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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. |
Which of the following is/are perfect squares ?A. `16a^(2) + 36b^(2) - 48 ab`B. `9x^(2) + 18xy + 9y^(2)`C. Both (a) and (b)D. Neither (a) nor (b) |
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Answer» Correct Answer - C Option (a) : `16a^(2) + 36 b^(2) - 48ab` `(4a)^(2) + (6b)^(2) - 2(4a)(6b) = (4a - 6b)^(2)` is a perfect square . Option (b) : `9x^(2) + 18 xy + 9y^(2) = (3x + 3y)^(2)` is a perfect square . Hence , the correct option is (c) . |
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| 2. |
If `a + (1)/(a) = 6` , then find `a^(4) + (1)/(a^(4))`. |
| Answer» Correct Answer - 1154 | |
| 3. |
Find the product of (3a + 4b) and (3a - 4b) and verify it when a = -1 and b = 1 . |
| Answer» Correct Answer - `9a^(2) - 16 b^(2)` | |
| 4. |
If `3x + (1)/(x) = 6` , then find `9x^(2) + (1)/(x^(2))`.A. 24B. 27C. 30D. 33 |
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Answer» Correct Answer - C `3x + (1)/(x) = 6` Squaring on both sides , we get `implies 9 x^(2) + (1)/(x^(2)) + 2(3x) ((1)/(x)) = 36` (`because (a + b)^(2) = a^(2) + b^(2) + 2ab)` `implies 9x^(2) + (1)/(x^(2)) + 6 = 36` `implies 9x^(2) + (1)/(x^(2)) = 30` Hence , the correct option is (c) . |
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| 5. |
Divide `(a^(4) - b^(4))` by a - b and find the quotient and remainder . |
| Answer» Correct Answer - `a^(3) + a^(2) b + ab^(2) + b^(3) , 0` | |
| 6. |
Divide `18x^(4) - 27 x^(3) + 6x` by 3x. |
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Answer» `(18x^(4) - 27x^(3) + 6x)/(3x) = (18x^(4))/(3x) - (27x^(3))/(3x) + (6x)/(3x) = 6x^(3) - 9x^(2) + 2` `therefore` The required result = `6x^(3) - 9x^(2) + 2`. |
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| 7. |
`x^(3) + xy^(2) - x^(2) y - y^(3) = "_______"`A. `(x^(2) + y^(2)) (x + y)`B. `(x^(2) + y^(2))( x- y)`C. `(x-y) (x + y)^(2)`D. `(x + y) (x- y)^(2)` |
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Answer» Correct Answer - B `x^(3) + xy^(2) - x^(2)y + y^(3)` = `x (x^(2) + y^(2)) - y(x^(2) + y^(2))` =`(x^(2) + y^(2)) (x - y)` . Hence , the correct option is (b) . |
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| 8. |
An equation which is true for all real values of its variables is called an identify . |
| Answer» Correct Answer - True | |
| 9. |
Zero of `3x - (3)/(2)` is `"________"`A. `(3)/(2)`B. `(2)/(3)`C. `(1)/(2)`D. `(1)/(2)` |
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Answer» Correct Answer - C `3x - (3)/(2) = 0` `implies 3x = (3)/(2)` `implies x = (1)/(2)` Hence , the correct option is (c) . |
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| 10. |
`x^(4) + y^(4) + 2x^(2)y^(2) = "_______"`A. `(x+ y)^(4)`B. `(x^(2) - y^(2))^(2)`C. `(x^(2) + y^(2)) (x^(2) - y^(2))`D. `(x^(2) + y^(2))^(2)` |
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Answer» Correct Answer - D `x^(4) + y^(4) + 2x^(2)y^(2) = (x^(2))^(2) + (y^(2))^(2) + 2x^(2) y^(2) = (x^(2) + y^(2))^(2)` Hence , the correct option is (d) . |
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| 11. |
5x + 10 y - 15 z = 5 (x + 2y - 3z) |
| Answer» Correct Answer - True | |
| 12. |
If `2y + (1)/(2y) = 3 ` , then `16y^(4) + (1)/(16y^(4)) = "_____"`.A. 81B. 79C. 49D. 47 |
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Answer» Correct Answer - D Given , `2y + (1)/(2y) = 3` Taking squares on both the sides , `(2y + (1)/(2y))^(2) = 3^(2)` `4y^(2) + (1)/(4y^(2)) + 2 = 9` `4y^(2) + (1)/(4y^(2)) = 7` Again taking squares on both the sides , `(4y^(2) + (1)/(4y^(2)))^(2) = 7^(2)` `16y^(4) + (1)/(16y^(4)) + 2 = 49` `16y^(2) + (1)/(16y^(4)) = 47` Hence , the correct option is (d) . |
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| 13. |
(x + 2) ( x- 5) = `x^(2) - 3x + 10` |
| Answer» Correct Answer - False | |
| 14. |
Simplify `(11x + 3y)^(2) - (11x - 3y)^(2)`. |
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Answer» Here a = 11 x and b = 3y , by using the identity `(a + b)^(2) - (a-b)^(2) = 4ab ` , we have `(11x + 3y)^(2) - (11x - 3y)^(2) = 4 (11x) (3y) = 132xy. ` |
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| 15. |
If ` x + (1)/(x) = 2 ` , then `x^(100) - (1)/(x^(100)) = "______"`. |
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Answer» Correct Answer - A Given , `x + (1)/(x) = 2`. `x^(2) + 1 = 2x implies x^(2) - 2x + 1 = 0` `implies (x - 1)^(2) = 0` `implies x - 1 = 0` `implies x = 1` `implies x^(100) - (1)/(x^(100)) = 1 - 1 = 0` Hence , the correct option is (a) . |
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| 16. |
`(a + 2b)^(2) - (a - 2b)^(2) = 8ab` |
| Answer» Correct Answer - True | |
| 17. |
Simplify : `(x^(4) - y^(4))/(x^(2) - y^(2))` |
| Answer» Correct Answer - `x^(2) - y^(2)` | |
| 18. |
Simplify : `sqrt((169p^(3)q^(3))/(225 pq^(4)))` |
| Answer» Correct Answer - `(13p)/(15q)` | |
| 19. |
If `a^(2) - b^(2) = 36` and `a + b = 4` then `(a - b)^(2) = "______"` .A. 36B. 9C. 81D. 144 |
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Answer» Correct Answer - C a + b = 4 `a^(2) - b^(2) = (a + b) (a - b) = 36` Eq. (2) `div` Eq. (1) , we get `((a -b)(a+b))/((a+b)) = (36)/(4) = 9` `a - b = 9` `implies (a - b)^(2) = 9^(2) = 81` Hence , the correct option is (c) . |
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| 20. |
If x + y = 7 and xy = 2 , then `x^*(2) - y^(2) = "_________" (x gt y)`A. `7sqrt(46)`B. `7sqrt(44)`C. `7sqrt(41)`D. `7sqrt(43)` |
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Answer» Correct Answer - C Given , x + y = 7 , and xy = 2 . `x- y = sqrt((x+y)^(2) - 4xy)` =` sqrt(7^(2) - 4(2)) = sqrt(41)` Now , `x^(2) - y^(2) = ( x + y) (x - y)` `7 sqrt(41)` Hence , the correct option is (c) . |
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| 21. |
`9.2 xx 8.8 = 72.96` |
| Answer» Correct Answer - False | |
| 22. |
Simplify `(13x - 9y) (13x + 9y)`. |
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Answer» Here , a = 13 x and b = 9y , by using the identify `(a + b) (a-b) = a^(2) - b^(2)` , we have `(13x + 9y) (13x - 9y)` . = `(13x)^(2) - (9y)^(2) = 169x^(2) - 81y^(2)` |
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| 23. |
If `496 xx 492 = x^(2) - 4 (x gt 0)` , then x = `"________"`.A. 495B. 494C. 493D. 496 |
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Answer» Correct Answer - B Given , `496 xx 492 = x^(2) - 4`. `implies (424 + 2) (494-2) = x^(2) - 2^(2)` `implies (494)^(2) - 2^(2) = x^(2) - 2^(2)` `x^(2) = (494)^(2)` `x = 494 ( x gt 0)` Hence , the correct option is (b) . |
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| 24. |
If `X = 3x^(3) + 3x^(2) + 3x + 3` and Y = `3x^(2) - 3x +3 ` , then X - Y = `"_______"`.A. `3x^(3)`B. `3x^(3) + 6x^(2) + 6x + 6`C. `6x^(2) + 6x + 6`D. `3x^(3) + 6x` |
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Answer» Correct Answer - D `{:(X = 3x^(3) + 3x^(2) + 3x + 3),(Y = " " + 3x^(2) - 3x + 3), (" " - " " + " " -):}/(X - Y = 3x^(3) + 6x)` Hence , the correct option is (d). |
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| 25. |
If x , y , and z are variables , then x + y + z is a `"________"`.A. monomialB. binomialC. trinomialD. None of these |
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Answer» Correct Answer - C x + y + z is a trinomial . Hence , the correct option is (c) . |
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| 26. |
Factorise `49x^(2) - 16y^(2)`. |
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Answer» Let a = 7x and b = 4y . Using the identify `a^(2) - b^(2) = (a-b) (a +b)` , we have `49x^(2) - 16y^(2) = (7x)^(2) - (4y)^(2) = (7x-4y) (7x + 4y)`. |
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| 27. |
The value of `998^(2)` is `"______"`A. 996064B. 996004C. 998004D. 998064 |
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Answer» Correct Answer - B `(998)^(2) = (1000 - 2)^(2)` = `(1000)^(2) - 2 (1000)(2) + 2^(2)` = `996004` Hence , the correct option is (b) . |
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| 28. |
Factorise `x^(4) + x^(2) + 1 . `A. `(x^(2) - x - 1) (x^(2) + x -1)`B. `(x^(2) + x + 1) (x^(2) - x + 1)`C. `(x^(2) - x + 1) (x^(2) + x)`D. `(x^(2) + x - 1) (x^(2) - 1)` |
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Answer» Correct Answer - B `x^(4) + x^(2) + 1` `x^(4) + 2x^(2) + 1 - x^(2)` `= (x^(2) - 1)^(2) - x^(2)` `= (x^(2) + x+1) (x^(2) - x+1)` Hence , the correct option is (b) . |
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| 29. |
The sum of the values of the expression `2x^(2) - 2x + 2 ` when x = -1 and x = 1 is `"______"`.A. 6B. 8C. 4D. 2 |
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Answer» Correct Answer - B When x = `-1 , 2x^(2) - 2x + 2` = `2(1)^(2) - 2(-1) + 2 = 6` When x = 1 , `2x^(2) - 2x + 2` `= 2(1)^(2) - 2(1) + 2 = 2` `therefore` The required sum = 6 + 2 = 8. Hence , the required option is (b) . |
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| 30. |
Which of the following is not an identify ?A. `a^(2) + 2ab + b^(2) = (a + b) (a + b)`B. `(x- y)^(2) = x^(2) - 2xy + y^(2)`C. `(p +q) (p-q) = p^(2) - q^(2)`D. x + 2 = 3 |
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Answer» Correct Answer - D x + 2 = 3 is not an identity . Hence , the correct option is (d). |
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| 31. |
`(4x^(2) + 19x^(2) + 25) div (2x^(2) - x + 5) = "_________"` .A. `2x^(2) - 9x + 5`B. `2x^(2) + 9 x + 5`C. `2x^(2) + x + 5`D. `2x^(2) - x + 5` |
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Answer» Correct Answer - C `4x^(4) + 19 x^(2) + 25 ` = `(2x^(2))^(2) + (5)^(2) + 20x^(2) - x^(2)` `= (2x^(2) + 5)^(2) - x^(2)` = `(2x^(2) + x + 5) (2x^(2) - x + 5)` `implies (4x^(4) + 19x^(2) + 25)/(2x^(2) - x+ 5) = 2x^(2) + x+ 5`. Hence , the correct option is (c). |
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| 32. |
Find the degree of `(x^(3) - x^(2))^(2).`A. 12B. 4C. 6D. 9 |
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Answer» Correct Answer - C `(x^(3) - x^(2))^(2)` = `(x^(3))^(2) - 2(x^(3)) (x^(2)) + (x^(2))^(2)` = `x^(6) - 2x^(5) + x^(4)` Degree = 6 Hence , the correct option is (c) . |
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| 33. |
(a) Factorise : `x^(2) - (z-5)x - 5z` (b) Factorise : `x^(2) + x - y + y^(2) - 2xy` |
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Answer» (a) `x^(2) - (z-5)x - 5z` = `x^(2) - xz + 5x - 5z = x(x-z) + 5(x-z) = (x-z) (x + 5)` `therefore x^(2) - (z-5)x - 5z = (x-z) (x + 5)` (b) `x^(2) + x - y + y^(2) - 2xy` `= x^(2) + y^(2) - 2xy + x - y = (x-y)^(2) + 1(x-y) = (x-y) (x+y + 1)` `therefore x^(2) + x - y + y^(2) - 2xy = (x-y) (x+y + 1)` |
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| 34. |
If `x + (1)/(x) = a` and ` x - (1)/(x) = b` , then `a^(2) - b^(2) = "_______"` .A. 4B. 3C. 2D. 1 |
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Answer» Correct Answer - A Given , `x + (1)/(x) = a` and `x - (1)/(x) = b` . Now , `a^(2) - b^(2) = (a+ b) (a-b)` `(x + (1)/(x) + x - (1)/(x) ) (x + (1)/(x) - x + (1)/(x))` `= (2x) ((2)/(x)) = 4` Hence , the correct option is (a) . |
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| 35. |
Find the area of the triangle with base (b) = 12 cm and the corresponding height (h) = 8 cm . |
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Answer» Area of a triangle = `(1)/(2) b xx h` Here , b = 12 cm and h = 8 cm `therefore` Required area = `(1)/(2) xx 12 xx 8 = 48 cm^(2)` |
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| 36. |
If a = 2 and b = -1 , then `a^(2) + b^(2) + 2ab = "________"`A. 9B. 4C. 2D. 1 |
| Answer» Correct Answer - D | |
| 37. |
If X = `2x^(2) , Y = 4x^(6) - 6x^(4)` , then find the value of `(Y)/(X)` when x = 1 .A. `-4`B. 2C. `-1`D. 3 |
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Answer» Correct Answer - C Given X = `2x^(2)`, `X = 4x^(6) - 6x^(4) ` and x = `-1` . `(Y)/(X) = (4x^(6) - 6x^(4))/(2x^(2))` `= 2x^(4) - 3x^(2)` `= 2 (-1)^(4) - 3(-1)^(2) = -1` . Hence , the correct option is (c) . |
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| 38. |
The zero of 3x + 2 is `"_____"`. |
| Answer» Correct Answer - C | |
| 39. |
The zero of 2x + 3 is `"______"`.A. `-2`B. `-3`C. `-(3)/(2)`D. `-(2)/(3)` |
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Answer» Correct Answer - C Let 2x + 3 = 0 `implies 2x = -3 implies x = -(3)/(2)` `therefore` Zero of 2x + 3 is `- (3)/(2)`. Hence , the correct option is (c) . |
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| 40. |
Factorise `y^(2) + 2xy + 2 xz - z^(2)` .A. `( x - y + z) ( y + z)`B. `(x + y + z) ( y-z ) `C. `(y-z) ( y + z + 2x)`D. `( y + z) ( y - z + 2x)` |
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Answer» Correct Answer - D `y^(2) + 2xy + 2xz - z^(2)` `= y^(2) - z^(2) + 2xy + 2xz` `= ( y + z) (y-z) + 2x (y +z)` `= (y + z) ( y - z + 2x)`. Hence , the correct option is (d) . |
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| 41. |
Find the HCF of `18p^(2)qr , 24pq^(2)r` and `27 pqr^(2)`.A. 216 pqrB. 3pqrC. `216(pqr)^(2)`D. `3(pqr)^(2)` |
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Answer» Correct Answer - B HCF `(18p^(2)qr, 24pq^(2)r and 27 pqr^(2))` HCF `[(pqr) (18 p) , (pqr) (24q) , (pqr) (27r)`] = (pqr) HCF (18p , 24 q , 27 r) = (par)HCF [3(6p) , 3(8q) , 3(9r)] = (3pqr) HCF (6p , 8q , 9r) = 3pqr (1) = 3pqr Hence , the correct option is (b) . |
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| 42. |
If ` x + (1)/(x) = 6` , then find `x^(2) + (1)/(x^(2))` .A. 34B. 36C. 32D. 38 |
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Answer» Correct Answer - A Given , `x + (1)/(x) = 6` Taking squares on both the sides , we get `(x + (1)/(x))^(2) = 6^(2)` `implies x^(2) + (1)/(x^(2)) + 2 = 36` `implies x^(2) + (1)/(x^(2)) = 34` Hence , the correct option is (a) . |
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| 43. |
If `3x - (1)/(2x) = 3` , then find the value of `(36x^(4) + 1)/(4x^(2))`.A. 9B. 12C. 15D. 6 |
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Answer» Correct Answer - B `3x - (1)/(2x) = 3 implies (3x - (1)/(2x))^(2) = 3^(2)` `implies 9x^(2) - 2.3x xx (1)/(2x) + (1)/(4x^(2)) = 9` `implies 9x^(2)- 3 + (1)/(4x^(2)) = 9 implies 9x^(2)+ (1)/(4x^(2)) = 12` `implies (36x^(4) + 1)/(4x^(2)) = 12` Hence , the correct option is (b) . |
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| 44. |
Find the zero of the polynomial `3x + 5` . |
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Answer» Equating the given polynomial 3x + 5 to zero , we have 3x + 5 = 0 . `implies 3x = - 5` and x = `- (5)/(3)` `therefore x = - (5)/(3)` is the zero of the given polynomial . |
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| 45. |
Factorise the following : `x^(2)(x + y) + y^(2) (x + y)` |
| Answer» Correct Answer - `(x + y) (x^(2) + y^(2))` | |
| 46. |
If A = (3x + 6) and B = `2 x^(2) + 3x + 4` , then the degree of AB is `"______"`A. 4B. 3C. 2D. 1 |
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Answer» Correct Answer - B Given , A = (3x + 6) and B = `2x^(2) + 3x + 4` . The degree of A is 1 and the degree of B is 2 . `therefore` Degree of AB is = 1 + 2 = 3 . Hence , the correct option is (b) . |
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| 47. |
If A = `(x - a) (x - b) (x -c) "……" ( x- z)` , then the number of terms in the expansion of (a + A) (b + A) ( c + A) …. (z + A) is `"________"`.A. 1B. 27C. 56D. 54 |
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Answer» Correct Answer - A A = (x-a) (x- b) (x-c) ..... (x-x) ......(x-z) = 0 (a + A) (b + A) (c + A)..... (z + A) = (a + 0) (b + 0) (c +0) ------------ (z + 0) = a.b.c......z `therefore` There is only one term . Hence, the correct option is (a) . |
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| 48. |
Which of the following pairs is/are like terms ? (A) x `" " (B) x^(2)` (C) `3x^(3) " " (D) 4x^(3)`A. A, BB. B , CC. C , DD. A , C |
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Answer» Correct Answer - C We know that terms which have same literal factors are called like terms . Only c and d are like terms . Hence , the correct option is (c) . |
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| 49. |
If x = -2 and `x^(2) + y^(2) + 3xy = -5` , then find y .A. `-2`B. 3C. `-4`D. 9 |
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Answer» Correct Answer - B Value of `x^(2) + y^(2) + 3xy = -5 ` and x = -2 `implies (-2)^(2) + y^(2) - 6y = -5` `implies y^(2) - 6y + 9 = 0` `implies (y - 3)^(2) = 0` `implies y - 3 = 0` `implies y = 3` Hence , the correct option is (b) . |
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| 50. |
`(a^(5) - a^(3)) div (a^(2) + a) = "__________"`A. `a^(2)(a + 1)`B. `a(a-1)`C. `a^(2) ( a-1)`D. `a^(3) (a+1)` |
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Answer» Correct Answer - C `(a^(5) - a^(3)) div (a^(2) + a)` =`a^(3) (a^(2) - 1) div a(a +1)` `= (a^(3) (a +1) (a -1))/(a(a +1)) = a^(2) (a-1)` Hence , the correct option is (c) . |
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