = 0 …(i) x2 - 3xy + 2y2 +... View Article

The angle between the line joining the points (1, -2), (3, 2) and the line x + 2y – 7 = 0 is

1) π 2) π/2 3) π/3 4) π/6 Solution: Let the given points be A(1, -2), B(3, 2). Slope of AB, m1 = (y2 - y1)/(x2 - x1) = (2 - (-2))/(3 - 1) =... View Article

The angle between lines joining origin and intersection points of line 2x + y = 1 and curve 3x² + 4yx – 4x + 1 = 0

1) π/2 2) π/3 3) π/4 4) π/6 Solution: Given 3x2 + 4yx - 4x + 1 = 0 3x2 + 4yx - 4x(1) + (1)2 = 0…(i) Given 2x + y = 1…(ii) Substitute (ii) in... View Article

The lines represents by ax² + 2hxy + by² = 0 are perpendicular to each other, if

1) h2 = a + b 2) a + b = 0 3) h2 = ab 4) h = 0 Solution: Given ax2 + 2hxy + by2 = 0 Let θ be the angle between the lines tan θ = 2√(h2 -... View Article

The area (in square unit) of the triangle formed by x + y + 1 = 0 and the pair of straight lines x² – 3xy + 2y²= 0 is

1) 7/12 2) 5/12 3) 1/12 4) 1/6 Solution: Given pair of straight lines x2 - 3xy + 2y2 = 0 => x2 - 2xy -xy + 2y2 = 0 => x(x - 2y) - y(x... View Article

The line parallel to the X-axis and passing through the point of intersection of the line ax + 2by + 3b = 0 and bx – 2ay – 3a = 0, where (a, b) ≠ (0, 0), is

1) above the X-axis at a distance of 3/2 2) above the X-axis at a distance of 2/3 3) below the X-axis at a distance of 2/3 4) below the X-axis... View Article

If line (tan² θ + cos² θ) x² – 2 tan θ xy + sin² θ y² = 0 makes angles α and β with X – axis, then tan α – tan β is equal to

1) 2 2) 4 3) tan θ 4) 2 tan θ Solution: Given (tan2 θ + cos2 θ) x2 - 2 tan θ xy + sin2 θ y2 = 0 Let m1 and m2 be the slopes of the given... View Article

Let α be the distance between the lines – x + y = 2 and x – y = 2 and β be the distance between the lines 4x – 3y = 5 and 6y – 8x = 1, then

1) 20√2β = 11α 2) 20√2α = 11β 3) 11√2β = 20α 4) None of the above Solution: Equation of given lines - x + y = 2 => y = x + 2 And x - y =... View Article

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