MCQs Number System - 4 - GM Statistics

MCQs Mathematics covers the topic of the Number system for the preparation of Intermediate mathematics.

1. The correct statement of De Mover’s Theorem is $(cos \theta + i\, sin\, \theta)^n$ is equal to

$(n\, cos\, \theta + i\, n \,sin\, \theta)$

$cos\, n\, \theta + i\, sin\, n \,\theta)$

$(cos\, \theta + i\, sin\, \theta)^{n+1}$

$(cos\, n\, \theta – i\, sin\, n\, \theta)$

2. Golden rule of fraction is that for $k\ne 0 $, $\frac{a}{b} =$

$\frac{ab}{k}$

$\frac{kb}{b}$

$\frac{kb}{ka}$

$\frac{ka}{kb}$

3. If $z_1=2+3i$, $z_2=1-i$ then $|z_1z_2|=$

$\sqrt{15}$

$\sqrt{13}$

$26$

$\sqrt{26}$

4. If $|x+5i|=3$ then $x$ is equal to

None of the option given

$\pm 4i$

$\pm 4$

$\pm22i$

5. If $z=a+ib$ then $(z^2+\overline{z}^2)$ is equal to

$(a^2+b^2)^2$

$2(a^2-b^2)$

$2(a^2+b^2)$

$4iab$

6. The modulus value of a complex number $z=x+iy$ is the distance from

X-axis

Y-axis

$(x, y)$

Origin

7. Imaginary part of $(-2+3i)^2$ is equal to

$9$

$26$

$-8$

$-2$

8. If a point $A$ of a coordinate plane corresponds to the ordered pair $(a, b)$, then $a$ and $b$ are called

Ordinates of point $A$

Coordinates of point $A$

Value of point $A$

Abscissa of point $A$

9. If $z$ is a real number then

$\overline{z} = |z|$

$\overline{z}=-z$

$z\overline{z}=|z|$

$\overline{z} = z$

10. The modulus of $z$ is

$a^2+b^2$

$\sqrt{a^2-b^2}$

$\sqrt{a^2+b^2}$

$\sqrt{a^2 -(ib)^2}$

11. The set $\{1, -1\}$ possesses closure property w.r.t.

Subtraction

Multiplication

Addition

Division

12. Polar form of $(\sqrt{3} + i)$ is

$2 \left(cos\, \frac{\pi}{6} + i\, sin\, \frac{\pi}{6} \right)$

$2 \left(cos\, \frac{\pi}{6} – i\, sin\, \frac{\pi}{6} \right)$

$2 \left(cos\, \frac{\pi}{3} + i\, sin\, \frac{\pi}{3} \right)$

$2 \left( cos\, \frac{\pi}{3} – i\, sin\, \frac{\pi}{3} \right)$

13. Real part of $(x+iy)^n$ is

$sin\, n\, \theta$

$cos\, n\, \theta$

$r^n\, sin\, n\, \theta$

$r^n \,cos\, n \,\theta$

14. The geometrical plane on which coordinate system has been specified is called

Argand diagram

Real line

Coordinate plane or real plane

Cartesian plane

15. If $z=3-5i$ then $|z|^2$ is equal to

None of the option given

$16$

$\sqrt{34}$

$34$

16. If $z=x+iy$ then $|z|=?

$\sqrt{x^2+y^2}$

$x-iy$

$\sqrt{x^2-y^2}$

$x^2+y^2$

17. If $R$ is the set of real number, then product $R\times R$ is called

Real line

Cartesian plane

Argand diagram

Ordered pair

18. If point $A$ of the coordinate plane corresponds to the ordered pair $(a,b)$ then

$a$ is abscissa of point $A$

$b$ is ordinate of point $A$

All of the given optoins

$a$ and $b$ are coordinates of point $A$

19. Polar form of $1+i\sqrt{3}$ is

$2(cos\, 60^o + i\, sin\, 60^o)$

$2(cos\, 60^o – i\,sin\, 60^o)$

$2(cos\, 30^o + i\, sin\,30^o)$

$cos\, 60^o + i\, sin\, 60^o$

20. 0.1428571428571…. is

Natural number

Irrational number

Decimal number

Rational number

MCQs Number System – 4

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