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Face value of digit - class-V

Description: face value of digit
Number of Questions: 19
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Tags: know the numbers numbers and place value play with numbers maths large numbers whole numbers and operations with whole numbers
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The difference between the place value and face value of 5 in 31520332 is

  1. 49998

  2. 499995

  3. 49995

  4. none


Correct Option: B
Explanation:

$\Rightarrow$  The given number is $31520332$.

$\Rightarrow$   Face value of 5 in the given number is $5$.
$\Rightarrow$   Place value of 5 in the given number is $500000.$
$\therefore$   Place value - Face value  = $500000-5=499995$
$\therefore$    Required difference is $499995$.

The difference between the value and face value of $5$ in $91,25,678$ is

  1. $4995$

  2. $0$

  3. $4095$

  4. $5000$


Correct Option: A
Explanation:

(A) Place value of 5 in 
$91,25,678=5000$
Face value of 5 in 
$91,25,678=5$
$\therefore :difference=5000-5$
$=4995$ 

Face value of 7 in 3728456

  1. 7,00,000

  2. 7000

  3. 7

  4. 70,000


Correct Option: C
Explanation:

Face value of a digit in any place will be the digit itself.

Hence, the correct answer is 7.

Difference between the face values of 5 and 9 in 165,234 and 842,928 is

  1. 44

  2. 5900

  3. 4

  4. 14


Correct Option: C
Explanation:

Face values of 5 and 9 are 5 and 9 respectively. 

Difference $= 9-5 = 4$

Difference of 88.888 and 100 is -

  1. 1111.2

  2. 111.12

  3. 11.112

  4. 1.1112


Correct Option: C
Explanation:

The difference between $88.888$ and $100$ is,

$100.000-88.888=11.112$
So the correct answer is option $C.$

Study the following number sequence and answer the given question.
5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
How many even numbers are there in the sequence which are immediately preceded by an odd number but immediately followed by an even number?

  1. 1

  2. 2

  3. 3

  4. 4


Correct Option: C
Explanation:

In the given sequence there are 3 such combinations where an even number is immediately preceded by an odd number and immediately followed by even number.


5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
Answer is Option $C$.

Nine added to thrice a whole number gives $45$. What will be number?

  1. $12$

  2. $21$

  3. $18$

  4. $20$


Correct Option: A
Explanation:

Let the required number be $n$
Then, $3n+9=45$
$\Rightarrow$  $3n=45-9$
$\Rightarrow$  $3n=36$
$\Rightarrow$  $n=\cfrac{36}{3}=12$
Hence the required number is $12$

The difference between the place value and face value of $5$ in $91,25,678$ is

  1. $4995$

  2. $0$

  3. $4095$

  4. $5000$


Correct Option: A
Explanation:

Place value of $5$ in
$91,25,678 = 5000$
Face value of $5$ in
$91,25,678 = 5$
$\displaystyle \therefore $ difference  $= 5000 - 5
= 4995$

The sum of the face values of all the digits of $749205$ is _____________ .

  1. $27$

  2. $45$

  3. $28$

  4. $74$


Correct Option: A
Explanation:

Sum of face values of all the digits of 
$749205=7+4+9+2+0+5=27$

Place value and face value are always equal at which place?

  1. Hundreds

  2. Ones

  3. Thousands

  4. Tens


Correct Option: B
Explanation:

Lets take an example : $245$- place value for Hundred's place digit is $200$ and face value is $2$.

Similarly, place value for ten's digit is $40$ and face value is $4$.
Now, place value for unit's Digit is $5$ and Face value is $?$
Thus the answer is $5$.
So, finally the answer is (b) ONES.

The digit in the units place of the number $2015!+3^{7886}$ is

  1. $1$

  2. $3$

  3. $7$

  4. $9$


Correct Option: D
Explanation:

$2015! + 3^{7886}$

$2015! \Rightarrow$ Unit digit $\Rightarrow \underline { 0 }$

$3^{7886}=3^{4n+2}$, So unit digit $\Rightarrow 9$

$\therefore 0+9 \Rightarrow \underline{9}$.

$\therefore$ Digit at unit place $\Rightarrow 9$ 

The sum of face values of 4 and 8 in any number having 4 and 8 as digits, is:

  1. 12

  2. 32

  3. 6

  4. 48

  5. None of these


Correct Option: A

The last two digits of the number $3^{400}$ are ...........

  1. $11$

  2. $91$

  3. $10$

  4. $01$


Correct Option: D

A man has 480 rupees in the denominations of one-rupee five rupee notes and ten-rupee notes The number of notes of each denomination is equal. What is the total number of notes that he has?

  1. 90

  2. 75

  3. 45

  4. 60


Correct Option: A
Explanation:

Let the numbers Of all kind is $x$

Then amount of one rupee note=$1\times x=x$
And  amount of Five rupee note=$5\times x=5x$
And  amount of Ten  rupee note=$10\times x=10x$

Then $x+5x+10x=480$
Or $16x=480$  or $x=30$

Then total numbers of note =$3\times 30=90$

Face value of '$3$' in $31005660$ is:

  1. $3$ crores

  2. $30$ lakhs

  3. $3$

  4. $0$


Correct Option: C
Explanation:

Face value of a digit is the value of the digit in the number. 

So, the face value of $3$ in $31005660$ is $3$.
Hence, the answer is $3$.

How many times does the digit $1$ appear in numbers from $1$ to $100$?

  1. $18$

  2. $19$

  3. $20$

  4. $21$


Correct Option: D
Explanation:

$\Rightarrow$  1–10 = 2 times

$\Rightarrow$  11–20 = 10 times
$\Rightarrow$  21–30 = 1 time
$\Rightarrow$  31–40 = 1 time
$\Rightarrow$  41–50 = 1 time
$\Rightarrow$  51–60 = 1 time
$\Rightarrow$  61–70 = 1 time
$\Rightarrow$  71–80 = 1 time
$\Rightarrow$  81–90 = 1 time
$\Rightarrow$  91–100 = 2 times
$\Rightarrow$  $Total = 2+10+1+1+1+1+1+1+1+2=21$
$\therefore$   The digit 1 appear in number from 1 to 100 is $21$.

What is the sum of all integers between $50$ and $350$ which have $1$ as the units digit?

  1. $5880$

  2. $5985$

  3. $6230$

  4. $6800$


Correct Option: A
Explanation:

The sequence $51+61+71...+341$ is an arithmetic progression.

$\Rightarrow$  To find the sum of n terms of an AP we use the formula.
$\Rightarrow$  Here, $n=30,\,a=51$ and $d=10$.
$\therefore$   $S _n=\dfrac{n}{2}[2a+(n-1)d]$

$\therefore$   $S _n=\dfrac{30}{2}[2\times 51+(30-1)10]$

$\therefore$   $S _n=15[102+290]$
$\therefore$   $S _n=15\times 392$
$\therefore$   $S _n=5880$

A number consists of two digits whose sum is $11$. If $27$ is added to the number, then the digits change their places. What is the number?

  1. $47$

  2. $65$

  3. $83$

  4. $92$


Correct Option: A
Explanation:

Let the ten's digit be $x$. Then, unit's digit $= \left(11 - x\right)$.
So, number $= 10x + \left(11 - x\right) = 9x + 11$.
Therefore $\left(9x + 11\right) + 27 = 10 \left(11 - x\right) + x  \Leftrightarrow  9x + 38 = 110 - 9x \Leftrightarrow   18x = 72 \Leftrightarrow   x = 4$.
Thus, ten's digit $= 4$ and unit's digit $= 7$.
Hence, required number $= 47$.

For $Z _1=\displaystyle \sqrt[6]{\frac{1-i}{1+i\sqrt{3}}}; Z _2=\sqrt[6]{\frac{1-i}{\sqrt{3}+i}}; Z _3=\sqrt[6]{\frac{1+i}{\sqrt{3}-i}}$ which of the following holds good?

  1. $\displaystyle\sum|Z _1|^2=\frac{3}{2}$

  2. $\displaystyle|Z _1|^4+|Z _2|^4=|Z _3|^{-8}$

  3. $\displaystyle\sum|Z _1|^3+|Z _2|^3=|Z _3|^{-6}$

  4. $|Z _1|^4+|Z _2|^4=|Z _3|^8$


Correct Option: B
Explanation:
$z _1 =\sqrt {\dfrac {1-i}{1+i\sqrt 3}}, z _2=\sqrt {\dfrac {1-i}{\sqrt 3 +i}}, z _3=\sqrt {\dfrac {1+i}{\sqrt 3-1}}$
$z _1 =\sqrt [6]{\dfrac {1-i}{1+\sqrt 3}}=\sqrt [6]{\dfrac {(1-i)(1-i\sqrt 3)}{1+3}}=\sqrt [6]{\dfrac {1(1-\sqrt 3)-i(1+\sqrt 3)}{4}}$
$|z _1|^2 =z _1 \bar {z} _1 =\sqrt [6]{\dfrac {(1-\sqrt 3)}{4}}\times \sqrt [6]{\dfrac {(1-\sqrt 3)+i(1+\sqrt 3)}{4}}$
$|z _1|^2 =\sqrt [6]{\dfrac {(1-\sqrt 3)^2 +(1+\sqrt 3)^2}{16}}$
$|z _1|^2 =\sqrt [6]{\dfrac {8}{16}}=\dfrac {1}{(2) 1/6}$
$z _2 =\sqrt [6]{\dfrac {1-i}{\sqrt 3+i}}=\sqrt [6]{\dfrac {(1-i) (\sqrt 3 -i)}{(3+1)}}=\sqrt [6]{\dfrac {(\sqrt 3-1)-i (1+\sqrt 3)}{4}}$
$|z _2|^2 =z _2 \bar {z} _2=\sqrt [6]{\dfrac {(\sqrt 3-1)-i (1+\sqrt 3)+i(1+\sqrt 3)}{4}}$
$|z _2|^2 =\sqrt [6]{\dfrac {(\sqrt 3-1)^2 +(1+\sqrt 3)^2}{16}}=\sqrt {\dfrac {8}{16}}=\dfrac {1}{(2) 1/6}$
$z _3 =z _3 \bar {z} _3 =\sqrt [6]{\dfrac {(\sqrt 3-1)+(1+\sqrt 3)}{4}\times \dfrac {(\sqrt 3-1)-i (1+\sqrt 3)}{4}}$
$=\sqrt [6]{\dfrac {(\sqrt 3-1)^2 +(1+\sqrt 3)^2}{16}}=\sqrt {\dfrac {8}{16}}=\dfrac {1}{(2)1/6}$
$|z _1|^4 =\dfrac {1}{2^{2/6}}\quad |z _2|^4 =\dfrac {1}{2^{2/6}}$
$|z _3|^8 =\dfrac {1}{2^{4/6}}\ \Rightarrow \ |z _3|^{-8}=2^{4/6}$
$\Rightarrow \ |z _1|^4 +|z _2|^4 =\dfrac {1}{2^{2/6}}+\dfrac {1}{2^{2/6}}=\dfrac {2}{2^{2/6}}=2^{4/6}$
$=|z _3|^{-8}$
so, $\boxed {|z _1|^4 +|z _2|^4 =|z _3|^{-8}}$ as
so, option $(B)$ is right.
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