11). Which one of the following is a polynomial?
| A). \( \Large x^{3}+\sqrt{3x^{2}}+4\sqrt{x} \) |
| B). \( \Large x^{6}+2\sqrt{x^{2}}+x^{-1} \) |
| C). \( \Large x^{5}+x^{4}+x^{-1}+x^{-5} \) |
| D). \( \Large x^{3}+\sqrt{5x^{2}}+x+\sqrt{3} \) |
|
12). If \( \Large X^{y}=Y^{z} \), then \( \Large \left(\frac{Y}{X}\right)^{\frac{x}{y}} \) equals
| A). \( \Large X^{\frac{x}{y}} \) |
| B). \( \Large X^{ \left(\frac{x}{y}\right)-1 } \) |
| C). \( \Large X^{\frac{y}{x}} \) |
| D). \( \Large X^{1-\frac{x}{y}} \) |
|
13). If \( \Large x+\frac{1}{x}=3 \), then value of \( \Large x^{3}+\frac{1}{x^{3}} \) is
| A). 18 |
| B). 24 |
| C). 27 |
| D). 36 |
|
14). If \( \Large x^{5}-9x^{2}+12x-14 \) is divided by \( \Large x-3 \), then the remainder is
| A). 1 |
| B). 2 |
| C). 56 |
| D). 184 |
|
15). If polynomial \( \Large f \left(x\right) \) is such that \( \Large f \left(-2\right)=0 \), then which of the following is always a factor of \( \Large f \left(x\right) \)?
| A). 2x |
| B). 2-x |
| C). x+2 |
| D). x-2 |
|
16). If \( \Large x^{2}+ax+b \) leaves the same remainder 5 when divided by x-1 or x+1, then values of 'a' and 'b' are respectively.
| A). 0 and 4 |
| B). 3 and 0 |
| C). 0 and 3 |
| D). 4 and 0 |
|
17). Product of zeroes of the polynomial \( \Large x^{3}-6x^{2}+11x-6 \) is
| A). 11 |
| B). -6 |
| C). 1 |
| D). 6 |
|
18). H.C.F. of \( \Large x^{5}+2x^{4}+x^{3}\ and\ x^{7}-x^{5} \) is
| A). x |
| B). \( \Large x \left(x+1\right) \) |
| C). \( \Large x^{3} \) |
| D). \( \Large x^{3} \left(x+1\right) \) |
|
19). H.C.F. of two polynomials is a - b, for the same polynomials, L.C.M. is \( \Large \left(a^{2}-b^{2}\right) \left(a^{2}+ab+b^{2}\right) \). If one of the polynomials is \( \Large a^{3}-b^{3} \), then other will be
| A). \( \Large a^{2}-b^{2} \) |
| B). \( \Large a^{2}+ab+b^{2} \) |
| C). \( \Large a^{2}+b^{2} \) |
| D). \( \Large \left(a+b\right) \) |
|
20). If \( \Large f \left(x\right) = 2x^{2}+\sqrt{2}x+8 \), then \( \Large f \left(x\right) \) is a polynomial over
| A). real numbers |
| B). irrational numbers |
| C). rational number |
| D). positive rationals |
|
