A line passes through the point of intersection of 2x + y = 5 and x + 3y + 8 = 0 and parallel to the line 3x + 4y = 7 is 1) 3x + 4y + 3 = 0 2) 3x + 4y = 0 3) 4x – 3y + 3 = 0 4) 4x – 3y = 3 Solution: Given 2x + y = 5 …(i) x + 3y + 8 = 0 …(ii) By solving (i) and... View Article
The equation of a line passing through the point of intersection of the lines x + 5y + 7 = 0, 3x + 2y – 5 = 0, and perpendicular to the line 7x + 2y – 5 = 0, is given by 1) 2x – 7y – 20 = 0 2) 2x + 7y – 20 = 0 3) – 2x + 7y – 20 = 0 4) 2x + 7y + 20 = 0 Solution: x + 5y + 7 = 0 …(i) 3x + 2y - 5 = 0 …(ii) By... View Article
The equation of a straight line passing through (-3, 2) and cutting an intercept equal in magnitude but opposite in signs from the axes is given by 1) x – y + 5 = 0 2) x + y – 5 = 0 3) x – y – 5 = 0 4) x + y + 5 = 0 Solution: Let the equation of line be x/a + y/b = 1 Given it cuts an... View Article
The equation of the line parallel to the line 2x – 3y = 1 and passing through the middle point of the line segment joining the points (1,3) and (1, -7), is 1) 2x – 3y + 8 = 0 2) 2x – 3y = 8 3) 2x – 3y + 4 = 0 4) 2x – 3y = 4 Solution: Equation of given line is 2x - 3y = 1 Slope, m = â…” Middle... View Article
A line meets x-axis and y-axis at the points A and B respectively. If the middle point of AB be (x1, y1), then the equation of the line is 1) y1x + x1y = 2x1 y1 2) x1x + y1y = 2x1y1 3) y1x + x1y = x1y1 4) x1x + y1y = x1y1 Solution: Given the middle point of AB is (x1, y1). Let... View Article
The set of values of x satisfying 2 ≤ |x – 3|< 4 is 1) (- 1, 1] ∪ [5, 7) 2) - 4 ≤ x ≤ 2 3) - 1 < x < 7 or x ≥ 5 4) x < 7 or x ≥ 5 5) -∞ < x ≤ 1 or 5 ≤ x < ∞ Solution: (1) (- 1, 1] ∪... View Article
The set of all x satisfying the inequality [4x – 1] / [3x + 1] ≥ 1 is 1) (- ∞, - 1 / 3) ⋃ (1 / 4, ∞) 2) (- ∞, - 2 / 3) ⋃ (5 / 4, ∞) 3) (- ∞, - 1 / 3) ⋃ [2, ∞) 4) (- ∞, - 2 / 3) ⋃ [4, ∞) 5) (- ∞, - 1 / 3) ⋃ (1 /... View Article
The set of values of x for which the inequalities x2 – 3x – 10 < 0, 10x - x2 – 16 > 0 hold simultaneously, is 1) (- 2, 5) 2) (2, 8) 3) (- 2, 8) 4) (2, 5) Solution: (4) (2, 5) x2 - 3x - 10 < 0 ⇒ (x + 2) (x - 5) < 0 ⇒ (x - (-2)) (x - 5) < 0 ⇒... View Article
If r is a real number that |r| < 1 and if a = 5(1 - r), then 1) 0 < a < 5 2) - 5 < a < 5 3) 0 < a < 10 4) 0 ≤ a < 10 5) - 10 < a < 10 Solution: (3) 0 < a < 10 ∵ |r|... View Article
Number of integral solutions of [x + 2] / [x2 + 1] > 1 / 2 is / are 1) 0 2) 1 3) 2 4) 3 5) 4 Solution: (4) 3 [x + 2] / [x2 + 1] > 1 / 2 2x + 4 > x2 + 1 ⇒ x2 - 2x - 3 < 0 ⇒ (x - 3) (x + 1) < 0 ⇒ -... View Article
If (x – 1)(x2 – 5x + 7) < (x - 1), then x belongs to 1) (1, 2) ∪ (3, ∞) 2) (- ∞, 1) ∪ (2, 3) 3) (2, 3) 4) None of the above Solution: (2) (- ∞, 1) ∪ (2, 3) (x - 1)(x2 - 5x + 7) < (x - 1) ∴... View Article
If [2x] / [2x2 + 5x + 2] > 1 / (x + 1), then 1) - 2 > x > - 1 2) - 2 ≥ x ≥ - 1 3) - 2 < x < - 1 4) - 2 < x ≤ - 1 Solution: (3) - 2 < x < - 1 [2x] / [2x2 + 5x + 2]... View Article
The set of admissible values of x such that [2x + 3] / [2x – 9] < 0 is 1) (- ∞, - 3 / 2) ⋃ (9 / 2, É‘) 2) (- ∞, 0) ⋃ (9 / 2, É‘) 3) (- 3 / 2, 0) 4) (0, 9 / 2) 5) (- 3 / 2, 9 / 2) Solution: (5) (- 3 / 2, 9 / 2)... View Article
If a, b and c are real numbers such that a/b > 1 and a/c < 0. Then, which one of the following is correct? 1) a + b - c > 0 2) a > b 3) (a - c) (b - c) > 0 4) a + b + c > 0 5) abc > 0 Solution: (3) (a - c) (b - c) > 0 Given... View Article
If x2 + 2x + n > 10 for all real numbers x, then which of the following conditions is correct? 1) n < 11 2) n = 10 3) n = 11 4) n > 11 5) n < - 11 Solution: (4) n > 11 x2 + 2x + n > 10 > 0 … (i) If ax + bx = + c >... View Article
If a, b and c > 0, then the minimum value of a / (b + c) + b / (c + a) + c / (a + b) is 1) 1 2) 3/2 3) 2 4) 5/2 Solution: (2) 3 / 2 AM ≥ GM [a / (b + c) + b / (c + a) + c / (a + b)] / 3 ≥ ∛abc / (a + b) (b + c) (c + a) ---- (1)... View Article
If a, b, c > 0 and abc = 1, then the value of a + b + c + ab + bc + ca lies in the interval 1) (∞, - 6) 2) (- 6, 0) 3) (0, 6) 4) [6, ∞) Solution: (4) [6, ∞) Since AM ≥ GM ⇒ [a + b + c] / 3 * [3 √abc] ⇒ [a + b + c] / 3 ≥ (1)⅓ (∵ abc... View Article
For (|x – 1|) / (x + 2) – 1 < 0, x lies in the interval 1) (- ∞, - 2) ∪ (- (1 / 2), ∞) 2) (- ∞, 1) ∪ (2, 3) 3) (- ∞, - 4) 4) (-(1/2) 1) Solution: (1) (- ∞, - 2) ∪ ( - (1 / 2), ∞) (|x - 1|) / (x +... View Article
The largest interval for which x12 – x9 + x4 – x + 1 > 0 is 1) - 4 < x < 0 2) 0 < x < 1 3) - 100 < x < 100 4) - ∞ < x < ∞ Solution: (4) - ∞ < x < ∞ It is given that x12 -... View Article
If x2 + 4ax + 2 > 0 for all values of x, then a lies in the interval 1) (- 2, 4) 2) (1 , 2) 3) (-√2, √2) 4) (- 1 / √2, 1 / √2) 5) (-4, 2) Solution: (4) (- 1 / √2, 1 / √2) x2 + 4ax + 2 > 0 ∴ (4a)2 - 4x2... View Article