Tag: operations on rational numbers

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Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Arrange in ascending order $\sqrt [ 6 ]{ 7 } ,\sqrt [ 4 ]{ 3 } ,\sqrt [ 12 ]{ 48 } $

  1. $\sqrt [ 4 ]{ 3 } ,\sqrt [ 12 ]{ 48 } ,\sqrt [ 6 ]{ 7 } $
  2. $\sqrt [ 12 ]{ 48 } ,\sqrt [ 4 ]{ 3 } ,\sqrt [ 6 ]{ 7 } $
  3. $\sqrt [ 6]{ 7 } ,\sqrt [ 12 ]{ 48 } ,\sqrt [ 4 ]{ 3 } $
  4. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Convert to powers: 7^(1/6) = 7^(2/12) = 49^(1/12); 3^(1/4) = 3^(3/12) = 27^(1/12); 48^(1/12). Comparing the bases: 27 < 48 < 49. Thus, 3^(1/4) < 48^(1/12) < 7^(1/6).

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

The ascending order of minimum values of the function  $P:\sin ^{ -1 }{ x } -\cos ^{ -1 }{ x } $, $Q=\tan ^{ -1 }{ x } -\cot ^{ -1 }{ x } $, $R=\sec ^{ -1 }{ x } -\csc ^{ -1 }{ x } $

  1. P, Q, R

  2. P, R, Q

  3. Q, P, R

  4. Q, R, P
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For P: sin^-1(x) - cos^-1(x) ranges from -pi/2 to pi/2, minimum is -pi/2. For Q: tan^-1(x) - cot^-1(x) ranges from -pi/2 to pi/2, minimum is -pi/2. For R: sec^-1(x) - csc^-1(x) ranges from -pi/2 to pi/2, minimum is -pi/2. However, evaluating the functions at their domain boundaries reveals P < Q < R.

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

The value of $1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$ is?

  1. $\dfrac{121}{108}$
  2. $\dfrac{3}{2}$
  3. $\dfrac{31}{2}$
  4. $\dfrac{91}{81}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$1+\dfrac{1}{4\times 3}+\dfrac{1}{4\times 3^2}+\dfrac{1}{4\times 3^3}+\dfrac{1}{4\times 3^4}$


$=1+\dfrac{1}{12}+\dfrac{1}{36}+\dfrac{1}{108}+\dfrac{1}{324}$


$=\dfrac{324+27+9+3+1}{324}$

$=\dfrac{364}{324}$

$=\dfrac{91}{81}$

Hence, the answer is $\dfrac{91}{81}.$

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

The ascending order of $\sqrt { 2 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 4 ]{ 6 } $ is

  1. $\sqrt { 2 } ,\sqrt [ 3 ]{ 4 } ,\sqrt [ 4 ]{ 6 } $
  2. $\sqrt { 2 } ,\sqrt [ 4 ]{ 6 } ,\sqrt [ 3 ]{ 4 } $
  3. $\sqrt [ 3 ]{ 4 }, \sqrt {2},\sqrt [ 4 ]{ 6 } $
  4. $\sqrt [ 4 ]{ 6 },\sqrt [ 3 ]{ 4 } ,\sqrt {2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Find the rational numbers between the following numbers. 

$-0.2$ and $-0.22$.

  1. $-0.210 > -0.211 > -0.312 > -0.213 > -0.314 > 0.220$
  2. $-0.210 > -0.211 > -0.212 > -0.213 > -0.314 > 0.220$
  3. $-0.210 > -0.211 > -0.312 > -0.213 > -0.214 > 0.220$
  4. $-0.210 > -0.211 > -0.212 > -0.213 > -0.214 > 0.220$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Rational number between two numbers $ a $ and $ b = \dfrac {(a +

b)}{2} $

So, a rational number between $ -0.2 $ and $ - 0.22 = \dfrac {(-0.2 - 0.22)}{2} = -0.21 $

Now, another rational number between $ -0.21 $ and $ - 0.22 = \dfrac {(-0.21 - 0.22)}{2} = -0.215 $

rational number between $ -0.215 $ and $ - 0.21 = \dfrac {(-0.215 - 0.21)}{2} = -0.212 $ 

rational number between $ -0.215 $ and $ - 0.212 = \dfrac {(-0.215 - 0.212)}{2} = -0.213 $ 

rational number between $ -0.215 $ and $ - 0.213 = \dfrac {(-0.215 - 0.213)}{2} = -0.214 $ 

Similarly,
rational numbers between $ -0.2 $ and $ - 0.22 $ are $-0.210, -0.211 , -0.212, -0.213 , -0.214$ etc

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Find the five rational numbers between $-5$ and $-6$

  1. $-5.1 ,-5.2 , -3.3 , -5.4 , -5.5 $
  2. $-5.1 ,-5.2 , -5.3 , -5.4 , -5.5 $
  3. $-5.1 , -6.2 , -5.3 , -5.4 , -5.5 $
  4. $-6.1 , -5.2 , -5.3 , -5.4 , -5.5 $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$−5>(−5−0.1)=−5.1>−5.2=(−5.1−0.1)>−5.3=(−5.2−0.1)>−5.4\\=(−5.3−0.1)>−5.5=(−5.4−0.1)>...>−6$

$-5>−5.1>−5.2>−5.3>−5.4>−5.5...>−6$

The five rational numbers between $−5$ and $−6$
$-5.1 ,-5.2 , -5.3 , -5.4 , -5.5 $
Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Which one is in the descending order in the following?

  1. $\displaystyle 6/7, 4/5, 3/4, 7/9$
  2. $\displaystyle 6/7, 4/5, 7/9, 3/4$
  3. $\displaystyle 3/4, 7/9, 4/5, 6/7$
  4. $\displaystyle 7/9, 3/4, 6/7, 4/5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Here we have four factors $\dfrac{3}{4},  \dfrac{4}{5},   \dfrac{6}{7},   \dfrac{7}{9}$
LCM of 4, 5, 7 and 9 is 1260
So, 
$\dfrac{3}{4} \times\dfrac{315}{315}$ = $\dfrac{945}{1260}$

$\dfrac{4}{5} \times\dfrac{252}{252}$ = $\dfrac{1008}{1260}$

$\dfrac{6}{7} \times\dfrac{180}{180}$ = $\dfrac{1080}{1260}$

$\dfrac{7}{9} \times\dfrac{140}{140}$ = $\dfrac{980}{1260}$
As, 
1080 > 1008 > 980 > 945
So, $\dfrac{6}{7} > \dfrac{4}{5} >  \dfrac{7}{9} >  \dfrac{3}{4}$

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Arrange in descending order:
$1,00,000; 99,999; 9,90,000; 1,10,000$

  1. $1,00,000; 99,999; 9,90,000; 1,10,000$
  2. $ 1,10,000; 9,90,000; 99,999; 1,00,000$
  3. $ 9,90,000; 99,999; 1,10,000; 1,00,000$
  4. $ 9,90,000; 1,10,000; 1,00,000; 99,999$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Comparing digits at lakh's place followed by ten thousand's, thousand's, hundred's, ten's and one's place,


We can arrange the given numbers in descending order as 
$9,90,000;\ 1,10,000;\ 1,00,000;\ 99,999$

Multiple choice maths concepts of seven and eight digit numbers comparison of numbers comparing numbers operations on rational numbers indian place value chart largest and smallest numbers writing and expanding numbers

Arrange the following in descending order.
$\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$, $\dfrac{9}{8}$ 

  1. $\dfrac{7}{2}$, $\dfrac{9}{8}$, $\dfrac{3}{2}$, $\dfrac{9}{5}$, $\dfrac{5}{2}$
  2. $\dfrac{7}{2}$, $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$
  3. $\dfrac{5}{2}$, $\dfrac{9}{5}$, $\dfrac{3}{2}$, $\dfrac{9}{8}$, $\dfrac{7}{2}$
  4. $\dfrac{9}{8}$, $\dfrac{5}{2}$, $\dfrac{3}{2}$, $\dfrac{7}{2}$, $\dfrac{9}{5}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2},\cfrac{9}{5},\cfrac{9}{8}$

We know that the number with largest denominator is the smallest one.
And among $\cfrac{5}{2},\cfrac{3}{2},\cfrac{7}{2}$ the one with largest numerator is the largest one.
Among $\cfrac{9}{5}$ and $\cfrac{3}{2},$ $\cfrac{9}{5}$ is larger.
Hence descending order is $\cfrac { 7 }{ 2 } ,\cfrac { 5 }{ 2 } ,\cfrac { 9 }{ 5 } ,\cfrac { 3 }{ 2 } ,\cfrac { 9 }{ 8 }.$

Multiple choice maths operations on rational numbers rational numbers on number line rational numbers and their decimal expansions rational numbers between two rational numbers

Milk is sold at $Rs\ 10\dfrac {3}{4}$ per liter, Find the cost of $6\dfrac {2}{5}$ liters of milk.

  1. $Rs \,107 \dfrac {1}{5}$
  2. $Rs \, 65 \dfrac {2}{5}$
  3. $Rs \, 103 \dfrac {1}{5}$
  4. $Rs \, 68 \dfrac {4}{5}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Price$=Rs\ 10\dfrac {3}{4}=Rs.\cfrac{43}{4}$ per liter


Price of $6\dfrac {2}{5} l=\cfrac{32}{5}l=Rs.\cfrac{43}{4}\times \cfrac{32}{5}=Rs.\cfrac{344}{5}=Rs.68\cfrac{4}{5}$