Mathematics Class VII

Question 1 of 25

1. Question
By what number should $\dfrac{-33}{8}$ divided to get $\dfrac{-11}{2}$ ?
- $\dfrac{-4}{7}$
- $\dfrac{4}{3}$
- $\dfrac{3}{4}$
- $\dfrac{-3}{4}$
Correct

Incorrect

Hint

$\dfrac{-33}{8} \div \dfrac{-11}{2} \rightarrow \dfrac{-33}{8} \times \dfrac{-2}{11} = \dfrac{3}{4}$

Question 2 of 25

2. Question

Express $\left[\dfrac{-1}{4} – \dfrac{-1}{6}\right] \div \left[\dfrac{1}{3} + \dfrac{1}{2}\right] $

$\dfrac{-2}{3}$
$\dfrac{-1}{10}$
$\dfrac{2}{3}$
$\dfrac{-1}{2}$

Correct

Incorrect

Hint

*** QuickLaTeX cannot compile formula:
\left[\dfrac{-1}{4} - \dfrac{-1}{6}\right] \div \left[\dfrac{1}{3} + \dfrac{1}{2}\right] = \dfrac{-3 + 2}{12} \div \dfrac{2 + 3}{6} \\ = \dfrac{-1}{12} \times \dfrac{6}{5} = \dfrac{-6]{60} = \dfrac{-1}{10} 

*** Error message:
File ended while scanning use of \@genfrac.
Emergency stop.

Question 3 of 25

3. Question
Given $ a = 1\dfrac{5}{7} , \ b = \dfrac{1}{4}, \ c = \dfrac{1}{9} \ and \ d = \dfrac{-5}{4} $ , evaluate $a(b – c)\div d$
- $\dfrac{-4}{21}$
- $\dfrac{-6}{23}$
- $\dfrac{-5}{27}$
- $\dfrac{4}{21}$
Correct

Incorrect

Hint

$\dfrac{12}{7} \left(\dfrac{1}{4} - \dfrac{1}{9}\right) \div \left(\dfrac{-5}{4}\right) \\ = \dfrac{12}{7}\left(\dfrac{9 - 4}{36}}\right) \div \left(\dfrac{-5}{4}\right) = \dfrac{5}{21} \times \dfrac{-4}{5} = \dfrac{-4}{21}$
Question 4 of 25

4. Question
Arrange in descending order
$\dfrac{17}{30} , \dfrac{-3}{-5} , \dfrac{4}{-15} , \dfrac{-7}{15} $
-  \dfrac{-3}{-5} < \dfrac{17}{30} < \dfrac{4}{-15} < \dfrac{-7}{15} [/latex]
- $ \dfrac{-3}{-5} > \dfrac{17}{30} > \dfrac{4}{-15} > \dfrac{-7}{15} $
- $\dfrac{17}{30} > \dfrac{-3}{-5} > \dfrac{4}{-15} > \dfrac{-7}{15} $
- none of these
Correct

Incorrect

Hint

$\dfrac{17}{30} , \dfrac{3}{5}, \dfrac{-4}{15} , \dfrac{-7}{15}$
LCM = 30
$\dfrac{3}{5} = \dfrac{18}{30} \\ \dfrac{-4}{5} = \dfrac{-8}{30} \\ \dfrac{-3}{-5} > \dfrac{17}{30} > \dfrac{4}{-15} > \dfrac{-7}{15}$
Question 5 of 25

5. Question
Which one of the following statement is true ?
- the equivalent of $\dfrac{p}{q}$ is different from $\dfrac{p}{q}$
- $\dfrac{35 p}{33 q}$ is equivalent of $\dfrac{p}{q}$
- There are only 5 equivalent rational numbers of the form $\dfrac{p}{q}$
- We can write infinite equivalent rational numbers of the form $\dfrac{p}{q}$
Correct

Incorrect
Question 6 of 25

6. Question
Find the value of $\dfrac{-1}{2} + \dfrac{1}3}+ \dfrac{-5}{6} + \dfrac{5}{3} + \dfrac{-7}{4} $
- $\dfrac{23}{12}$
- $\dfrac{15}{12}$
- $\dfrac{-13}{12}$
- $\dfrac{-11}{12}$
Correct

Incorrect

Hint

$\dfrac{-6 + 4 + (-10) + 20 + (-21)}{12} = \dfrac{-13}{12}$
Question 7 of 25

7. Question
The value of $ (17 \times 12)^{-1} = $
- $17^{-1} \times 12^{-1}$
- $17 \times \dfrac{1}{12}$
- $\left(\dfrac{1}{17}\right)^{-1} \times \dfrac{1}{12}$
- $\dfrac{1}{17} \times (12)^{-1}$
Correct

Incorrect

Hint

$17^{-1} \times 12^{-1} = \dfrac{1}{17} \times (12)^{-1}$
Question 8 of 25

8. Question
If $(-24)^{-1}$ is divided by $3^{-1}$ then the quotient will be
- $\dfrac{-1}{8}$
- $ -8 $
- $ 8 $
- $\dfrac{1}{8} $
Correct

Incorrect

Hint

$\dfrac{-1}{24} \div \dfrac{1}{3} = \dfrac{-1}{24} \times \dfrac{3}{1} = \dfrac{-1}{8}$
Question 9 of 25

9. Question
Simplify $ \left[7^{-1} + \left(\dfrac{3}{2}\right)^{-1}\right]^{-1} \div \left[6^{-1} + \left(\dfrac{3}{2}\right)^{-1}\right]^{-1}$
- $\dfrac{34}{35}$
- $\dfrac{35}{34}$
- $\dfrac{21}{105}$
- $\dfrac{5}{121}$
Correct

Incorrect

Hint

$\left(\dfrac{1}{7} + \dfrac{2}{3}\right)^{-1} \div \left(\dfrac{1}{6} + \dfrac{2}{3}\right)^{-1} = \dfrac{21}{17} \div \dfrac{6}{5} \\ \dfrac{21}{17} \times \dfrac{5}{6} = \dfrac{35}{34}$
Question 10 of 25

10. Question
Which one of the following statement is false ?
- The product of 10 negative integers and 15 positive integers is always positive
- The product of 15 positive integers and 10 negative integers is always negative
- The product of rational number and its reciprocal is always 1
- none of these
Correct

Incorrect
Question 11 of 25

11. Question
Steve has a negative rational number which is reciprocal of itself. If he multiplies the rational number with $ x = \left[\dfrac{1}{7} \times 4\dfrac{3}{5} + 4\dfrac{3}{5} + 7\dfrac{3}{5} + 4\dfrac{9}{17} \div 8\dfrac{7}{17} \right]$ then which one of the following is correct statement ?
- When x will be multiplied by that number product will be reciprocal of x
- When x will be multiplied by that number product will be additive inverse of x
- x will be doubled
- none of these
Correct

Incorrect

Hint

There is only one negative rational number which is reciprocal of itself is -1.
Question 12 of 25

12. Question
Stephen has three boxes whose total weight is $\dfrac{121}{2}$ pound. If the first box weight is $3\dfrac{1}{2}$ pound more than the second box and third box weight $5\dfrac{1}{3}$ pound more than first box, then the weight of second box is _____.
- $\dfrac{289}{18}$ pound
- $\dfrac{18}{289}$ pound
- $\dfrac{279}{18}$ pound
- $\dfrac{18}{279}$ pound
Correct

Incorrect

Hint

Let the weight of second box = x
Let the weight of first box = $x + \dfrac{7}{2}$
Third = $x + \dfrac{7}{2} + \dfrac{16}{3}$
x + x + \dfrac{7}{2} + x + \dfrac{7}{2} + \dfrac{16}{3} = \dfrac{121}{2} \rightarrow x = \dfrac{289}{18}[/latex] pound
Question 13 of 25

13. Question
The height of a triangle is three fifth of it corresponding base. If the height increased by $4\%$and base decreased by $2\%$ then area of triangle remains same. The base of triangle is :
- $\dfrac{45}{3}$ cm
- $\dfrac{33}{5}$ cm
- cannot be determined
- $\dfrac{15}{3}$ cm
Correct

Incorrect

Hint

Let base of the triangle = x
Height = $\dfrac{3x}{5}$
Are $= \dfrac{1}{2} \times \dfrac{3x}{5} \times x = \dfrac{3}{10}x^{2}$
New Height $= \dfrac{4}{100} \times \dfrac{3x}{5} + \dfrac{3x}{5} \rightarrow \dfrac{3x}{5} +\dfrac {3x}{125} = \dfrac{78x}{125}$
Base $= x -\dfrac{2x}{100} = \dfrac{98x}{100}$
Area $= \dfrac{1}{2} \times \dfrac{78x}{125} \times \dfrac{98x}{100} = \dfrac{3x^{2}}{10}$
Hence, we cannot determine the value of x.
Question 14 of 25

14. Question
Find a number which is 28 greater than the average of its one third, quarter and one – twelfth.
- 36
- 72
- 33
- 90
Correct

Incorrect

Hint

$\dfrac{1}{3}\left(\dfrac{x}{3} + \dfrac{x}{4} + \dfrac{x}{12}\right) + 28 = x \rightarrow x = 36$
Question 15 of 25

15. Question
If the length of a rectangle is $3\dfrac{1}{3}$ cm more than the breadth which is equal to the side of a square whose perimeter is 24 cm then the area of rectangle is :
- $64 \ cm^{2}$
- $59 \ cm^{2}$
- $84 \ cm^{2}$
- $56 \ cm^{2}$
Correct

Incorrect

Hint

Side of square = 6 cm
Breadth of rectangle = 6 cm
Length $= 6 + \dfrac{6}[10} = \dfrac{28}{3}/latex] cm Area [latex] = \dfrac{28}{3} \times 6 = 56 \ cm^{2}$
Question 16 of 25

16. Question
Find the length of square in which an equilateral triangle formed as shown in figure whose half of the perimeter is $4\dfrac{5}{17}$ m.
- $3\dfrac{12}{17}$ m
- $\dfrac{412}{57}$ m
- $2\dfrac{44}{51}$ m
- $\dfrac{57}{216}$ m
Correct

Incorrect

Hint

Perimeter of equilateral triangle = $3 \times side \ of \ square$
Half of the perimeter = [altex] \dfrac{73}{17}[\latex] cm
Perimeter $= \dfrac{73}[17} \times 2 = \dfrac{146}{17}/latex] cm Side [latex] = \dfrac{146}{17} \times \dfrac{1}{3} = \dfrac{146}{51} = 2\dfrac{44}{51}$ m
Question 17 of 25

17. Question
The perimeter is rectangle is $3\dfrac{1}{3}$ more than the perimeter of square. A triangle whose perimeter is $\dfrac{1}{3]$ times of the circumference of the circle whose radius is 5 cm and is equal to the length of sides of the square. Find the perimeter of rectangle is :
- $ 23.3 $ cm
- $15\dfrac{1}{3}$cm
- $15\dfrac{1}{9}$cm
- $25\dfrac{1}{9}$cm
Correct

Incorrect

Hint

Perimeter of square $4 \times 5 = 20$ cm
Perimeter of rectangle $20 + \dfrac{10}{3} = 23\dfrac{1}{3} = 23.3$ cm
Question 18 of 25

18. Question
Peter defines a rational number in the following ways. “It is of the form $\dfrac{p}{q}$ , where q is the smallest whole number.” This definition is :
- always true
- represents some rational number only
- some as the definition of rational number
- always false
Correct

Incorrect
Question 19 of 25

19. Question
Which of the following statement is false ?
- “0” is a positive rational number
- A positive rational number is in the form of $\dfrac{p}{q}$ , where p and q are integers of same sign and $ q \neq 0 $
- A negative rational number is in the form of $\dfrac{p}{q}$ , where p and q are integers of opposite sign and $ q \neq 0 $
- none of these
Correct

Incorrect
Question 20 of 25

20. Question
If $ P = \dfrac{-4}{5} \times \dfrac{-10}{9} \times \dfrac{3}{4}$ and $ Q = (-6) \times \dfrac{7}{5} \times \dfrac{2}{3}$ then P + Q is equal to :
- $-2\dfrac{14}{15}$
- $-4\dfrac{14}{15}$
- $-3\dfrac{14}{15}$
- $-1\dfrac{14}{15}$
Correct

Incorrect

Hint

$P = \dfrac{-4}{5} + \dfrac{-10}{9} \times \dfrac{3}{4} = \dfrac{2}{3}$
$Q = -6 \times \dfrac{7}{5} \times \dfrac{2}{3} = \dfrac{-28}{5}$
$P \ + \ Q = \dfrac{2}{3} + \left(\dfrac{-28}{5}\right) = \dfrac{-74}{15} = -4\dfrac{14}{15}$
Question 21 of 25

21. Question
Which of the following is equivalent to $\dfrac{4}{5}$ ?
- $\dfrac{5}{4}$
- $\dfrac{16}{25}$
- $\dfrac{16}{20}$
- $\dfrac{15}{25}$
Correct

Incorrect
Question 22 of 25

22. Question
How many rational numbers are there between two rational numbers ?
- 1
- 0
- unlimited
- 100
Correct

Incorrect
Question 23 of 25

23. Question
In the standard form, the denominator is always a
- 0
- negative integer
- positive integer
- 1
Correct

Incorrect
Question 24 of 25

24. Question
To reduce a rational number to its standard form we divide its numerator and denominator by
- LCM
- HCF
- product
- multiple
Correct

Incorrect
Question 25 of 25

25. Question
In the standard form of rational number, the common factor is always
- 0
- 1
- -1
- 2
Correct

Incorrect

Mathematics Class VII

Olympiad Questions – Rational Numbers – Class VII

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