Tag: maths

Questions Related to maths

In a two digit no. the digit at units place is $\left| x-2 \right| $ and digit at tens place is $\left| x+1 \right| $, then that number is

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. 2x+3

  2. 11x+12

  3. 10x+1

  4. 11x+21

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Correct Option: A

if $76$ is divided into four parts proportional to $7,5,3.4$ then the smallest part is:

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $12$

  2. $15$

  3. $16$

  4. $19$

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Correct Option: A
Explanation:
Four parts proportional to 

$7,5,3$ and $4$

$\therefore $  Four part are equal to$7x, 5x, 3x,$ and $4x.$

$\therefore7x+5x+3x+4x=76$

$\therefore 19x=76$

$\therefore x=\dfrac {76}{19}$

$\therefore x=4$

$\therefore 7x=4\times7=28$

$\therefore 5x=5\times4=20$

$\therefore 3x=3\times 4=12$

$\therefore 4x=4\times4=16$

$\therefore $ For parts are $28, 20, 12$ and $16$.

The ratio of the volumes of water and glycerine in 240cc of mixture is 1:3 .The quantity of water (in cc) that should be added to the mixture so the volumes of water and glycerine 2:3 is: 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $55$

  2. $60$

  3. $62.5$

  4. $64$

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Correct Option: B
Explanation:
The ratio of the volume of water and Glycerine in $240$cc of mixture is $1:3$. 

The quantity of water(in cc) that should be added to the mixture so that the new ratio of the volume of water and glycerine becomes $2:3$

Let the ratio of the volume of water and glycerine be $x$ and $3x$.

$x+3x=240$

$\Rightarrow 4x=240$

$\Rightarrow x=60$

So the volume of water is $60cc$

Volume of glycerine is $60cc$

Volume of glycerine is $(3\times 60)cc=180$cc

Let x litre of water is added

$\dfrac{60+x}{180}=\dfrac{2}{3}$

$\Rightarrow 3(60+x)=360$

$\Rightarrow 180+3x=360$

$\Rightarrow 3x=360-180$

$\Rightarrow 3x=180$

$\Rightarrow x=60$.

$8$% of the voters in an election did not cast their votes. In this election, there were only two candidates. The winner by obtaining $48$% of the total votes, defeated his contestant by $1100$ votes. The total number of voters in the election was?

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $21000$

  2. $23500$

  3. $22000$

  4. $27500$

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Correct Option: D

Which of the equation satisfy the given statement ?
"Perimeter of an equilateral triangle is three times its side l" 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $l \times l \times l$

  2. $3 \times 3 \times 3$

  3. $3 \times l$

  4. $3 + l$

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Correct Option: C
Explanation:
An equilateral triangle is a triangle in which all three sides are equal.Let $l$ be the length of the side of a triangle.
Thus, perimeter is equal to sum of all its sides$3\times side=3\times l$

Equation of the statement 'Thrice the length (l) of room is $340$ metres' is ____ 

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  1. $3l=430$

  2. $3l=340$

  3. $3+l=340$

  4. $3l+340=0$

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Correct Option: B
Explanation:

Let $l$ be the length of the room

Thrice the length of the room$=3l$
Given:Thrice the length of the room$=340\ m$
Equation is $3l=340\ m$

An algebraic expression, $11-y$ can be written in the statement form as  ____ 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $11$ less than $y$

  2. $y$ less than $11$

  3. $y$ more than $11$

  4. $y$ divided by $11$

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Correct Option: B
Explanation:
$y$  less than $11$

If fives of a number is $80$, then the number is ___ 

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $-16$

  2. $1$

  3. $16$

  4. $40$

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Correct Option: C
Explanation:
Let $x$ be a number.
$\Rightarrow\,5x=80$
$\Rightarrow\,x=\dfrac{80}{5}=16$
$\therefore\,x=16$
The number is $16$

If a $\in { 1,2,3,4 } ,$ then number of equations of the form $x ^ { 2 } + a x + 1 = 0$ having real roots is

maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: C

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digit of that number ?

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  1. 3

  2. 4

  3. 9

  4. Cannot be determined

  5. None of these

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Correct Option: B
Explanation:
Let the ten's digit be $x$ and unit's digit be $y$.

Then, $(10x + y) - (10y + x) = 36$

$9(x - y) = 36$

$x - y = 4$

Therefore, the difference between the two digit of that number is $4$