Iota

Q.

If ${\left(\frac{(1+i)}{(1-i)}\right)}^m=1$, then least integral value of $m$ is

Q.

If $n$ is odd positive integer and $(1+x+x^2+x^3{)}^n$=$\sum _{r=0}^{3n}{a}_r{x}^r$ then $a_0+a_1+a_2+.......a_{3n}$ is equal to

1. $4^n$

2. $1$

3. $-1$

4. $0$

Q.

For all positive integral values of n, $3^{2n}$ - 2n + 1 is

divisible by

1. 2

2. 4

3. 8

4. 12

Q. If $(x-2{)}^2-5|x-2|+6=0$, then $x\in$

1. $\{0,4\}$
2. $\{-1,5\}$
3. $\{-1,0,4,5\}$
4. $\{2,3\}$

Q. If n is a positive integer, then ${\left(\frac{1+i}{1-i}\right)}^{4n+1}$ =

1. 1
2. -1
3. i
4. -i

Q. If ${\left(\frac{1+i}{1-i}\right)}^m=1,$ then the least integral value of m is
[IIT 1982; MNR 1984; UPSEAT 2001; MP PET 2002]

1. 2
2. 4
3. 8
4. None of these

Q. If $(1-i{)}^n=2^n,thenn=$
[RPET 1990]

1. 1

2. 0

3. -1
4. None of these

Q. If x = 3 + i, then $x^3+3x^2-8x+15$ =
[UPSEAT 2003]

1. 6
2. 10
3. -18
4. -15

Q. $\sqrt{-2}\sqrt{-3}=$
[Roorkee 1978]

1. $\sqrt{6}$
2. $-\sqrt{6}$
3. $i\sqrt{6}$
4. None of these

Q.

Which of the following statements are true ?

${\left(\frac{5}{10}\right)}^3\times {\left(\frac{3}{10}\right)}^3={\left(\frac{15}{10}\right)}^3$.

1. True
2. False

Q.

Which of the following statements are true ?

${\left(\frac{3}{5}\right)}^2\times {\left(\frac{3}{5}\right)}^3={\left(\frac{3}{5}\right)}^5$.

1. True
2. False