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√12 – √68 + 48 √2 =

1) √2 -3 2) 2 + √2 3) 2 - √2 4) 6 - 2√2 Solution: (3) 2 - √2 √12 - √68 + 48 √2 = √12 - 2 √17 + 12 √2 = √12 - 2 √(√9 + √8)2 = √12 - 2 (3 + 2... View Article

The greatest number among ∛9, ∜11 and is

1) ∛9 2) ∜11 3) 4) Cannot be determined Solution: (1) ∛9 To compare irrational numbers, convert them to the same radical sign by taking... View Article

√2 + √5 – √6 – 3√5 + √14 – 6 √5 =

1) 1 2) 2 3) 3 4) 4 Solution: (2) 2 √2 + √5 - √6 - 3√5 + √14 - 6 √5 = √2 + √5 - √6 - 3 √5 + √9 - √5 = √2 + √5 - √5 + √4 = √2 + 2 = 2... View Article

If x = √{(2 + √3) / (2 – √3)}, then x² (x – 4)² =

1) 7 2) 4 3) 2 4) 1 Solution: (4) 1 x = √{(2 + √3) / (2 - √3)} x = √{(2 + √3) (2 - √3) / [2 - √3] [2 + √3]} = √(2 + √3)2 / 2 x = 2 + √3 Then... View Article

If x = (1 / 2) (√7 + (1 / √7)), then (√x² – 1) / [x – √x² – 1] =

1) 1 2) 2 3) 3 4) 4 Solution: (3) 3 x = (1 / 2) (√7 + (1 / √7)) On squaring, x2 = (1 / 4) (7 + (1 / 7) + 2) 4x2 - 4 = 7 + (1 / 7) + 2 - 4 =... View Article

The value of {(√√3 + 1 + √√3 – 1)² (√3 – √2)} / (√√3 + 1)² – (√√3 – 1)² is

1) [√3 + √2] / √3 2) 1 3) √3 4) 1/√3 Solution: (2) 1 {(√√3 + 1 + √√3 - 1)2 (√3 - √2)} / (√√3 + 1)2 - (√√3 - 1)2 = {[√3 + 1 + √3 - 1 + 2... View Article

Given that, a, b ϵ {0,1,2…9} with a + b ≠ 0 and (a + [b / 10])^x = ([a / 10] [b / 100])^y = 1000. Then, (1 / x) – (1 / y) =

1) 1 2) 1 / 2 3) 1 / 3 4) 1 / 4 Solution: (3) 1 / 3 (a + [b / 10])x = ([a / 10] [b / 100])y = 1000 (a + [b / 10])x = 1000 Apply logarithm, x... View Article

The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have

1) Only one solution 2) Only two solutions 3) Infinite number of solutions 4) None of these Solution: (3) Infinite number of solutions x + 2y... View Article

If l, m, n are real, l ≠ m, then the roots by the equation: (l – m) x² – 5 (l + m) x – 2 (l – m) = 0 are

1) x > y 2) x < y 3) x = y 4) real and unequal Solution: (4) real and unequal (l - m)x2 - 5 (l + m) x - 2 (l - m) = 0 D = {-5 (l + m)2... View Article

Solve the linear programming problem.Maximise z = x + 2y, subject to constraints x – y ≤ 10 , 2x + 3y ≤ 20 and x ≥ 0 , y ≥ 0.

1) z = 10 2) z = 30 3) z = 40 4) z = 50 5) None of the above Solution: (5) None of the above z = x + 2y Subject to constraints, x - y ≤ 10,... View Article

The feasible region for the following constraints L₁ ≤ 0, L₂ ≥ 0, L₃ = 0, x ≥ 0, y ≥ 0 in the diagram shown is

1) area DHF 2) area AHC 3) line segment EG 4) line segment GI 5) line segment IC Solution: (3) line segment EG The feasible region for... View Article

Maximum value of z = 3x + 4y subject to constraints x – y ≤ -1, -x + y ≤ 0 and x , y ≥ 0, is given by

1) 1 2) 4 3) 6 4) no feasible region Solution: (4) no feasible region There is no common point or no common feasible area.... View Article

The coordinate of the point at which minimum value of z = 7x – 8y subject to constraints x + y – 20 ≤ 0, y ≥ 5, x ≥ 0, y ≥ 0 is attained, is

1) (20, 0) 2) (15, 5) 3) (0, 5) 4) (0, 20) Solution: (4) (0, 20) z = 7x - 8y Subject to constraints x + y - 20 ≤ 0, y ≥ 5, x ≥ 0, y ≥ 0... View Article

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Archives

√12 – √68 + 48 √2 =

The greatest number among ∛9, ∜11 and is

√2 + √5 – √6 – 3√5 + √14 – 6 √5 =

If x = √{(2 + √3) / (2 – √3)}, then x² (x – 4)² =

If x = (1 / 2) (√7 + (1 / √7)), then (√x² – 1) / [x – √x² – 1] =

The value of {(√√3 + 1 + √√3 – 1)² (√3 – √2)} / (√√3 + 1)² – (√√3 – 1)² is

Given that, a, b ϵ {0,1,2…9} with a + b ≠ 0 and (a + [b / 10])^x = ([a / 10] [b / 100])^y = 1000. Then, (1 / x) – (1 / y) =

The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have

If l, m, n are real, l ≠ m, then the roots by the equation: (l – m) x² – 5 (l + m) x – 2 (l – m) = 0 are

Solve the linear programming problem.Maximise z = x + 2y, subject to constraints x – y ≤ 10 , 2x + 3y ≤ 20 and x ≥ 0 , y ≥ 0.

The feasible region for the following constraints L₁ ≤ 0, L₂ ≥ 0, L₃ = 0, x ≥ 0, y ≥ 0 in the diagram shown is

Maximum value of z = 3x + 4y subject to constraints x – y ≤ -1, -x + y ≤ 0 and x , y ≥ 0, is given by

The coordinate of the point at which minimum value of z = 7x – 8y subject to constraints x + y – 20 ≤ 0, y ≥ 5, x ≥ 0, y ≥ 0 is attained, is

Shaded region is represented by

The minimum value of the objective function Z = 2x + 10y subject to constraints x ≥ 0, y ≥ 0, x – y ≥ 0, x – 5y ≤ – 5 is

If given constraints are 5x + 4y ≥ 2 , x ≤ 6 and y ≤ 7, then the maximum value of the function Z = x + 2y is

The maximum value of Z is where, Z = 4x + 2y subject to constraints 4x + 2y ≥ 46 , x + 3y ≤ 24 and x, y ≥ 0, is

The maximum value of Z = 4x + 2y subject to constraints 2x + 3y ≤ 18 , x + y ≥ 10 and x , y ≥ 0 is

Which of the term is not used in a linear programming problem?

The constraints -x₁ + x₂ ≤ 1, -x₁ + 3x₂ ≤ 9 and x₁, x₂ ≥ 0 defines on