Tag: maths

Questions Related to maths

$n$  is a whole number which when divided by  $4$  gives  $3 $ as remainder. What will be the remainder when  $2n$  is divided by $4$ ?

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. $7$

  2. $5$

  3. $4$

  4. $2$

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Correct Option: D
Explanation:

Let $n = 4q + 3$. Then $2n = 8q + 6$   $= 4(2q + 1 ) + 2$.

Thus, when 2n is divided by 4, the remainder is 2.

Sum of digits of the smallest number by which $1440$ should be multiplied so that it becomes a perfect cube is

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. $4$

  2. $6$

  3. $7$

  4. $8$

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Correct Option: B
Explanation:

$\because  1440 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5$
The pairs of $2$ and $3$ and $5$ are incomplete to make it perfect cube.
$\therefore$ Smallest  number  to  be  multiplied  $=  2 \times 3 \times 5 \times 5 = 150$

$\therefore$  The  sum  of  its  digits  $= 1+5+0 = 6.$

Say true or false:
A positive integer is of the form $3q + 1,$ $q$  being a natural number, then you write its square in any form other than  $3m + 1$, i.e.,$ 3m $ or $3m + 2$  for some integer $m$.

maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

  1. True

  2. False

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Correct Option: B
Explanation:

Let the positive integer $n$ is of the form $3q, 3q+1,$ and $ 3q+2$
If $n=3q$
Squaring both sides, we get,
    $=>{ n }^{ 2 }=9{ q }^{ 2 }$
    $=>{ n }^{ 2 }=3\left( { 3q }^{ 2 } \right) $
    $=>{ n }^{ 2 }=3m$, where $m=3{ q }^{ 2 }$
Now, if $n=3q+1$
    $=>{ n }^{ 2 }={ \left( 3q+1 \right)  }^{ 2 }$
    $=>{ n }^{ 2 }=9{ q }^{ 2 }+6q+1$
    $=>{ n }^{ 2 }={ 3q\left( 3q+2 \right)  }+1$
    $=>{ n }^{ 2 }=3m+1 ,$ where $  m=q\left( 3q+2 \right) $
Now, if $n=3q+2$
    $=>{ n }^{ 2 }={ \left( 3q+2 \right)  }^{ 2 }$
    $=>{ n }^{ 2 }=9{ q }^{ 2 }+12q+4$
    $=>{ n }^{ 2 }={ 3q\left( 3q+4 \right)  }+4$
    $=>{ n }^{ 2 }={ 3q\left( 3q+4 \right)  }+3+1$
    $=>{ n }^{ 2 }=3m+1$ where $m=\left( 3{ q }^{ 2 }+4q+1 \right) $
Hence, ${ n }^{ 2 }$ integer is of the form $3m$ and $3m+1$ not $3m+2$

Investment in funds like ELSS are admissible for deduction under section $80\text{C}$ of income tax.

investement and financial planning banking compound interest comparing quantity maths

  1. True

  2. False

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Correct Option: A
Explanation:

Investments in Equity Linked Saving Schemes or ELSS qualify for tax deduction under Section $80C$ of the Income Tax Act. The maximum tax deduction allowed under Section $80C$ is Rs 1.5 lakh under Section $80C$.

You invest Rs. $3,000$ in a two year investment that pays you $12\%$ p.a. Calculate the future value of the investment.

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. $3,367.20$

  2. Rs. $3,673.20$

  3. Rs. $3,763.20$

  4. Rs. $3,736.20$

Show answer
Correct Option: C
Explanation:

$F=C.F. (1+i)^n$
Where, $F=$ Future value
$C.F. =$ Cash flow $=$Rs. $3,000$
$i=$ rate of interest $=0.12$
$n=$ time period $=2$
$F=$Rs. $3,000(1+0.12)^2$
$=$Rs. $3,000\times 1.2544$
$=$Rs. $3,763.20$

Which statement is wrong regarding Systematic Investment Plan:

investement and financial planning banking compound interest comparing quantity maths

  1. Advantage of long terms and short-term gains

  2. It has huge risks but high returns

  3. Redemption of units can be done

  4. Safe and transparent mode of investment

Show answer
Correct Option: B
Explanation:

Systematic Investment Plan (SIP) is an investment vehicle offered by mutual funds to investors, allowing them to invest small amounts periodically instead of lump sums. It is good for investors who don't have much financial market's understanding. It involves lesser risks and low returns because investment is done in small amounts over a period of time.

A man borrows $Rs. 6000$ at $5\% $ $C.I.$ per annum$.$ if the repays $Rs.1200$ at the end of the each year$,$ find the amount of the loan outstanding at the beginning of the third year$.$ 

investement and financial planning banking compound interest comparing quantity maths

  1. Rs 4155.0

  2. Rs 5555.5

  3. Rs 5452.0

  4. Rs 4452.5

  5. None of these

Show answer
Correct Option: A
Explanation:
Given Principle amount $= Rs . 6000$
And$,$
Rate of interest $= r = 5\% $ compounded annually

So$,$
Interest after $1 year = 6000 × \dfrac{5}{100} × 1 = 60× 5 = Rs . 300$
Total money owed after $1 year = 6000 + 300 = 6300$

And$,$
$Rs. 1200$ paid $,$ So
Total money starting of second year $= 6300 - 1200 = Rs.5100$

And$,$
Interest after $2 year = 5100 × 5 × 1100 = 51× 5 = Rs . 255$
money owned after $2 year = 5100 + 255 = 5355$

And$,$
$Rs. 1200$ paid $,$ So
Total money outstanding starting of Third year $= 5355 - 1200$ $= Rs.4155$

Hence,
option $(A)$ is correct answer.

A man borrowed Rs.4000 at 10% per annum compound interest.At the end of each year he has repaid Rs.1000.The amount of money he still incurs after the third year is -------- .

investement and financial planning banking compound interest comparing quantity maths

  1. Rs.2740

  2. Rs.2104

  3. Rs.2014

  4. Rs.3400

Show answer
Correct Option: C

Mutual Fund is a professionally managed investment scheme, run by an AMC i.e. Asset Management Company and they invest their own money in different schemes.

investement and financial planning banking compound interest comparing quantity maths

  1. True

  2. False

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Correct Option: B
Explanation:

Mutual Fund is a professionally managed investment scheme, which is run by AMC. Mutual Fund is a mediator that brings together a group of people and invests 'their' money in stocks, bonds and other securities.

The price of a T.V. set worth Rs. 20,000 is to be paid in 20 instalments of Rs. 1000, each. If the rate of interest be 6% per annum, and th6 first instalment be paid at the time of purchase, then, the value of the last instalment covering the interest as well will be : (Hotel Management, 1998)

investement and financial planning banking compound interest comparing quantity maths

  1. Rs. 1050

  2. Rs. 2050

  3. Rs. 3000

  4. None of these

Show answer
Correct Option: A