CBSE Class 8 Mathematics Rational Numbers Assignment Set 04

Question. How many whole numbers are there between 1 lakh and 1 crore (excluding both)?
(a) 9000000
(b) 9900000
(c) 9899999
(d) 10000000

Answer : C

Question. Which of the following is equal to 13²?
(a) 13⁷/ 13⁶
(b) 13⁶ / 13⁴
(c) 122 + 1²
(d) 13³ / 13⁵

Answer : B

Question. 9.03 divided by 899.8 is closest to
(a) 0.01
(b) 0.001
(c) 1
(d) 100

Answer : A

Question. What do you get on adding the smallest 2-digit positive integer and the smallest 2-digit negative integer?
(a) 0
(b) -20
(c) -89
(d) -109

Answer : C

Question. p and q are two numbers such that p x q is an integer but p - q is NOT an integer. Which of the following could be the values of p and q?
(a) -4 , 4
(b) 4 , 4
(c) 1/4  , 1/4 
(d) 4 , 1/4 

Answer : D

Question. What is the number midway between 12345 and 54321?
(a) 20988
(b) 32423
(c) 33333
(d) 41976

Answer : C

Question. Which of the following is closest to 0.1?
(a) 0.09
(b) 0.12
(c) 1
(d) 1/5

Answer : A

Question. For what value of k is the expression  undefined?
K - 5 / K + 3
(a) 0
(b) 3
(c) -3
(d) 5

Answer : C

Question. An operation is defined as follows: For what values of x and y is x, y = 6?
X Δ Y = (x + y) / y
(a) 6 and 1 respectively
(b) 6 and 30 respectively
(c) 35 and 7 respectively
(d) 9 and 18 respectively     

Answer : C

Question. In which of the following cases will the result be a negative number?
(a) - 1 + 2 - 3 + 4 -......- 19 + 20  
(b) (- 1) x  (-2) x ( -3) x ......x (-19) x (-20)  
(c) (- 1) x  (2) x ( -3) x (4)......x (-19) x (20)
(d) 1 - 2 + 3 - 4 -......+ 19 - 20

Answer : D

Question. A pizza is divided into equal slices as shown. What part of the pizza below would remain if you ate two of the slices?

(a) 0.4
(b) 0.6
(c) 0.667
(d) 0.775

Answer : C

Question. Numbers that can be written in the form m/n   are integers and is not equal to 0 are called rational numbers. Which of the numbers in the list below are rational numbers? 12/5, 12.5, 12
(a) 12 and 12/5
(b) Only 12/5
(c) Only 12
(d) All of them

Answer : D

Question. Two numbers whose sum is 0 are called 'opposite' numbers. According to this, what number would be the 'opposite' of  - 2x
(a) 2x
(b) -2
(c) 2
(d) 2  +  x

Answer : A

Question. The integer that is 25 more than (-435) is
(a) -450
(b) -460
(c) -410
(d) 460

Answer : C

Question. c and d are two integers. Which of the following MUST BE TRUE if (-3d) &divided by c is to be a rational number?
(a)  d should be a positive number.
(b) d and c should be of opposite signs.
(c) d should be completely divisible by c.
(d) c should not be 0.

Answer : D
 

Multiple Choice Questions Carrying 1 Mark each :-

Q.12 Between any two rational numbers, there lie :
a) two rational number
b) No rational number
c) infinite rational numbers
d) infinite fractions

Q.13 The additive inverse of a/b is
a) - b/a
b) b/a
c) a/b
d) - a/b

Q.14 Addition is associative for
a) Natural numbers
b) Whole Numbers
c) Rational Numbers
d) All of these

Q.15 Rational numbers are not closed under :
a) Subtraction
b) Division
c) Addition
d) Multiplication

Find five rational numbers between:

Question. \( \frac{2}{3} \) and \( \frac{4}{5} \)
Answer: \( \frac{41}{60}, \frac{42}{60}, \frac{43}{60}, \frac{44}{60}, \frac{45}{60} \)

Question. \( \frac{-3}{2} \) and \( \frac{5}{3} \)
Answer: \( -\frac{8}{6}, -\frac{7}{6}, 0, \frac{1}{6}, \frac{2}{6} \)

Question. \( \frac{1}{4} \) and \( \frac{1}{2} \)
Answer: \( \frac{9}{32}, \frac{10}{32}, \frac{11}{32}, \frac{12}{32}, \frac{13}{32} \)

Question. Write five rational numbers greater than –2.
Answer: \( -\frac{3}{2}, -1, -\frac{1}{2}, 0, \frac{1}{2} \)

Question. Find ten rational numbers between \( \frac{3}{5} \) and \( \frac{3}{4} \).
Answer: \( \frac{97}{160}, \frac{98}{160}, \frac{99}{160}, \frac{100}{160}, \frac{101}{160}, \frac{102}{160}, \frac{103}{160}, \frac{104}{160}, \frac{105}{160}, \frac{106}{160} \)

Question. What expression to be added to \( (5x^2 - 7x + 2) \) to produce \( (7x^2 - 1) \).
(A) \( 2x^2 + 7x + 3 \)
(B) \( 2x^2 + 7x - 3 \)
(C) \( 12x^2 - 7x + 1 \)
(D) \( 2x^2 - 3 \)
Answer: (B) \( 2x^2 + 7x - 3 \)

Question. What must be added to \( 1 - x + x^2 - 2x^3 \) to obtain \( x^3 \)?
(A) \( x^3 - x^2 + x - 1 \)
(B) \( - 1 + x + x^2 - 3x^3 \)
(C) \( 3x^3 - x^2 + x - 1 \)
(D) None of the options
Answer: (C) \( 3x^3 - x^2 + x - 1 \)

Question. What must be added to the sum of \( 4x^2 + 3x - 7 \) and \( 3x^2 + 6x + 5 \) to get : 1?
(A) \( 7x^2 + 9x - 3 \)
(B) \( 3 - 9x - 7x^2 \)
(C) \( 7x^2 + 9x - 2 \)
(D) None of the options
Answer: (B) \( 3 - 9x - 7x^2 \)

Question. By what number should \( \left( \frac{1}{-15} \right) \) be divided so that the quotient equal to \( \left( -\frac{1}{5} \right) \).
Answer: \( \frac{1}{3} \)

Question. Simplify each of the following: \( \left[ \left\{ \left( -\frac{1}{5} \right)^{-2} \right\}^2 \right]^{-1} \)
Answer: \( \frac{1}{625} \)

Question. Simplify each of the following: \( \left\{ \left( \frac{1}{3} \right)^{-3} - \left( \frac{1}{2} \right)^{-3} \right\} \div \left( \frac{1}{4} \right)^{-2} \)
Answer: \( \frac{19}{16} \)

Simplify:

Question. \( \left( \frac{5}{8} \right)^{-7} \times \left( \frac{8}{5} \right)^{-5} \)
Answer: \( \frac{64}{25} \)

Question. \( \left( \frac{-2}{3} \right)^{-2} \times \left( \frac{4}{5} \right)^{-3} \)
Answer: \( \frac{1125}{256} \)

Question. \( \left( \frac{3}{4} \right)^{-4} \div \left( \frac{3}{2} \right)^{-3} \)
Answer: \( \frac{32}{3} \)

Question. \( \left( \frac{3}{7} \right)^{-2} \times \left( \frac{7}{6} \right)^{-3} \)
Answer: \( \frac{24}{7} \)

Question. Evaluate : \( \frac{8^{-1} \times 5^3}{2^{-4}} \)
Answer: 250

Simplify:

Question. \( \frac{25 \times a^{-4}}{5^{-3} \times 10 \times a^{-8}} \)
Answer: \( \frac{625}{2} a^4 \)

Question. \( \frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}} \)
Answer: \( 5^5 \)

Question. By what number should \( (-4)^{-2} \) be multiplied so that the product may be equal to \( 10^{-2} \)?
Answer: \( \frac{4}{25} \)

Question. By what number should \( (-12)^{-1} \) be divided so that the quotient may be \( \left( \frac{2}{3} \right)^{-1} \)?
Answer: \( -\frac{1}{18} \)

Question. By what number should \( \left( -\frac{3}{2} \right)^{-3} \) be divided so that the quotient may be \( \left( \frac{4}{27} \right)^{-2} \)?
Answer: \( -2 \times \left( \frac{4}{27} \right)^3 \)

Question. Find m so that \( \left( \frac{2}{9} \right)^3 \times \left( \frac{2}{9} \right)^{-6} = \left( \frac{2}{9} \right)^{2m-1} \)
Answer: m = – 1