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1). Which of the following gives the correct factors of $$\Large 4x^{2}- \left(x^{2}-3\right)^{2}$$?
I. $$\Large \left(x-2\right) \left(x-1\right)$$
II. $$\Large \left(x-1\right) \left(x+3\right)$$
III. $$\Large \left(3-x\right) \left(x+1\right)$$
IV. $$\Large \left(2x-1\right) \left(2x+3\right)$$
Select the correct answers from the codes given below :

 A). I and III B). II and IV C). II and III D). I, II and III
2). The remainder when $$\Large 2x^{3}-3x^{2}+4x-1$$ is divided by x - 1 is
 A). -10 B). 2 C). 1 D). 10
3). If $$\Large x+\frac{1}{x}=\sqrt{3}$$, then $$\Large x^{3}+\frac{1}{x^{3}}$$ is equal to
 A). 0 B). 1 C). 3 D). $$\Large \left(x+1\right)$$
4). One of the factors of $$\Large x^{3}+6x^{2}+11x+6$$ is
 A). $$\Large \left(x-\frac{1}{2}\right)$$ B). $$\Large \left(x+\frac{1}{2}\right)$$ C). $$\Large \left(x-1\right)$$ D). $$\Large \left(x+1\right)$$
5). If polynomial $$\Large x^{3}-3x^{2}+kx+42$$ is divisible by $$\Large x+3$$, then value of k will be
 A). 4 B). 14 C). -4 D). -14

6). H.C.F. and L.C.M. of polynomials $$\Large \left(x-2\right)$$, $$\Large x^{2}-4$$ are respectively
 A). 1, $$\Large x - 2$$ B). $$\Large x - 2$$, 8 C). $$\Large x - 2$$, $$\Large x + 2$$ D). $$\Large x - 2$$, $$\Large x^{2}-4$$
7). If $$\Large a+b+c=0$$, thena $$\Large a^{3}+b^{3}+c^{3}$$ is equal to
 A). $$\Large a^{2} \left(b+c\right)+b^{2} \left(c+a\right)+c^{2} \left(a+b\right)$$ B). $$\Large 3 \left(b+c\right) \left(c+a\right) \left(a+b\right)$$ C). $$\Large 3 abc$$ D). $$\Large 6 a^{2}b^{2}c^{2}$$
8). If $$\Large a^{m^{n}}= \left(a^{m}\right)^{n}$$, then the value of m is
 A). n B). $$\Large \frac{n}{n^{n-1}}$$ C). $$\Large \frac{1}{n^{n-1}}$$ D). $$\Large n^{\frac{n-1}{n}}$$
9). Value of $$\Large \left(X^{b-c}\right)^{b+c},\ \left(X^{c-a}\right)^{c+a},\ \left(X^{a-b}\right)^{a+b}$$ is
 A). 0 B). X C). 1 D). X+1
10). If $$\Large 2^{x}=4^{y}=8^{z} and \frac{1}{2x}+\frac{1}{4y}+\frac{1}{6z}=\frac{24}{7}$$, then value of z is
 A). $$\Large \frac{7}{16}$$ B). $$\Large \frac{7}{32}$$ C). $$\Large \frac{7}{48}$$ D). $$\Large \frac{7}{46}$$
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