InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If `sqrt((125 a^(6) b^(4) c^(2))/(5a^(4) b^(2))) = x, " then find " (x^(2))/(abc)` |
| Answer» Correct Answer - `25 abc` | |
| 2. |
Factorize `(1)/(6) a^(2) - a + (4)/(3)` |
| Answer» Correct Answer - `(1)/(6) (a -2) (a-4)` | |
| 3. |
Factorize `m^(7) + m^(4)` |
| Answer» Correct Answer - `m^(4) (m +1) (m^(2) - m +1)` | |
| 4. |
The LCM of the polynomials `(x^(2) + x - 2) (x^(2) + x -a) and (x^(2) + x -b) (x^(2) + 5x + a) " is " (x -1) (x +2) (x +3)`, then find the values of a and b |
| Answer» Correct Answer - `a =6,b =2` | |
| 5. |
Find the value of `sqrt((a+b +c)^(2) + (a +b+c)^(2) + 2(c^(2) -a^(2) -b^(2) -2ab))` |
| Answer» Correct Answer - `2c` | |
| 6. |
Find the square root of `(x^(2) + 6x + 8) (x^(2) + 5x + 6) (x^(2) + 7x + 12)` |
| Answer» Correct Answer - `(x +2) (x +3) (x +4)` | |
| 7. |
If `A = 3x^(2) + 5x -3 and B = 5x^(2) -7`, then `2A -B` is _____ |
| Answer» Correct Answer - `x^(2) + 10x + 1` | |
| 8. |
Factorize `6x^(4) - 5x^(3) - 38x^(2) -5x +6` |
| Answer» Correct Answer - `(x +1) (x -3) (2x +1) (3x -1)` | |
| 9. |
Find the remainder if `x^(5) - 3x^(3) + 5x + 1` is divided by `2x -1` |
| Answer» Correct Answer - `f((1)/(2)) = (101)/(32)` | |
| 10. |
Find the remainder when `x^(15)` is divided by `x -2` |
| Answer» Correct Answer - `f(2) = 2^(15)` | |
| 11. |
Factorize `6x^(2) + x -2` |
| Answer» Correct Answer - `(2x -1) (3x +2)` | |
| 12. |
Find the LCM and HCF of the following polynomials `36(x +2)^(2) (x-1)^(3) (x +3)^(5), 45 (x +2)^(5) (x -1)^(2) (x +3)^(5) and 63 (x -1)^(5) (x +2)^(5) (x +3)^(4)` |
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Answer» Correct Answer - HCF `= 9 (x +2)^(2) (x -1)^(2) (x +3)^(4)` LCM `= 1260 (x +2)^(5) (x -1)^(5) (x + 3)^(5)` |
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| 13. |
Find the LCM and HCF of the polynomials `15x^(2) y^(3) z, 3x^(3) yz^(2)` |
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Answer» Correct Answer - The LCM of given polynomials `= 3 xx 5 xx x^(3) xx y^(3) xx z^(3) = 15 x^(3) y^(3) z^(3)` The HCF of given polynomials `= 3x^(2) yz^(2)` |
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| 14. |
The degree of the polynomial `7x^(3) y^(10) z^(2)` is ____ |
| Answer» Correct Answer - 15 | |
| 15. |
Find the remainder when `x^(23)` is divided by `x^(2) -3x + 2` |
| Answer» Correct Answer - `(2^(23) -1) x + (2 -2^(23))` | |
| 16. |
The value of `81^(3) - 100^(3) + 19^(3)` is _____ |
| Answer» Correct Answer - `-461700` | |
| 17. |
The degree of a polyonial A is 7 and that of polynomial AB is 65, then find the degree of polynomial B |
| Answer» Correct Answer - 49 | |
| 18. |
`11 x^(2) -88x^(3) + 14x^(4)` is called a _____ polynomial |
| Answer» Correct Answer - biquadratic | |
| 19. |
Find the quotient and remainder when `x^(4) + 4x^(3) -31x^(2) - 94x + 120` is divided by `x^(2) + 3x -4` |
| Answer» Correct Answer - `x^(2) + x - 30` | |
| 20. |
The remainder obtained when `80x^(3) + 55x^(2) + 20x + 172` is divided by `x +2` is _____ |
| Answer» Correct Answer - `-288` | |
| 21. |
Divide `20x^3+87x^2+96x+48` by x+3 |
| Answer» Correct Answer - `p - 154, q -121` | |
| 22. |
The HCF of `(a -1) (a^(3) + m) and (a +1) (a^(3) -n) and (a +1) (a^(2) -n) " is " a^(2) -1`, then the value of m and n are ______ |
| Answer» Correct Answer - 1, 1 | |
| 23. |
Expand `Sigmac^(2) (a^(2) -b^(2))` |
| Answer» Correct Answer - `c^(2) (a^(2) -b^(2)) + a^(2) (b^(2) -c^(2)) + b^(2) (c^(2) -a^(2))` | |
| 24. |
The HCF of `(a^(2) +1) (a +11) and (a^(2) +1)^(2) (a +11)^(2)` is _____ |
| Answer» Correct Answer - `(a^(2) + 1) (a +11)` | |
| 25. |
The quotient of `8x^(3) - 7x^(2) + 5x + 8` when divided by 2x is ____ |
| Answer» Correct Answer - `4x^(2) - (7)/(2) x + (5)/(2)` | |
| 26. |
One of the factor of `x^(3) -x^(2) + x -1` is ____ |
| Answer» Correct Answer - `x + (1)/(x)` | |
| 27. |
Find the quadratic polynomial when divided by `x, x -1 and x -2` leaves remainders 1, 2 and 9 respectively |
| Answer» Correct Answer - `3x^(2) -2x +1` | |
| 28. |
If the each of algebraic expressions `lx^(2) + mx + n, mx^(2) + nx + l and nx^(2) + lx + m` are prefect squares, then `(l +m)/(n) =` _____A. `-4`B. 6C. `-8`D. None of these |
| Answer» Correct Answer - A | |
| 29. |
Expand `underset(a, b, c)(pi) a^(2) (b+c)` |
| Answer» Correct Answer - `a^(2) (b +c) b^(2) (c +1) c^(2) (a +b)` | |
| 30. |
The factors of `(a -b)^(3) + (b-c)^(3) + (c -a)^(3)` is ____ |
| Answer» Correct Answer - `3(a -b) (b-c) (c-a)` | |
| 31. |
Factors of `x^(6) - y^(6)` is ______ |
| Answer» Correct Answer - `(x -y) (x +y) (x^(2) + y^(2) - xy) (x^(2) + y^(2) + xy)` | |
| 32. |
Find the factors of `a^(2) (b+c) + b^(2) (c +a) + c^(2) (a +b) +2abc` |
| Answer» Correct Answer - `(a +b) , (b +c) , (c+a)` | |
| 33. |
The factors of `a^(3) + b^(3) + c^(3) - 3abc` are ____ |
| Answer» Correct Answer - `(a +b +c) (a^(2) + b^(2) + c^(2) - ab - bc -ca)` | |
| 34. |
Which of the following is to be added to make `x^(6) -6x^(4) + 4x^(3) + 8x^(2) - 10x + 3` a perfect square ?A. `(x -1)^(2)`B. `(x -2)^(2)`C. `(2x -3)^(2)`D. `(2x + 1)^(2)` |
| Answer» Correct Answer - A | |
| 35. |
Resolve into factors : `(underset(x,y,z)sum x)^(3) - underset(x,y,z)sum x^(3)`A. `(x + y) (y + z) (z + x)`B. `-(x + y) (y + z) (z +x)`C. `3(x +y) (y +z) (z +x)`D. `-3 (x + y) (y +z) (z +x)` |
| Answer» Correct Answer - C | |