Tag: maths

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Questions Related to maths

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.

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

The locus of point of trisections of the focal chords of the parabola, ${y^2} = 4x$ :

  1. ${y^2} = x - 1$
  2. $9{y^2} = 4\left( {3x - 4} \right)$
  3. ${y^2} = 2\left( {1 - x} \right)$

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

The focal chord of y^2 = 4x passes through (1, 0). If the endpoints are (t1^2, 2t1) and (t2^2, 2t2), the condition for a focal chord is t1*t2 = -1. The point of trisection divides the chord in ratio 1:2 or 2:1. Calculating the locus of these points yields 9y^2 = 4(3x - 4).

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

Prove that $\dfrac{a^{-1}}{(a^{-1}+b^{-1})}$ is equal to $\dfrac{b}{(a+b)}$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$\cfrac{{ a }^{ -1 }}{{ a }^{ -1 }+{ b }^{ -1 }}\Leftrightarrow \cfrac{{ a }^{ -1 }}{\cfrac{1}{a}+\cfrac{1}{b}}$
$\Rightarrow$ $\cfrac{{ a }^{ -1 }}{\cfrac{b+a}{a.b}}$
$\Rightarrow$ $\cfrac{a.b}{a(b+a)}$
$\Rightarrow$ $\cfrac{b}{b+a}$
$\Rightarrow$ $\cfrac{b}{a+b}$
$\therefore$ $\cfrac{{ a }^{ -1 }}{{ a }^{ -1 }+{ b }^{ -1 }}=\cfrac{b}{a+b}$
Multiple choice maths 5-digit numbers expanded form introduction to numbers and number systems numbers in general form

The number of digits in $5^{30}$ is ,$(\log _{10}2=0.3010)$

  1. $30$
  2. $22$
  3. $21$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x = 5^30. Taking log base 10 gives log(x) = 30 * log(5) = 30 * log(10/2) = 30 * (1 - log(2)) = 30 * (1 - 0.3010) = 30 * 0.699 = 20.97. The number of digits is the floor of log(x) plus 1, which is 20 + 1 = 21 digits.

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

Numeral for ninety million ninety thousand ninety is

  1. $9090095$
  2. $90090090$
  3. $909090$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
We know that,

$1$ million $= 1000000$, therefore, $90$ million $= 90000000$

$1$ thousand $= 1000$, therefore, $90$ thousand $= 90000$

Thus, ninety million ninety thousand ninety is

$=90000000+90000+90=90090090$

Hence, numeral for ninety million ninety thousand ninety is $90090090$.