Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

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

$8,52\underline 3,615$

  1. Millions

  2. Thousands

  3. Hundreds

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

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

So, the place value of 3 is thousands

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

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

  1. $50x+5$
  2. $10x+5$
  3. $x+50$
  4. $5x+4$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $10x+5$

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

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

  1. $-1$
  2. $1$
  3. $\log 2$
  4. $-\log 2$
Reveal answer Fill a bubble to check yourself
A Correct answer
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, $y'(1)=-1$

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

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

  1. $10$
  2. $\dfrac {1}{10}$
  3. $100$
  4. $1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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: 

  1. $\displaystyle 10t+u+1$
  2. $\displaystyle 100t+10u+1$
  3. $\displaystyle 1000t+10u+1$
  4. $\displaystyle t+u+1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

Place value and face value are always equal for

  1. $0$
  2. $1$

  3. any digit
  4. $10$
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

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:

  1. $l0t + u + 1$
  2. $100t + 10u + 1$
  3. $t + u + 1$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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