The constraints -x1 + x2 ≤ 1, -x1 + 3x2 ≤ 9 and x1, x2 ≥ 0 defines on
1) bounded feasible space 2) unbounded feasible space 3) both bounded and unbounded feasible space 4) None of the above... View Article
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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 /... 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... 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 –... 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 –... 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 +... 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... 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... 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)... 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... 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).... 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,... 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 +... 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... 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... 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... 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... 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 =... 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... 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 –... View Article
