Tag: maths

Questions Related to maths

Expenditure incurred in cultivating a square field at the rate of Rs. $170$ per hectare is Rs. $680$. What would be the cost of fencing the field at the rate of Rs. $3$ per meter?

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. Rs. $2400$

  2. Rs. $3600$

  3. Rs. $3000$

  4. Rs. $2000$

Show answer
Correct Option: A
Explanation:
Total cost of cultivation$=$Rs.$680$
Cost per hectare$=$Rs. $170$
$\therefore $Area of cultivation$=\cfrac { 680 }{ 170 } =4$ hectare$=4\times { 10 }^{ 4 }m^2$
Now, field's shape is square, therefore area $=side \times side$
$\Rightarrow 4\times { 10 }^{ 4 }={ (side) }^{ 2 }$
$\Rightarrow $ side$=\sqrt { 4\times { 10 }^{ 4 } } =200m$
Perimeter of field$=4\times 200=800m$
$\therefore $ Cost of fencing $800m=$ Rs.$\left( 3\times 800 \right) =$ Rs.$2400$

Choose the correct option:

$8$m $5$ cm = .......... cm

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. $850$

  2. $8005$

  3. $8050$

  4. $805$

Show answer
Correct Option: D
Explanation:

$1m=100 cm$

$\Rightarrow 8m=800cm$
$\therefore 8m 5cm = 800+5=805 cm$

A person bought $32$L of water for the football game and he divided the water equally into $8$ cooler. Find the quantity of water in each of the coolers by converting it into millilitres.

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. $40$ ml

  2. $400$ ml

  3. $4000$ ml

  4. $40000$ ml

Show answer
Correct Option: C
Explanation:
Quantity of water$=32ℓ=32000㎖$
Number of cooler$=8$
$\therefore $Quantity of water in each cooler$=\cfrac { 32000 }{ 8 } =4000㎖$

Rekha started her homework at $1:59$ pm point and finished her homework  $96$ minutes later. Rekha had volleyball practice at $4:00$ pm. How much time(in minutes) did Susan have between finishing her homework and the beginning of volleyball.

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. $25$ m

  2. $205$ m

  3. $30$ m

  4. $35$ m

Show answer
Correct Option: A
Explanation:
Starting time of homework$=1.59pm$
Time taken$=96$ minutes $=1$ hour $36$ minutes
i.e., Home work complete by $3:35pm$
Time between finishing homework and beginning of
Volley ball$=4:00pm-3:35pm=25$ minutes.

Capacity of measuring flask is $1$ litre.What it will be in cubic centimeter $?$

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. $1$ Cubic centimetre

  2. $10$ Cubic centimetre

  3. $100$ Cubic centimetre

  4. $1000$ Cubic centimetre

Show answer
Correct Option: D
Explanation:

$1000$ cubic centimetre
$1$ litre $=  1000 cm^3$

$\therefore$ The solution is $1000$ cubic centimetre.



State the following statement is True or False
$891$ cm can also be written as $89$ m $3$ cm

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

$891$ cm $=890$ cm $+$ $1$ cm $=89$ m $1$ cm

Thus $891$ cm cannot be written as $89$ m $3$ cm.

How many meters are there in $1.25$ kilometers?

maths measurement (length) conversion of length using decimals in units of length define weight and units of weight how much does it weigh?

  1. $10.25$ m

  2. $125$ m

  3. $1250$ m

  4. $12500$ m

Show answer
Correct Option: C
Explanation:

We know that $1km=1000m$

Suppose $1.25km = x$
$\Rightarrow x={1.25}\times 1000$
$\Rightarrow x=1250$ m
Hence, the answer is $1250$ m.

If $\sin { x } +\sin ^{ 2 }{ x } =1$, then the value of $\cos ^{ 12 }{ x } +3\cos ^{ 10 }{ x } +3\cos ^{ 8 }{ x } +\cos ^{ 6 }{ x } -2$ is equal to

taylor's and maclaurin's series applications of differential calculus maths

  1. $0$

  2. $-1$

  3. $-2$

  4. $2$

Show answer
Correct Option: B
Explanation:
$sinx+sin^2x=1$

or, $sinx=1−sin^2x=cos^2x $

or, $sin^2x=cos^4x$

$cos^{12}x+3cos^{10}x+3cos^8x+cos^6x-2$

$=cos^6x(cos^6x+3cos^4x+3cos^2x+1)-2$

$=cos^6x((cos^2x)^3+3(cos^2x)^2.1+3.cos^2x.1^2+1^3)-2$

$=(cos^2x)^3(cos^2x+1)^3-2$

$=(cos^4x+cos^2x)^3-2$

$=(sin^2x+cos^2x)^3-2$

$=1^3-2$

$=1-2=-1$

In the Taylor series expansion of $\exp \left( x \right) + \sin \left( x \right)$ about the point $x = \pi $, the coefficient of ${\left( {x = \pi } \right)^2}$ is

taylor's and maclaurin's series applications of differential calculus maths

  1. $\exp \left( \pi \right)$

  2. $0.5\exp \left( \pi \right)$

  3. $\exp \left( \pi \right) + 1$

  4. $\exp \left( \pi \right) - 1$

Show answer
Correct Option: A

If the sum of the series $\dfrac{3}{1!}+\dfrac{5}{2!}+\dfrac{7}{3!}+\dfrac{9}{4!}+...\infty=Ae+B$
Find the value of $A+B$

taylor's and maclaurin's series applications of differential calculus maths

  1. $1$

  2. $7$

  3. $0$

  4. $None\ of\ these$

Show answer
Correct Option: A
Explanation:

Its general term is $\dfrac{2n+1}{n!}$

So we have to calculate $\sum^{n=\infty} _{n=0}\dfrac{2n+1}{n!}=2\sum^{k=\infty} _{k=0}\dfrac{1}{k!}+\sum^{n=\infty} _{n=0}\dfrac{1}{n!}-2=3e-2$ (using  taylor's expansion for $e^x$)

So A+B=1