Tag: maths

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Questions Related to maths

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
$

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

A 3-digit number 4a3 is added to another 3-digit number 984 to give the four-digit number 13b7 which is divisible by 11 Then (a + b) is

  1. 10

  2. 11

  3. 12

  4. 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the question
$4 a 3 + 9 8 4 = 1 3 b 7$
$a + 8 = b$
Then$b - a = 8$
According to the question  13b7 is divisible by 11
$(7 + 3) - (b + 1) = (9 - b)$
$(9 - b) = 0$
$b = 9$
$b = 9   and   a = 1$
Then $a+b=9+1=10$

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

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If she attempts in all 50 questions and scores 120 marks, the number of questions she attempts correct is........

  1. 62

  2. 44

  3. 42

  4. 34
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let student get x correct answer then 50-x student get wrong answer 
Then 4(x)+(50-x)(-1)=120
Or 4x-50+x=120
Or 5x=120+50=170
Or x=34