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If 9x 3y = 2187 and 23x 22y - 4xy = 0 , then what can be the value of (x + y )? |
A) 1 B) 3 C) 5 D) 7 Correct Answer : 5 Explanation : 9x * 3y = 2187 x + y = 5 or 21/4 |
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If x= √(a+b) - √(a-b) / √(a+b) + √(a-b) , then what is bx2 -2ax + b equals to? |
A) 0 B) 1 C) ab D) 2ab Correct Answer : 0 Explanation : x = √(a+b) - √(a-b) / √(a+b) + √(a-b) |
If x = t 1 / t-1 and y = t t / t-1 , t > 0, t ≠ 1 then what is the relation between x and y ? |
A) yx = x1/y B) x1/y = y1/x C) xy =yx D) xy = y1/x Correct Answer : xy =yx Explanation : Now, y = t t / t-1 = ( t 1 / t-1)t = xt …..(i) |
If x=2 + 21/3 + 22/3, then the value of x3- 6x2 + 6x is? |
A) 3 B) 2 C) 1 D) 0 Correct Answer : 2 Explanation : x = 2 + 21/3 + 22/3 …..(i) |
If √(x/y) = 24/5 + √(y/x) and x + y = 26, then what is the value of xy? |
A) 5 B) 15 C) 25 D) 30 Correct Answer : 25 Explanation : Let z=√(x/y) , then, z = 24/5 + 1/z As is given x + y = 26 |
If α and β are the roots of the equation x2 + px + q = 0, then what is α2 + β2 equal to? |
A) p2 - 2q B) q2 - 2p C) p2 + 2q D) q2 - q Correct Answer : p2 - 2q Explanation : As α αnd β αre the roots of the equqtion x2 + px + q = 0 |
If a3 = 335 + b3 and a = 5 + b, then what is the value of a + b (given that a > 0 and b > 0)? |
A) 7 B) 9 C) 16 D) 49 Correct Answer : 9 Explanation : As is given, a3 = 335 + b3 and a = 5 + b , thus As, (a - b)3 = a3 - b3 - 3ab(a - b) Hence a + b = 9 |
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The pair of linear equations kx + 3y +1 = 0 and 2x + y + 3 = 0 intersect each other, if? |
A) k = 6 B) K ≠ 6 C) k = 0 D) k ≠ 0 Correct Answer : K ≠ 6 Explanation : linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 for the euqation, |
The values of x which satisfy the equation 51 + x +51 - x = 26 are? |
A) 18 days B) 20 days C) 24 days D) 25 days Correct Answer : 20 days Explanation : 51 + x + 51 - x = 26 Let 5x = y , then |
If a + b = 5 and ab = 6, then what is the value of a3 + b3 ? |
A) 35 B) 40 C) 90 D) 125 Correct Answer : 35 Explanation : a3 + b3 = (a + b)3 - 3ab(a + b) |
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If (7 - 12x) - (3x - 7) = 14, then the value of x is ? |
A) -4 B) 0 C) 5 D) 2 Correct Answer : 0 Explanation : (7 - 12x) - (3x - 7) = 14 |
Find the roots of the quadratic equation 6x2 - 11x - 35 = 0 |
A) 5/3, - 7/2 B) - 5/3, 7/2 C) - 3/5, 2/7 D) 3/5, - 2/7 Correct Answer : - 5/3, 7/2 Explanation : 6x2 - 11x - 35 = 0 |
The distance between the points (4,-8) and (k,0) is 10. Find k? |
A) k = 6 or - 2 B) k = 10 or - 2 C) k = 10 or - 4 D) k = 6 or - 4 Correct Answer : k = 10 or - 2 Explanation : the distance between the points, c2 = (xA − xB)2 + (yA − yB)2 (K - 4)2 + (0 + 8)2 = (10)2 |
What is the equation of the line which passes through the points (2, 3) and (- 4, 1)? |
A) x - 3y = - 7 B) x + 3y = 7 C) x - 3y = 7 D) x + 3y = - 7 Correct Answer : x - 3y = - 7 Explanation : Let (2, 3) is (x1, y1) and (-4, 1) is (x2, y2) The equation of a line passing through two points (x1, y1) and (x2, y2) is given by there, m = (y2 - y1)/(x2 - x1) = (1-3)/(-4-2) = -2/-6 = 1/3 Then the equation is: |
Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3). Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are? |
A) -4, -3 B) 6, 1 C) 4, 3 D) -6, -1 Correct Answer : 6, 1 Explanation : Let quadratic equation be Since Aman made a mistake in writing down the constant term. |
The system of equations 2x + 4y = 6 and 4x + 8y = 8 is ? |
A) consistent with a unique solution B) consistent with infinitely many solutions C) inconsistent D) None of the above Correct Answer : inconsistent Explanation : We have, 2x + 4y = 6 and 4x + 8y = 8 a1 = 2, b1 = 4, c1 = -6 When there is no solution, the equations are called inconsistent. This happens, when the lines are parallel. Here, a1/a2 = b1/b2 = 1/2 ≠ c1/c2 Hence, system of equation is inconsistent. |
If 3x + 2y = 12 and xy = 6, then 9x2 + 4y2 = ______. |
A) 36 B) 144 C) 72 D) 52 Correct Answer : 72 Explanation : Given, 3x+2y=12 , xy=6 (3x+2y)2 =122 |