Tag: maths

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Questions Related to maths

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

If a number has a non-terminating and non-recurring decimal expansion, then it is.

  1. A rational number

  2. A natural number

  3. An irrational number

  4. An integer
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A number having non-terminating and non-recurring decimal expansion is an Irrational Number


for example 

$\pi$  is an irrational number 

$\pi = 3.1415926535897932384626433832............$


the number has non-terminating decimal expansion and non-recurring.

So option $C $ is correct

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

State the following statement is True or False

$\dfrac {15}{1600}$ has a terminating decimal expansion .

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $\displaystyle \frac {15}{1600}= \frac {15}{5^{2}2^{6}}$
As it is in the form of ${ 2 }^{ m }\times { 5 }^{ n }$ where ($n=6,m=2$).
So, the rational number $\displaystyle \frac {15}{1600}$ has a terminating decimal expansion

Multiple choice maths real number first forms rational numbers as recurring/terminating decimals decimal expansions of real numbers

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
$\dfrac {29}{343}$

  1. Terminating

  2. Non-terminating

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given, $\displaystyle \frac {29}{343}= \frac {29}{7^{3}}$
As it is not in the form of ${ 2 }^{ m }\times { 5 }^{ n }$.
So, the rational number $\displaystyle \frac {29}{343}$ has a non terminating decimal expansion

Multiple choice maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

If $z _{1}=8 +4i,\ z _{2}=6+4i$ and $arg \left(\dfrac {z-z _{1}}{z-z _{2}}\right)=\dfrac {\pi}{4}$, then $z$ satisfy 

  1. $|z-7-4i|=1$
  2. $|z-7-5i|=\sqrt {2}$
  3. $|z-4i|=8$
  4. $|z-7i|=\sqrt {18}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation arg((z-z1)/(z-z2)) = pi/4 represents an arc of a circle passing through z1 and z2. Given z1=8+4i and z2=6+4i, the midpoint is 7+4i. The geometry of the angle pi/4 implies a specific circle equation.