11). If a four-digit number of the form aabb is a perfect square, then the number is
| A). 7744 |
| B). 7755 |
| C). 7766 |
| D). 7799 |
|
12). Which of the following is largest number?
| A). \( \Large 3^{2^{2^{2}}} \) |
| B). \( \Large \{\left(3^{2^{2}}\right) \}^{2} \) |
| C). \( \Large 3^{2.22} \) |
| D). 3222 |
|
13). If \( \Large f \left(x\right)=ax+b,\ f \left(1\right)=-2,\ and\ f \left(2\right)=6,\ then\ f \left(3\right)\) is equal to:
| A). -24 |
| B). -12 |
| C). 12 |
| D). 14 |
|
14). The value of x in the equation \( \Large 2^{x-6}=256 \) is
| A). 14 |
| B). 15 |
| C). 13 |
| D). 2 |
|
15). If \( \Large 16^{x+1}=\frac{64}{4^{x}} \), then value of x is
| A). 2 |
| B). \( \Large \frac{1}{2} \) |
| C). \( \Large \frac{2}{3} \) |
| D). \( \Large \frac{1}{3} \) |
|
16). If x = 2a - 1, y = 2a - 2, z = 3 - 4a, then value of \( \Large x^{3}+y^{3}+z^{3} \) will be
| A). \( \Large 6 \left(3-13a+18a^{2}-8a^{3}\right) \) |
| B). \( \Large 6 \left(3+13a-18a^{2}+8a^{3}\right) \) |
| C). \( \Large 6 \left(3+13a+18a^{2}-8a^{3}\right) \) |
| D). \( \Large 6 \left(3-13a-18a^{2}-8a^{3}\right) \) |
|
17). Value of \( \Large \frac{ \left(a^{2}-b^{2}\right)^{3}+ \left(b^{2}-c^{2}\right)^{3}+ \left(c^{2}-a^{2}\right)^{3} }{ \left(a-b\right)^{3}+ \left(b-c\right)^{3}+ \left(c-a\right)^{3} } \)
| A). \( \Large \left(a+b\right)^{3}+ \left(b+c\right)^{3}+ \left(c+a\right)^{3} \) |
| B). \( \Large \left(a+b\right)+ \left(b+c\right)+ \left(c+a\right) \) |
| C). \( \Large \left(a+b\right)^{3}+ \left(b+c\right)^{3}+ \left(c+a\right)^{3} \) |
| D). \( \Large \left(a+b\right)+ \left(b+c\right)+ \left(c+a\right) \) |
|
18). If x + y = a and xy = b, then value of \( \Large \frac{1}{x^{3}}+\frac{1}{y^{3}} \) is
| A). \( \Large a^{3}-3ab \) |
| B). \( \Large \frac{a^{3}+3ab}{b^{3}} \) |
| C). \( \Large \frac{a^{3}-3ab}{b^{3}} \) |
| D). \( \Large a^{3}+3ab \) |
|
19). The value of \( \Large X^{a-b} \times X^{b-c} \times X^{c-a} \) is equal to
| A). 1 |
| B). 15 |
| C). 13 |
| D). 2 |
|
20). Solution of \( \Large 4^{2x}=\frac{1}{32} \) is
| A). \( \Large x = -5 \) |
| B). \( \Large x = -\frac{5}{2} \) |
| C). \( \Large x = \frac{5}{2} \) |
| D). \( \Large x = -\frac{5}{4} \) |
|
