Mashaal Masha
Choose the correct options for the following questions.
If $\alpha$ and $\beta$ are the roots of the equation $ax^{2}+bx+c=0$, then the equation with roots $\frac{1}{ \alpha}$ and $\frac{1}{ \beta}$ is
Difficulty: Easy
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A:

$\frac{x^{2}}{ a}+\frac{x}{ b}+\frac{1}{ c}=0$

B:

$ay^{2}+by+c=0$

C:

$cy^{2}+by+a=0$

D:

$ax^{2}+bx+c=0$

If $n$ is any real number and $\omega^{n} =\omega^{2}$ where $\omega$ is cube root of unity then which of the following can be a possible value of n?
Difficulty: Easy
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A:

$4$

B:

$-2$

C:

$6$

D:

$-1$

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The equation which does not change by replacing $x$ with $\frac{1}{x}$ is known as
Difficulty: Easy
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A:

Linear

B:

Proportional

C:

Quadratic

D:

None of these

$\omega^{-23} + \omega^{-28}$
Difficulty: Easy
A:

1

B:

$2\omega$

C:

0

D:

$\omega^{2}$

Product of cube roots of unity is
Difficulty: Easy
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A:

0

B:

1

C:

$-1$

D:

$\omega$

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If $x^{4}-3x^{2}-4=0$ then its roots are
Difficulty: Easy
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A:

$2,-2,i$ and $-i$

B:

$1,-1,i$ and $-i$

C:

$i$

D:

None of these

Cube roots of unity are
Difficulty: Easy
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A:

$1,\omega,\omega^{2}$

B:

$-1,1,\omega^{2}$

C:

$1,-1,\omega$

D:

None of these

Which of the following are the roots of the equation $x^{2}-3x-4=0$
Difficulty: Easy
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A:

$1,4$

B:

$3,4$

C:

$-1,4$

D:

$-3,4$

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What will be the value of $a$ in $x^{4}+x^{3}+ax+1$ if 1 is the root of the expression?
Difficulty: Easy
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A:

0

B:

1

C:

$-2$

D:

$-3$

The sum of all the fourth roots of unity is
Difficulty: Easy
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A:

0

B:

1

C:

$-1$

D:

$i$

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