Tag: maths

Questions Related to maths

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.

Place value and face value are always equal for

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

  1. $0$

  2. $1$

  3. any digit

  4. $10$

Show answer
Correct Option: A
Explanation:

Place value of a digit depends on the place of the digit in the number, while the face value is same as the digit itself. 

Hence, place value and face value are always equal for the digit $0$,
as place value of $0$ is always $0$, irrespective of its position in the number.
So, option A is correct. 

Face value of $4$ in $408,356,112$ is

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

  1. $400$ million

  2. $4$

  3. hundred million

  4. $0$

Show answer
Correct Option: B
Explanation:

Face value of a digit is the digit itself.
So, Face value of $ 4 $ in $ 408, 356, 112 $ is $ 4 $.

If the digit $1$ is placed after a two digit number whose tens digit is $'t' $and units digit is $'u',$  the new number is:

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

  1. $l0t + u + 1$

  2. $100t + 10u + 1$

  3. $t + u + 1$

  4. None of these

Show answer
Correct Option: B
Explanation:

Placing 1 after two digit number is the indication that,

shift the given digit towards left, so that $t$ is now hundred's digit and $u$ is now tens digit so the value becomes $100t+10u+1$
So $100t+10u+1$ is correct answer

Ten lakhs comes under ______ period

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

  1. crores

  2. lakhs

  3. thousands

  4. millions

Show answer
Correct Option: B
Explanation:

Ten lakhs & lakhs places are in
the lakhs period

$10$ million $=$ _______ crore

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

  1. $10$

  2. $1$

  3. $5$

  4. $100$

Show answer
Correct Option: B
Explanation:

As we know that $10$ lakh $= 1$ million.

So, $10$ million $= 10 \times 10 $ lakh which is equal to $1$ crore.
Hence, the answer is $1$.