Tag: numbers in general form

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Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

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. $9 \times 100 + 5 \times 10 + 2$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
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.

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

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. $\dfrac{gT^2}{4\pi^2}$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

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

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

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

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
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

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. $80y$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $=y\times10+8=10y+8$

Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

 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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since f is non-decreasing and g is non-increasing, h(x) = f(g(x)) is a non-increasing function. Given h(1) = 1 and the range is [1, 10], for a non-increasing function, h(2) must be less than or equal to h(1). Since the range starts at 1, h(2) must be 1.