QUADRATIC EQUATIONS AND INEQUATIONS (CDS)

Total Questions: 67

41. Solve the following equation [2016 (I) Morning Shift ]

The linear inequations, for which the shaded area in the figure given above is the solution set, are

Correct Answer: (a) 2x + 6y ≤ 21, 5x - 2y ≤ 10
Solution:Consider the line, 2x + 6y = 21 ... (i)

42. If the sum of the roots of ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then which one of the following relations is correct? [2016 (I) Morning Shift ]

Correct Answer: (a) ab² + bc² = 2a²c
Solution:Let α β and be the roots of equation ax² + bx + c = 0.

43. Consider the following statements in respect of two different non-zero integers p and q. [2016 (I) Morning Shift ]

1. For (p + q) to be less than (p - q), q must be negative.
2. For (p + q) to be greater than (p - q), both p and q must be positive.

Which of the above statement(s) is/are correct?

Correct Answer: (a) Only 1
Solution:Given, p and q are non-zero integers.

44. Solve the following equation [2016 (I) Morning Shift ]

Correct Answer: (a) 0
Solution:Since, the roots of equation


45. Solve the following equation [2016 (I) Morning Shift ]

Correct Answer: (a) − 15
Solution:


46. Solve the following equation [2016 (I) Morning Shift ]

Correct Answer: (c) 1
Solution:


47. If the equations x² - px + q = 0 and x² + qx - p = 0 have a common root, then which one of the following is correct? [2016 (I) Morning Shift ]

Correct Answer: (d) p - q - 1 = 0
Solution:Given, x² - px + q = 0  ...(i)

48. The sum and difference of two expressions are 5x² - x - 4 and x² + 9x - 10, respectively. The HCF of the two expressions will be [2016 (I) Morning Shift ]

Correct Answer: (b) (x - 1)
Solution:

49. Solve the following equation [2015 (II) Evening Shift]

Correct Answer: (c) 55
Solution:


50. Consider the following in respect of the equation [2015 (II) Evening Shift]

1. y = l if x > 1
2. y = - 1 if x < 1
3. y exists for all values of x

Which of the above statement(s) is/are correct?

Correct Answer: (c) 1 and 2
Solution: