Quadratic Equation-1

First-year (Intermediate) Pre-Engineering mathematics examination preparation.
Pakistan All boards Pre-Engineering Mathematics MCQs Online Test

1. The cube roots of unity are

$ 1, \frac{-1 +i\sqrt{3} }{2}, \frac{1+i\sqrt{3}}{2} $

$ 1, \frac{-1 – i\sqrt{3} }{2}, \frac{1- i\sqrt{3}}{2} $

$ 1, \frac{-1 +i\sqrt{3} }{2}, \frac{-1- i\sqrt{3}}{2} $

$ 1, \frac{-1- i\sqrt{3} }{2}, \frac{1- i\sqrt{3}}{2} $

2. The roots which satisfy radical free equation but not radical equation are called

Extraneous roots

Radical roots

Original roots

Exact roots

3. The equation $ax^2 + bx + 9 =0$ will be quadratic if

$ a=0, b \ne 0 $

$ a \ne 0 $

$ a = b = 0 $

$b =$ any real number

4. The equations involving radical expressions of the variable are called

Reciprocal equations

Radical equations

Quadratic equations

Exponential equations

5. The convert $ax^{2n} + bx^n + c =0 (a\ne 0) $ into quadratic form, the correction substitution

$ y = x^n $

$ y = x^{2n} $

$ y = x ^{-n} $

$ y = \frac{1}{x} $

6. The product of all four fourth roots of 81 is

$ -81 $

$ 81 $

$ 0 $

$ 1 $

7. Product of all cube roots of $-1$ is

$ 0 $

$ -1 $

$ 1 $

None

8. The quadratic formula for solving the equation $ax^2 + bx + c =0$ is $(a\ne 0)$

$ x = – b \pm \frac{\sqrt{b^2 – 4ac} } {2a} $

$ x = – b \pm \sqrt{ \frac{b^2 – 4ac} {2a} }$

$ x = – b \pm \frac{\sqrt{b^2 + 4ac} } {2a} $

$ x = – b \pm \sqrt{ \frac{b^2 + 4ac} {2a} } $

9. Solution set of the equation $x^2 – 4x + 4 = 0$ is

$ \{2, -2 \} $

$ \{ 2\} $

$ \{ -2\} $

$ \{ 4, -4\} $

10. The sum of all four fourth roots of unity is

Unity

$ -1 $

None

11. The complex cube roots of unit are ______________ each other

Additive inverse of

Equal to each other

Conjugate of each other

None of these

12. To convert $ 4^{1+x} + 4^{1-x} =10$ into quadratic, the substitution is

$ y = 4^{1-x} $

$ y= 4^{1+x} $

$ y = 4^ x $

$ y= 4^{-x} $

13. $16\omega^4 + 16 \omega^8$

$ 0 $

$ -16 $

$ 16 $

$ -1 $

14. The sum of all four fourth roots are 16 is

$ 16 $

$ -16 $

$ 0 $

$ 1 $

15. The equation which remains unchanged if $x$ is replaced by $\frac{1}{x}$, then it is called

Exponential function

Exponential equation

Reciprocal equation

Quadratic equation

16. The equation in which variable quantity occurs in exponent is called

Exponential function

Exponential equation

Reciprocal equation

Quadratic equation

17. Sum of all cube roots of 64 is

$ 0 $

$ 1 $

$ 64 $

$ -64 $

18. The product of all four fourth roots of unity is

Unity

$ 0 $

$ -1 $

None

19. $(-1 + \sqrt{-3})^5 + (-1 – \sqrt{-3})^5$ is equal to

$ 0 $

$ 32 $

$ -32 $

$ -1 $

20. The cube roots of $-1$ are

$ -1, \frac{-1+i\sqrt{3}}{2}, \frac{1-i\sqrt{3}}{2} $

$ -1, \frac{-1-i\sqrt{3}}{2}, \frac{1+i\sqrt{3}}{2} $

$ -1, \frac{1+i\sqrt{3}}{2}, \frac{1-i\sqrt{3}}{2} $

$ -1, \frac{-1-i\sqrt{3}}{2}, \frac{-1+i\sqrt{3}}{2} $

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