Tag: writing and expanding 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

Which of the following is ninth to the right of the seventeenth from the right end of the given arrangement?

M O K T % J 9 I B @ 8 $\circledS$ C # F 1 V 7 $\Box$ 2 E G 3 Y 5 $ 6 T

  1. E

  2. %

  3. I

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

For the given arrangement we can see that the $17$ th no from right end is $\circledS$, 

and we can easily see that $9$ th no from the right of the $17$ th element from the right is E .

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

If the digits of the number $5726489$ are arranged in ascending order, then how many digits will remain at the same position?

  1. None

  2. One

  3. Two

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

The given number is $5726489$.


After arranging digits of number in ascending order the number becomes $2456789$

Now, we can see after arranging number in ascending order digits $6,8$ and $9$ remain at the same position.

$\therefore$  $3$ digits will  remain at the same position.

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

Write the following rational numbers in ascending order:

$\dfrac{3}{4},\dfrac{7}{12}, \dfrac{15}{11}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{-4}{5}, \dfrac{-102}{81}, \dfrac{-13}{7}$.

  1. $\dfrac{-13}{7},\dfrac{-102}{81}, \dfrac{-4}{5}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{15}{11}, \dfrac{7}{12}, \dfrac{3}{4}$.
  2. $\dfrac{-13}{7},\dfrac{-102}{81}, \dfrac{-4}{5}, \dfrac{7}{12}, \dfrac{3}{4}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{15}{11}$.
  3. $\dfrac{-13}{7},\dfrac{-102}{81}, \dfrac{-4}{5}, \dfrac{7}{12}, \dfrac{3}{4}, \dfrac{101}{100}, \dfrac{22}{19}, \dfrac{15}{11}$.
  4. $\dfrac{3}{4},\dfrac{7}{12}, \dfrac{15}{11}, \dfrac{22}{19}, \dfrac{101}{100}, \dfrac{-4}{5}, \dfrac{-102}{81}, \dfrac{-13}{7}$.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Convert to decimals: -13/7 approx -1.85, -102/81 approx -1.26, -4/5 = -0.8, 7/12 approx 0.58, 3/4 = 0.75, 101/100 = 1.01, 22/19 approx 1.16, 15/11 approx 1.36. The ascending order matches option C.

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

If the following numbers  are arranged in ascending order, what will be the middle number?
$687,\ 789,\ 648,\ 693,\ 672$

  1. 687

  2. 789

  3. 693

  4. 672
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given numbers in ascending order is, 


$648, 672, 687, 693, 789$


It can be clearly seen that middle number is $687.$ 

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

Among $\dfrac{5}{6},\dfrac{5}{7}$ and $\dfrac{5}{8}$, the greatest fraction is 

  1. $\dfrac{5}{6}$
  2. $\dfrac{5}{7}$
  3. $\dfrac{5}{8}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Since all the fractions having same numarator so the greatest fraction will one with lowest denominator
 So the greatest fraction is $\dfrac{5}{6}$
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

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