MCQOPTIONS
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MCQOPTIONS
This section includes 30 Mcqs, each offering curated multiple-choice questions to sharpen your ALGEBRA knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If x = 2 then the value of x3 + 27x2 + 243x + 631 is: |
| A. | 1211 |
| B. | 1231 |
| C. | 1233 |
| D. | 1321 |
| Answer» D. 1321 | |
| 2. |
If ab + bc + ca = 0, then the value of {1 / (a2 – bc)} +{1 / (b2 – ac)} +{1 / (c2 – ab)} is |
| A. | 2 |
| B. | –1 |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 3. |
If x + (1 / x) = 5, then {2x / (3x2 – 5x + 3)} is equal to |
| A. | 5 |
| B. | 1 / 5 |
| C. | 3 |
| D. | 1 / 3 |
| Answer» C. 3 | |
| 4. |
If x = 332, y = 333, z = 335 then the value of x3+ y3+ z3– 3xyz = ? |
| A. | 1000 |
| B. | 9000 |
| C. | 7000 |
| D. | 65000 |
| Answer» D. 65000 | |
| 5. |
When 2x + (2 / x) = 3, then value of x3 + ( 1 / x3) + 2 is |
| A. | 2 / 7 |
| B. | 7 / 8 |
| C. | 7 / 2 |
| D. | 8 / 7 |
| Answer» C. 7 / 2 | |
| 6. |
If x = 6 + (1 / x), then the value of x4 + (1 / x4) is |
| A. | 1448 |
| B. | 1442 |
| C. | 1444 |
| D. | 1446 |
| Answer» C. 1444 | |
| 7. |
If x2 – 3x + 1 = 0, then the value of (x6 + x4 + x2 +1) / x3 will be |
| A. | 18 |
| B. | 15 |
| C. | 21 |
| D. | 30 |
| Answer» D. 30 | |
| 8. |
If x3 + (3 / x) = 4(a3 + b3) and 3x + (1 / x3) = 4(a3 – b3), then a2 – b2 is equal to: |
| A. | 4 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 9. |
If x + (1 / x) = 5, then the value of x6 + (1 / x6) is |
| A. | 12098 |
| B. | 12048 |
| C. | 14062 |
| D. | 12092 |
| Answer» B. 12048 | |
| 10. |
If x + y = 15, then (x – 10)3+ (y – 5)3is |
| A. | 25 |
| B. | 125 |
| C. | 625 |
| D. | 0 |
| Answer» E. | |
| 11. |
If a + b + c = 0, then the value of (a + b – c)2+ (b + c – a)2+ (c + a – b)2is |
| A. | 0 |
| B. | 8 abc |
| C. | 4(a2+ b2+ c2) |
| D. | 4(ab + bc + ca) |
| Answer» D. 4(ab + bc + ca) | |
| 12. |
If x = p + (1 / p) and y = p – (1 / p) then the value of x4 – 2x2y2 + y4 is |
| A. | 24 |
| B. | 4 |
| C. | 16 |
| D. | 8 |
| Answer» D. 8 | |
| 13. |
If p3+ 3p2+ 3p = 7, then the value of p2+ 2p is |
| A. | 4 |
| B. | 3 |
| C. | 5 |
| D. | 6 |
| Answer» C. 5 | |
| 14. |
If x = 2015, y = 2014 and z = 2013, then value ofx2+ y2+ z2– xy – yz – zx is |
| A. | 3 |
| B. | 4 |
| C. | 6 |
| D. | 2 |
| Answer» B. 4 | |
| 15. |
If x + (1 / x) = 3, then the value of (3x2 – 4x + 3) / (x2 – x + 1) is |
| A. | 4 / 3 |
| B. | 3 / 2 |
| C. | 5 / 2 |
| D. | 5 / 3 |
| Answer» D. 5 / 3 | |
| 16. |
If x + (1 / 2x) = 2, find the value of 8x3 + (1 / x3). |
| A. | 48 |
| B. | 88 |
| C. | 40 |
| D. | 44 |
| Answer» D. 44 | |
| 17. |
The expression x4– 2x2+ k will be a perfect square when the value of k is |
| A. | 2 |
| B. | 1 |
| C. | –1 |
| D. | –2 |
| Answer» C. –1 | |
| 18. |
If x + (1 / x) = 99, find the value of {100x / (2x2 + 102x + 2)} |
| A. | 1 / 6 |
| B. | 1 / 2 |
| C. | 1 / 3 |
| D. | 1 / 4 |
| Answer» D. 1 / 4 | |
| 19. |
If x = 1 / (√2 + 1) then (x + 1) equals to: |
| A. | 2 |
| B. | (√2 + 1) |
| C. | (√2 – 1) |
| D. | √2 |
| Answer» E. | |
| 20. |
If x = 2 then the value of x3+ 27x2+ 243x + 631 is: |
| A. | 1211 |
| B. | 1231 |
| C. | 1233 |
| D. | 1321 |
| Answer» D. 1321 | |
| 21. |
If {x2 + (1 / x2)} = 17 / 4, then what is {x3 – (1 / x3)} equal to? |
| A. | 75 / 16 |
| B. | 63 / 8 |
| C. | 95 / 8 |
| D. | None of these |
| Answer» C. 95 / 8 | |
| 22. |
Consider the following statements I. x + 3 is the factor of x3+ 2x2+ 3x + 8. II. x – 2 is the factor of x3+ 2x2+ 3x + 8. Which of the statements given above is/are correct? |
| A. | Only I |
| B. | Only II |
| C. | Both I and II |
| D. | Neither I nor II |
| Answer» E. | |
| 23. |
What is {(x2 + y2) (x – y) – (x – y)3} / (x2y – xy2) equal to? |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | –2 |
| Answer» C. 4 | |
| 24. |
If the expression x3+ 3x2+ 4x + k has a factor x + 5, then what is the value of k? |
| A. | –70 |
| B. | 70 |
| C. | 48 |
| D. | –48 |
| Answer» C. 48 | |
| 25. |
The quantity which must be added to (1 – x) (1 + x2)to obtain x3is: |
| A. | 2x3+ 3x2+ x + 1 |
| B. | 2x3+ x2+ x – 1 |
| C. | 2x3– x2+ x – 1 |
| D. | –x2+ x – 1 |
| Answer» D. –x2+ x – 1 | |
| 26. |
If x - (1 / x) = √5 than √x (√x – 1) = ? |
| A. | √5 / 2 |
| B. | 10√5 |
| C. | 1 |
| D. | √5 / 4 |
| Answer» D. √5 / 4 | |
| 27. |
If {(a2 + b2 + c2) / ( a2 – b2 – c2)} + {(b2 + c2 + a2) / b2 – c2–a2)} + {(c2 + a2 +b2) / (c2 – a2 –b2)} = ? |
| A. | 0 |
| B. | 1 |
| C. | 3 |
| D. | – 1 |
| Answer» B. 1 | |
| 28. |
If (a28+ 1) / a14= 23 than (a42+ 1) / a21= ? |
| A. | 110 |
| B. | 23 |
| C. | 52 |
| D. | 69 |
| Answer» B. 23 | |
| 29. |
If x = √3 + √4 + √5 than x4 – 8x3 + 8x2 + 32x = ? |
| A. | 36 |
| B. | 29 |
| C. | 44 |
| D. | 52 |
| Answer» D. 52 | |
| 30. |
{(x2– y2)2/ (1 – x2)(y2– 1)} + {(1–x2)2/ (x2–y2) (y2– 1)} + {(y2– 1)2/ (x2– y2) (y2– 1) = ? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| Answer» E. | |