Tag: introduction to numbers and number systems

Questions Related to introduction to numbers and number systems

Determine the number which are not in general form?

  1. $3 \times 10 + 2 + 2 \times 10$

  2. $2 \times 100 + 5 \times 10 + 9$

  3. $2 \times 100 + 2 - 0 \times 10$

  4. $9 \times 100 + 5 \times 10 + 2$


Correct Option: A,C
Explanation:

The general form of any three digit number is, $abc = a \times 100 + b \times 10 + c$
Here, $3 \times 10 + 2 + 2 \times 10$ and $2 \times 100 + 2 - 0 \times 10 $ are not in generalised form.


So, options A and C are correct.

Find the number for the generalised form: $3 \times 100 + 0 \times 10 + 0$

  1. $300$

  2. $303$

  3. $310$

  4. $301$


Correct Option: A
Explanation:

The general form of any three digit number is, $abc = a \times 100 + b \times 10 + c$
Here, $300 = 3 \times 100 + 0 \times 10 + 0$

So, option A is correct.

If $P = EI $ and $E = IR, P =$
1) $I^2R$
2) $\frac{I}{2}$
3) $E^2R$
4) $\dfrac{E^2}{R}$

  1. 1 only

  2. 4 only

  3. 1 and 4 only

  4. 1 and 3 only

  5. 2 and 4 only


Correct Option: C
Explanation:

Given that $P=EI$ and $E=IR$
which implies $P=(IR)I = {I}^{2}R$
Since $I=\dfrac {E}{R}$, we get $P={E}^{2}/R$
So, the correct option is $C$.

The general form of $302$ is

  1. $3 \times 100 + 1 \times 10 - 8 \times 1$

  2. $3 \times 100 + 2 \times 1$

  3. $302 \times 1$

  4. None of the above


Correct Option: B
Explanation:

$302$ can genarally expressed as
$302$= $300 \times 100 + 2 \times 1$

In the formula $T = 2\pi \sqrt{\dfrac{L}{g}}, \pi$ and $g$ are constants. If we solve the formula for $L$

  1. $\dfrac{Tg}{2\pi}$

  2. $\dfrac{Tg^2}{2\pi}$

  3. $\dfrac{T^2}{4\pi^2g}$

  4. $\dfrac{T^2}{4\pi g^2}$

  5. $\dfrac{gT^2}{4\pi^2}$


Correct Option: E
Explanation:

Given $T = 2\pi \sqrt{\dfrac{L}{g}}$
Now square it on both sides

$\Rightarrow {T}^{2} =4{\pi}^{2}\dfrac{L}{g}$ 
$\Rightarrow L=\dfrac{g{T}^{2}}{4{\pi}^{2}}$

Ninety million ninety thousand ninety is _______ .

  1. $9090090$

  2. $90090090$

  3. $909090$

  4. $9090900$


Correct Option: B
Explanation:

$1$ million = $10$ lakhs $= 10,00,000$

Ninety million ninety thousand ninety $= 9,00,90,090$
Henc etghe correct answer is option B.

If a new number is formed by interchanging the tens and thousands place digits of $8727$, then what is the relation between them?

  1. New number is greater than original number.

  2. New number is smaller than original number.

  3. New number is equal to the original number.

  4. Can't be determined


Correct Option: B
Explanation:

Original number $= 8727$
After interchanging tens and thousands of place digits, we get $2787$.
So, new member is smaller than original number.

$2+(8\times 0.1)+(6\times 0.01)+(4\times 0.001)=$.

  1. $0.2864$

  2. $2.864$

  3. $28.64$

  4. $2864$


Correct Option: B
Explanation:

$2 + ( 8 × 0.1 ) + ( 6 × 0.01 ) + ( 4 × 0.001 )$

$= 2 + ( 0.8 ) + ( 0.06 ) + ( 0.004 )$

$= 2.864$

In a two digit number, if number in units place is $8$ and number in tens place is $y$ then that number is __________.

  1. $y+8$

  2. $y+80$

  3. $10y+8$

  4. $80y$


Correct Option: C
Explanation:

Lets take an example of $23$
The digit at units place$=3$
The digit at tens place$=2$
The number$=2\times10+3=23$
In the question
The digit at units place is $8$
Thus, the number $=y\times10+8=10y+8$

 If $f:\left[ {1,10} \right] \to \left[ {1,10}
\right]$ is a non-decreasing function and $g:\left[ {1,10} \right] \to \left[
{1,10} \right]$ is a non-increasing function. Let $h\left( x \right) =
f\left( {g\left( x \right)} \right)$ with $h\left( 1 \right) = 1$, then $h\left(
2 \right)$

  1. Lies in $\left( {1,2} \right)$

  2. Is more than $2$

  3. Is equal to $1$

  4. Is not defined


Correct Option: C