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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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