31). If polynomial \( \Large x^{3}+x^{5}+x^{7}+x^{11}+x^{13} \) is divided by \( \Large x^{2}+1 \), then the remainder will be
| A). \( \Large x-1 \) |
| B). \( \Large x+1 \) |
| C). -x |
| D). x |
|
32). If \( \Large x^{3}+x^{2}+x+a \) is divisible by \( \Large x-1 \), then value of a is
| A). 3 |
| B). 1 |
| C). -1 |
| D). -3 |
|
33). L.C.M. of \( \Large a \left(a+b\right),\ a^{2} \left(a^{2}-b^{2}\right)\ and\ ab^{2} \left(a+b\right)^{2} \) is
| A). \( \Large ab \left(a-b\right) \left(a+b\right) ^{2} \) |
| B). \( \Large a^{2}b^{2} \left(a+b\right) \left(a-b\right)^{2} \) |
| C). \( \Large a^{2}b^{2} \left(a-b\right) \left(a+b\right)^{2} \) |
| D). \( \Large ab \left(a-b\right) \left(a-b\right)^{2} \) |
|
34). L.C.M. of \( \Large x^{3}-1\ and\ x^{4}+x^{2}+1 \) will be
| A). \( \Large \left(x-1\right) \left(x^{2}+x+1\right) \left(x^{2}-x+1\right) \) |
| B). \( \Large \left(x-1\right) \left(x^{2}+x+1\right) \left(x^{2}-x-1\right) \) |
| C). \( \Large \left(x-1\right) \left(x^{2}+x-1\right) \left(x^{2}-x+1\right) \) |
| D). \( \Large \left(x+1\right) \left(x^{2}+x+1\right) \left(x^{2}-x+1\right) \) |
|
35). If \( \Large a+b+c=11\ and\ ab+bc+ca=20 \) then value of the expression \( \Large a^{3}+b^{3}+c^{3}-3abc \) will be
| A). 121 |
| B). 341 |
| C). 671 |
| D). 781 |
|
36). If \( \Large x+\frac{1}{x}=2 \), then value of \( \Large x^{3}+\frac{1}{x^{3}} \) is
|
37). Which one of the following statements is NOT correct?
| A). \( \Large x^{2}+x+\frac{1}{4} \) is a perfect square. |
| B). \( \Large x^{2}+2x+3 \) cannot be factored |
| C). \( \Large x^{2}+y^{2} \) is a factor of \( \Large \left(x-y\right)^{2} \left(x^{3}+y^{3}\right) \) |
| D). \( \Large p \left(x\right)=x^{2}+x+1 \), then \( \Large p \left(\sqrt{2}\right)=3+\sqrt{2} \). |
|
38). If \( \Large x^{2}+ax+b \) leaves the same remainder when divided either by \( \Large x-1\ or\ x+1 \), then values of a and b respectively, are
| A). 4 and 0 |
| B). 0 and 3 |
| C). 3 and 0 |
| D). 0 and -1 |
|
39). If cost of 3 apples and 5 mangoes is Rs.18 and that of 5 apples and 3 mangoes is Rs.14, then cost of 5 apples is equal to
| A). Rs.5 |
| B). Rs.4 |
| C). Rs.3 |
| D). Rs.2 |
|
40). If \( \Large f \left(x\right)=mx+n\ and\ f \left(1\right)=-1\ and\ f \left(2\right)=2 \) then values of m and n, respectively are
| A). 3 and -4 |
| B). 3 and 4 |
| C). -3 and 4 |
| D). -3 and -4 |
|
