Tag: operations

Quizzes (1) Questions (91)

Questions Related to operations

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

Two pipes X and Y can fill a cistern in 24 min. and 32 min. respectively. If both the pipes are opened together, then after how much time Y should be closed so that the tank is full in 18 minutes?

  1. 6 min

  2. 8 min

  3. 10 min

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Y closed pipe after a min .
Then part filled by (X+Y) in a min +Part filled by X in (18-x) 
So $a(\frac{1}{24}+\frac{1}{32})+(18-a)\frac{1}{24}= 1$
Multy by 96 
Or 4a+3a+72-4a=96
Or 3x=24
Or x=8 min

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

If $\displaystyle x=\frac{4\sqrt{2}}{\sqrt{2}+1}$ then find the value of $\displaystyle \frac{1}{\sqrt{2}}\left ( \frac{x+2}{x-2}+\frac{x+2\sqrt{2}}{x-2\sqrt{2}} \right )$

  1. $\displaystyle \sqrt{2}$
  2. $12+8\displaystyle \sqrt{2}/5$
  3. $12-8\displaystyle \sqrt{2}$
  4. $\displaystyle \frac{16\sqrt{2}+24}{5}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$x=\frac{4\sqrt{2}}{\sqrt{2+1}}$
$\frac{1}{\sqrt{2}}\left ( \frac{x+2}{x-2}+\frac{x+2\sqrt{2}}{x-2\sqrt{2}} \right )$
Put the value of x
$\frac{1}{\sqrt{2}}\left ( \frac{\frac{4\sqrt{2}}{\sqrt{2+1}}+2}{\frac{4\sqrt{2}}{\sqrt{2+1}}-2}+\frac{\frac{4\sqrt{2}}{\sqrt{2+1}}+2\sqrt{2}}{\frac{4\sqrt{2}}{\sqrt{2+1}}-2\sqrt{2}} \right )$
=$\frac{1}{\sqrt{2}}\left ( \frac{4\sqrt{2}+2\sqrt{2}+2}{4\sqrt{2}-2\sqrt{2}-2} \right )+\left ( \frac{4\sqrt{2}+4+2\sqrt{2}}{4\sqrt{2}-4-2\sqrt{2}} \right )$
=$\frac{6\sqrt{2}+2}{2\sqrt{2-2}}+\frac{6\sqrt{2}+4}{2\sqrt{2}-4}$
=$\frac{1}{\sqrt{2}}\left ( \frac{32-24\sqrt{2}}{16-12\sqrt{2}} \right )$
=$\sqrt{2}$

Multiple choice maths operations adding and subtracting numbers using place value addition & subtraction mental additions and subtractions

If P : Q : R = 6 : 5 : 4 and $\displaystyle P^{2}+Q^{2}+R^{2}=192500$ then find $\displaystyle \frac{(P+Q-R)}{2}$

  1. 175

  2. 165

  3. 185

  4. 200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$
:Q:R\quad =\quad 6:5:4\ Let\quad P\quad \quad =\quad 6x\ Q=\quad 5x\ R\quad =\quad 4x\ { P }^{ 2 }+{ Q }^{ 2 }{ +\quad R }^{ 2 }\quad =\quad 192500\ { (6x) }^{ 2 }+{ (5x) }^{ 2 }+(4x)^{ 2 }\quad =\quad 192500\ 77{ x }^{ 2 }\quad =\quad 192500\ { x }^{ 2 }\quad =\quad 2500\ x\quad =\quad 50\ \ \frac { P+Q-R }{ 2 } \quad =\quad \frac { 6x+5x-4x }{ 2 } \quad =\quad \frac { 7x }{ 2 } \quad =\quad \frac { 7\times 50 }{ 2 } \quad =\quad 175
$