Tag: maths

Questions Related to maths

$\sqrt{21-4\sqrt{5}+8\sqrt{3}-4\sqrt{15}}=$...........

maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

  1. $\sqrt{5}-2+2\sqrt{3}$

  2. $\sqrt{5}-\sqrt{4}-\sqrt{12}$

  3. $-\sqrt{5}+\sqrt{4}+\sqrt{12}$

  4. $-\sqrt{5}-\sqrt{4}+\sqrt{12}$

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Correct Option: C

State whether the following statements are true or false. 
$\sqrt {n}$ is not irrational if n is a perfect square

maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

  1. True

  2. False

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Correct Option: A
Explanation:

False ,

$\sqrt{4}=2$ where 2 is a rational number.Here n is perfect square the  $\sqrt{n}$ is rational number 
$\sqrt{5}=2.236..$ is not rational  number But it is irrational number . here n is not a perfect square the  $\sqrt{n}$ is  irrational  number
So $\sqrt{n}$ is not irrational number if n is perfect square

If $p$ is prime, then $\sqrt {p}$ is:

maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

  1. Composite number

  2. Rational number

  3. Positive integer

  4. Irrational number

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Correct Option: D
Explanation:

SInce, we know that prime numbers are those which are never perfect square and not divisible by any other number except by itself.
which are $2,3,5,7,...$
Clearly, if $p$ is prime then $\sqrt p $ is irrational number.
Option $D$ is correct. 

State the following statement is true or false

$3\sqrt{18}$ is an irrational number.

maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

  1. True

  2. False

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Correct Option: A
Explanation:

$3\sqrt{18}=9\sqrt{2},$ which is the product of a rational and an irrational number and so an irrational number.

$6+\sqrt{2}$ is a rational number.

maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

Let's assume that $6+\sqrt2$ is rational..... 

then 

$6+\sqrt2 = p/q $

$\sqrt2 =( p-6q)/(q) $ 

now take $p-6q$ to be P and $q$ to be Q........where P and Q are integers 

which means, $\sqrt2= P/Q$...... 

But this contradicts the fact that $\sqrt2$ is rational 

So our assumption is wrong and $6+\sqrt2$ is irrational.

Solve for $x$:

$\dfrac {9x}{7-6x}=15$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $\dfrac{99}{105}$

  2. $-\dfrac{105}{99}$

  3. $\dfrac{105}{99}$

  4. $-\dfrac{99}{105}$

Show answer
Correct Option: C
Explanation:

$\dfrac{9x}{7 - 6x} = 15$


$9x = 15(7 - 6x)  = 105 - 90x$

$9x + 90x = 105 $

$99x = 105$

$x = \dfrac{105}{99}$

If $17x+51y=85$, then $13x+39y=$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $67$

  2. $61$

  3. $63$

  4. $65$

Show answer
Correct Option: D
Explanation:

$17x+51y=85$

 dividing both sides by $17$

$\Rightarrow x+3y=5$ 
 on multiplying both sides by $13$
$\Rightarrow 13x+39y=65$
Therefore, $13x+39y=65$

Sabarmati express take 18 second to pass completely through a stations $162$m long and $15 second $ through another station $120m$ long. The length of the sabarmathi express os 

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $132m$

  2. $100m$

  3. $80m$

  4. $90m$

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Correct Option: A

The manufacturer of a certain item can sell all he can produce at the selling price of $Rs. 60$ each. It costs him $Rs. 40$ in materials and labour to produce each item and he has overhead expenses of $Rs. 3000$ per week in order to operate the plant. The number of units he should produce and sell in order to make a profit of at least $Rs\,1000$ per week, is : 

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $200$

  2. $250$

  3. $300$

  4. $400$

Show answer
Correct Option: A
Explanation:

Let the no of units sold be $x$ per week.

$60x$ = sales should include all the expenses and profit required to balance things out.
$60x = 1000+40x+3000$

$20x = 4000$
$x =200$

The value of $x$ for which $\cfrac{x-3}{4}--x< \cfrac{x-1}{2}-\cfrac{x-2}{3}$ and $2-x> 2x-8$

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $[-1,10/3]$

  2. $(1,10/3)$

  3. $R$

  4. none of these

Show answer
Correct Option: A
Explanation:

$\dfrac{x-3}{4}-x<\dfrac{x-1}{2}-\dfrac{x-2}{3}$


$\dfrac{-3{x}-3}{4}<\dfrac{x+1}{6}$


$\implies x>-1$

$2-x>2{x}-8\implies x<\dfrac{10}{3}$

$\implies x\in (-1,10/3)$