MCQOPTIONS
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MCQOPTIONS
This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If, x4 + 4x3 + 6ax2 + 6bx + c is divisible by x3 + 3x2 + 9x + 3. Then, what is the value of a + b + c? |
| A. | 4 |
| B. | 6 |
| C. | 7 |
| D. | 10 |
| Answer» D. 10 | |
| 2. |
Let S denotes the set of all real values of the parameter ‘a’ for which every solution of the inequality log1/2 x2 ≥ log1/2 (x + 2) is the solution of the inequality 49x2 – 4a4 ≤ 0. What is the value of S? |
| A. | (-∞, -√7) ∪ (√7, ∞) |
| B. | (-∞, -√7] ∪ [√7, ∞) |
| C. | (-√7, √7) |
| D. | [-√7, √7] |
| Answer» C. (-√7, √7) | |
| 3. |
A real number ‘a’ is called a good number if the inequality (2x2 – 2x – 3) / (x2 + x + 1) ≤ a is satisfied for all real x. What is the set of all real numbers? |
| A. | (-∞, 10/3] |
| B. | (10/3, ∞) |
| C. | [10/3, ∞) |
| D. | [-10/3, ∞) |
| Answer» D. [-10/3, ∞) | |
| 4. |
For what value of θ, 1 lies between the roots of the quadratic equation 3x2 – 3sinθ x – 2cos2θ = 0? |
| A. | 2nπ + π/6 < θ < 2nπ + 5π/6 |
| B. | 2nπ + π/3 < θ < 2nπ + 5π/3 |
| C. | 2nπ + π/6 ≤ θ ≤ 2nπ + 5π/6 |
| D. | 2nπ + π/3 ≤ θ ≤ 2nπ + 5π/3 |
| Answer» B. 2nπ + π/3 < θ < 2nπ + 5π/3 | |
| 5. |
What is the set of values of p for which the roots of the equation 3x2 + 2x + p(p – 1) = 0 are of opposite sign? |
| A. | (-∞, 0) |
| B. | (0, 1) |
| C. | (1, ∞) |
| D. | (0, ∞) |
| Answer» C. (1, ∞) | |
| 6. |
Which one is the complete set of values of x satisfying log x2 (x + 1) > 0? |
| A. | (1, ∞) |
| B. | (-1, 0) – {0} |
| C. | (-1, 1) – {0} |
| D. | (1, 0) ∪ (1, ∞) |
| Answer» E. | |
| 7. |
Which is the largest negative integer which satisfies (x2 – 1)/(x – 2)(x – 3)? |
| A. | -4 |
| B. | -3 |
| C. | -1 |
| D. | -2 |
| Answer» E. | |
| 8. |
What is the number of solution(s) of the equation |√x – 2| + √x(√x – 4) + 2 = 0? |
| A. | 2 |
| B. | 4 |
| C. | No solution |
| D. | Infinitely many solutions |
| Answer» B. 4 | |
| 9. |
What will be the sum of the real roots of the equation x2 + 5|x| + 6 = 0? |
| A. | Equal to 5 |
| B. | Equal to 10 |
| C. | Equal to -5 |
| D. | Does not exist |
| Answer» E. | |
| 10. |
What will be the value of f(x) if, 2A, A + B, C are integers and f(x) = Ax2 + Bx + C = 0? |
| A. | Natural Number |
| B. | Unpredictable |
| C. | Integer |
| D. | Complex Number |
| Answer» D. Complex Number | |
| 11. |
What is the value of x if (a + 2b – 3c)x2 + (b + 2c – 3a)x + (c + 2a – 3b) = 0 where a, b, c are in A.P? |
| A. | 1/2 |
| B. | 1/4 |
| C. | 2/3 |
| D. | 3/4 |
| Answer» C. 2/3 | |
| 12. |
If x1, x2 are real roots of ax2 – x + a = 0. Then, find the set of all values of parameter ‘a’ for which |x1 – x1| < 1? |
| A. | (1 – 5a)/ a2 < 0 |
| B. | (1 – 5a)/ a2 = 0 |
| C. | (1 – 5a)/ a2 > 0 |
| D. | (1 – 5a)/ a < 0 |
| Answer» B. (1 – 5a)/ a2 = 0 | |
| 13. |
If, (a + 1)x2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have imaginary roots? |
| A. | (-∞, -1) |
| B. | (-1, ∞) |
| C. | (-1, 1) |
| D. | (-∞, ∞) |
| Answer» B. (-1, ∞) | |
| 14. |
If, (a + 1)x2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have equal roots? |
| A. | (-∞, -1) |
| B. | [-1, ∞) |
| C. | (0, 1) |
| D. | Not possible |
| Answer» E. | |
| 15. |
If, (a + 1)x2 + 2(a+1)x + (a – 2) = 0, then, for what parameter of ‘a’ the given equation have real and distinct roots? |
| A. | (-∞, ∞) |
| B. | (-1, ∞) |
| C. | [-1, ∞) |
| D. | (-1, 1) |
| Answer» C. [-1, ∞) | |