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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. 
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If x= √(a+b)  √(ab) / √(a+b) + √(ab) , then what is bx^{2} 2ax + b equals to? 
A) 0 B) 1 C) ab D) 2ab Correct Answer : 0 Explanation : x = √(a+b)  √(ab) / √(a+b) + √(ab) 
If x = t ^{1 / t1} and y = t ^{t / t1} , t > 0, t ≠ 1 then what is the relation between x and y ? 
A) y^{x} = x^{1/y} B) x^{1/y} = y^{1/x} C) x^{y} =y^{x} D) x^{y} = y^{1/x} Correct Answer : x^{y} =y^{x} Explanation : Now, y = t ^{t / t1} = ( t ^{1 / t1})^{t }= x^{t} …..(i) 
If x=2 + 2^{1/3} + 2^{2/3}, then the value of x^{3} 6x^{2 }+ 6x is? 
A) 3 B) 2 C) 1 D) 0 Correct Answer : 2 Explanation : x = 2 + 2^{1/3} + 2^{2/3 }…..(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 x^{2} + px + q = 0, then what is α^{2} + β^{2} equal to? 
A) p^{2}  2q B) q^{2}  2p C) p^{2} + 2q D) q^{2}  q Correct Answer : p^{2}  2q Explanation : As α αnd β αre the roots of the equqtion x2 + px + q = 0 
If a^{3} = 335 + b^{3} 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, a^{3} = 335 + b^{3 }and a = 5 + b , thus As, (a  b)^{3} = a^{3}  b^{3}  3ab(a  b) Hence a + b = 9 

If 9^{x }3^{y} = 2187 and 2^{3x }2^{2y}  4^{xy }= 0 , then what can be the value of (x + y )? 
A) 1 B) 3 C) 5 D) 7 Correct Answer : 5 Explanation : 9^{x} * 3^{y} = 2187 x + y = 5 or 21/4 
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 5^{1 + x} +5^{1  x} = 26 are? 
A) 18 days B) 20 days C) 24 days D) 25 days Correct Answer : 20 days Explanation : 5^{1 + x }+ 5^{1  x }= 26 Let 5^{x} = y , then 

If a + b = 5 and ab = 6, then what is the value of a^{3} + b^{3} ? 
A) 35 B) 40 C) 90 D) 125 Correct Answer : 35 Explanation : a^{3} + b^{3} = (a + b)^{3}  3ab(a + b) 
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 6x^{2}  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, c^{2} = (x_{A} − x_{B})^{2} + (y_{A} − y_{B})^{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) = (13)/(42) = 2/6 = 1/3 Then the equation is: 
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 9x^{2} + 4y^{2} = ______. 
A) 36 B) 144 C) 72 D) 52 Correct Answer : 72 Explanation : Given, 3x+2y=12 , xy=6 (3x+2y)^{2 } =12^{2} 