Tag: numbers to 1 million

Questions Related to numbers to 1 million

Place value of a digit decreases by _______ times as it moves place by place from left to right

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. 10

  2. $\displaystyle \frac{1}{10}$

  3. 100

  4. 1

Show answer
Correct Option: B
Explanation:

From left to right  the place value of the number decreases by 1/10.

So option B is the correct answer.

The place which comes on immediate right of the hundreds place in the place value chart is

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. thousands

  2. tens

  3. ones

  4. ten thousands

Show answer
Correct Option: B
Explanation:

A place value chart helps us to recognize large numbers. 

We read the place value chart from left to right. 

In the Indian system, we start grouping the number from right in the group of 3 and further in group of 2. 

The place that comes on the immediate right of the hundreds place is the tens place then one's place.

So option B is the correct answer.

Place of $3$ in given amount is $30,25,69,214$

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. ten crores

  2. millions

  3. $3,00,00,000$

  4. $30,00,00,000$

Show answer
Correct Option: A
Explanation:

Place of 3 in 30,25,69,214 is ten crores

The number of zeroes that come after 1 for 10 crores is

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. 6

  2. 7

  3. 8

  4. 9

Show answer
Correct Option: C
Explanation:

1 crores=10,00,000
10 crores = 10,00,00,000

Which of the following statements is INCORRECT?

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. The place value of the digit $3$ in the number $543765$ is $3000$

  2. The place value of the digit $6$ in the number $6734581$ is predecessor of $5999999$

  3. In the number $1876523$, the place value of the digit $1$ is $1000000$

  4. The place value of the digit $5$ in the number $7658321$ is successor of $49999$

Show answer
Correct Option: B
Explanation:

(a) Place value of $3$ in number $27543765$ is $3000$
(b) Place value of $6$ in number $6734591$ is $6000000$ which is predecessor of $6000001$
(c) In the number $1876523$, place value of $1$ is $1000000$
(d) Place value of $5$ in $7658321$ is $50000$ which is successor of $49999$.

Hence the option B is incorrect.

Identify the place value for the underlined digit of the number below. 

$8,52\underline 3,615$

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. Millions

  2. Thousands

  3. Hundreds

  4. Tens

Show answer
Correct Option: B
Explanation:

Mlns     hth tthous thous     hund tens ones
8            5    2        3             6       1       5

So, the place value of 3 is thousands

In a two digit number, the digit at unit place is $x$ at the digit at tens place is $5$, then the new number obtained by interchanging the digits of that number is

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. $50x+5$

  2. $10x+5$

  3. $x+50$

  4. $5x+4$

Show answer
Correct Option: B
Explanation:

The digit in units place is $x$


The digit in tens place is $5$

So the number is $50+x$

If the number is reversed,

The units digit is $5$

The tens digit is $x$

So the number is $10x+5$

If y is an implicit function of x defined by ${ x }^{ 2x }-{ 2x }^{ x }coty-1=0.$ Then, $y' (1)$ is equal to

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. $-1$

  2. $1$

  3. $\log 2$

  4. $-\log 2$

Show answer
Correct Option: A
Explanation:

${ x }^{ 2x }-{ 2x }^{ x }coty-1=0.$ ...............[1]


At $x=1$; we have


$1-\cot y-1=0$

$\implies y=\dfrac{\pi}{2}$

Differentiating w.r.t $x$, we get:

$2x^{2x}(1+\ln x)-2[x^x(-cosec^2y\dfrac{dy}{dx}+\cot yx^x(1+\ln x))]=0$

At $P(1,\dfrac{\pi}{2})$, we have

$2(1+\ln 1)-2[1(-1)\dfrac{dy}{dx}| _P+0]=0$

$\implies 2+2\dfrac{dy}{dx}| _P=0$

$\implies \dfrac{dy}{dx}| _P=-1$

Hence, $y'(1)=-1$

Place value of a digit becomes ........... times as it moves place by place from left to right

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. $10$

  2. $\dfrac {1}{10}$

  3. $100$

  4. $1$

Show answer
Correct Option: B
Explanation:

As we know the number system value increases by $10$times as we from right to left.

Crore, Ten lakhs,  Lakhs, Ten thousand, Thousand, Hundred, Ten, ones
Since the value from right to left is increasing by $10$times
So that we go from left to right it will decrease by $\dfrac{1}{10}$times.

If the digit $1$ is placed after a two digit number whose ten's digit is $t$ and unit's digit is $u$, then the new number is: 

maths numbers in indian and international systems indian system of numeration numbers to 1 million formation of large numbers

  1. $\displaystyle 10t+u+1$

  2. $\displaystyle 100t+10u+1$

  3. $\displaystyle 1000t+10u+1$

  4. $\displaystyle t+u+1$

Show answer
Correct Option: B
Explanation:

Given, ten's place digit $= t$ and one's place digit $= u$
Two digit number $= 10\times$ten's place digit+one's place digit
                             $= 10t+u = tu$

If the digit 1 is placed after a two digit number, the new number is $tu1$, 
which now becomes a three digit number. 

The hundreds place digit $= t$, ten's place digit $= u$ and one's place digit $= 1$

$\therefore$ Number $=100\times$hundred's place digit + $10\times$ten's place digit + one's place digit
                   $=100t+10u+1$

So, Option B is correct.