Tag: maths

Questions Related to maths

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. $\dfrac{gT^2}{4\pi^2}$


Correct Option: E
Explanation:

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

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

Ninety million ninety thousand ninety is _______ .

  1. $9090090$

  2. $90090090$

  3. $909090$

  4. $9090900$


Correct Option: B
Explanation:

$1$ million = $10$ lakhs $= 10,00,000$

Ninety million ninety thousand ninety $= 9,00,90,090$
Henc etghe correct answer is option B.

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


Correct Option: B
Explanation:

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

$2+(8\times 0.1)+(6\times 0.01)+(4\times 0.001)=$.

  1. $0.2864$

  2. $2.864$

  3. $28.64$

  4. $2864$


Correct Option: B
Explanation:

$2 + ( 8 × 0.1 ) + ( 6 × 0.01 ) + ( 4 × 0.001 )$

$= 2 + ( 0.8 ) + ( 0.06 ) + ( 0.004 )$

$= 2.864$

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. $80y$


Correct Option: C
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 $=y\times10+8=10y+8$

 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


Correct Option: C

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


Correct Option: B

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

  1. True

  2. False


Correct Option: A
Explanation:
$\cfrac{{ a }^{ -1 }}{{ a }^{ -1 }+{ b }^{ -1 }}\Leftrightarrow \cfrac{{ a }^{ -1 }}{\cfrac{1}{a}+\cfrac{1}{b}}$
$\Rightarrow$ $\cfrac{{ a }^{ -1 }}{\cfrac{b+a}{a.b}}$
$\Rightarrow$ $\cfrac{a.b}{a(b+a)}$
$\Rightarrow$ $\cfrac{b}{b+a}$
$\Rightarrow$ $\cfrac{b}{a+b}$
$\therefore$ $\cfrac{{ a }^{ -1 }}{{ a }^{ -1 }+{ b }^{ -1 }}=\cfrac{b}{a+b}$

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

  1. $30$

  2. $22$

  3. $21$

  4. $none\ of\ these$


Correct Option: A

Numeral for ninety million ninety thousand ninety is

  1. $9090095$

  2. $90090090$

  3. $909090$

  4. None of these


Correct Option: B
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 $90090090$.