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Q1. is standard form is:
None of these
1 Mark
Ans: 1. Solu on: The denominator of the ra onal number is posi vr. In order to write the ra onal number in standerd form, divide its numerator and denominator by the HCF of 102 and 119. HCF of 102 and 119 = 17 Dividing the numerator and denominator of by 17, We have:
Thus the standard form of Hence, the correct answer is op on (a).
Q2.
1 Mark
Ans: 1. Solu on:
(LCM of 3, 4 and 6 = 12)
(Dividing numerator and denominator by 3)
Hence, the correct answer is op on (a).
Q3. Reciprocal of is: 1 Mark
None of these.
Ans: (^) 3. Solu on: We know that the reciprocal of the ra onal number Reciprocal of
6 7
− 102119 = − 102÷17119÷17 = −^67
− 102119 is −^67
3 4
− (^127) 12 3 4
= 54 + ( −7 6 ) +^23 [ − ( −2 3 ) = 23 ]
= 5×3+(−7)×2+2×4 12
= 12÷39÷
− 3 4 (^44) (^3) − 3
− 3
is ( )
−
ab ab = ba
−3 − 4
= −3^4
= −3×(−1)4×(−1)
Hence, the correct answer is op on (c).
Q4. Which of the following ra onal numbers is nega ve?
1 Mark
Ans: 4. Solu on:
Q5. Mark against the correct answer in the following: in standard form is:
None of these.
1 Mark
Ans: 2. Solu on:
H.C.F of 33 and 55 is 11
Q6. Mark against the correct answer in the following:
Not defined.
1 Mark
Ans: 4. Not defined. Solu on: This is because is not defined.
Q7. Mark against the correct answer in the following: What should be subtracted from to get
1 Mark
Ans: (^) 2. Solu on: The correct op on is (b). Let the number that is to be subtracted be x.
− −8 9 (^83) − 3 −
−( −3 7 ) =^37
−7^3 = −3 7
33 −55 (^3) −5− (^533) −
− 5
= −33÷1155÷11 = −3 5
−3 8 ÷ = 0?
− 8
− 3
−3 8 ÷ 0
−
5 19 6 (^12) − 112 (^12) − 12 − 12
−3 4 − x = 56
⇒ −x = 56 − ( −3 4 )
Q12. What is the mul plica ve iden ty element in the set of whole numbers?
- 0
- 1
- None of these.
1 Mark
Ans: 2. 1 Solu on: We know that if a is a whole number, then a × 1 = a = 1 × a. Therefore, 1 is the mul plica ve iden ty element for mul plica on of whole numbers because it does not change the iden ty or value of the whole number during the opera on of mul plica on. Hence, the correct answer is op on (b).
Q13. The mul plica ve inverse of of:
1 Mark
Ans: 3. Solu on: We know that the mul plica ve inverse of the ra onal number Mul plica ve inverse of Hence, the correct answer is op on (c).
Q14. Mark against the correct answer in the following:
1 Mark
Ans: 2. Solu on: The correct op on is (b).
LCM of 3 and 7 is 21
Q15. Which of the following is not zero?
1 Mark
Ans: 4. Solu on: If any number is mul plied by 0, the product is 0.
If 0 is divided by any number the quo ent is always 0.
Division of any number by 0 is meaningless and is not defined. is not defined. Hence, the correct answer is op on (d).
Q16. What should be subtracted from to get 1 Mark
4 −
5 (^45) −4− − 5 −
ba^ is ba
∴ −5^4 = −5 4 = −4^5
5 (^21) − 21
2 3
12 7
0 × 0
0 (^3) 7− 3
9 ÷ 0
9 ÷ 0
∴ 0 × 0 = 0
∴ 03 and 7−7 3 = 03 = 0
∴ 9 ÷ 0
−
4 5
Ans: 2. Solu on: Difference of the given number and required number Given number Required number = Given number - Difference of the numbers
Hence, the correct answer is op on (b).
Q17.
1 Mark
Ans: (^) 2. Solu on:
Hence, the correct answer is op on (b).
Q18. Mark against the correct answer in the following:
1 Mark
Ans: 3. Solu on: The correct op on is (c).
LCM of 13 and 15 is 195
Q19. Mark against the correct answer in the following: then the value of x is:
- 14
- 21
1 Mark
22 (^15) − 1515 (^22) − 22 − 15
= −2 3 −^45
= −2×5+(−4)×3 15
8 (^13) − −18^13 1813 13 − 13
⇒? = −1 + 135 [ − ( −5 13 = 135 )]
⇒? = −1×13+5 13
− 181195 (^1951) (^195) − 195 1 195
−6 13 − [−7] 15
−6 13 −[−7] 15
if x 6 = −3^7
Hence, the correct answer is op on (a).
Q24. The whole number nearest to 457 and divisible by 11 is:
- 450
- 451
- 460
- 462
1 Mark
Ans: 4. 462 Solu on: The numbers 450 and 460 are not divisible by 11. Now, both the numbers 451 and 462 are divisible by 11. Distance between 457 and 451 on the number line = 457 - 451 = 6 Distance between 457 and 462 on the number line = 462 - 457 = 5 Thus, the whole number nearest to 457 and divisible by 11 is 462. Hence, the correct answer is op on (d).
Q25. The reciprocal of is:
- 3
- 2
- 0
1 Mark
Ans: 2. 2 Solu on: (b) Reciprocal of
Q26. The standard form of is:
1 Mark
Ans: 3. Solu on: Given ra onal number is For standrad/ simplest form, divide numerator and denomin by their HCF i.e. Hence, the standard form of is
Q27.
1 Mark
Ans: 2. Solu on:
Hence, the correct answer is op on (b).
Q28. Mark against the correct answer in the following: The product of two numbers is If one of them is the other number is:
1 Mark
⇒ x = −
1 2
2 − 48 60 (^60) − −4^48 −4^5 − − 5
−
− 5
− 117 −45^7 457 7 11 7
⇒? = − 177 +^41
⇒? = −17×1+4×7 7
− 6
− −4^8 15
Ans: 2. Solu on: Let the other number to be x
Q29. Mark against the correct answer in the following: in standard form is:
None of these.
1 Mark
Ans: (^) 2. Solu on:
H.C.F of 102 and 119 is 17
The standard from of
Q30. How many ra onal numbers are there between two ra onal numbers?
- 1
- 0
- Unlimited.
- 100
1 Mark
Ans: 3. Unlimited. Solu on: (c) There are unlimited numbers between two ra onal numbers.
Q31. Which of the following is correct?
1 Mark
Ans: (^) 1. Solu on: Consider the ra onal numbers We write the ra onal number with posi ve denominator.
Now, we write the ra onal numbers so that they have a common denominator. LCM of 8 and 9 = 72 So, and Now,
4 (^1515) −15^4 4 4 15
−5 8 × x = −1 6
⇒ x = −1 6 ÷ ( −5 8 )
= −1 6 × ( −5^8 )
− (^119) − −6^7 −6^7 17
− 7
= −102÷11119÷17 = −6 7
−102 119 is −6 7
−3^2 < −8 7
−3^4 > −8 7
59 and−3−
− −
−3−8 = −3×(−1)−8×(−1) = 38
59 = 5×89×8 = 4072 38 = 3×98×9 = 2772
Ans: 1. Solu on: Let the number to be subtracted be x
LCM of 3 and 4 is 12
Q36. Mark against the correct answer in the following: Which is larger out of and
Cannot be compared.
1 Mark
Ans: 1. Solu on: The correct op on is (a).
LCM of 3 and 5 is 15 and Thus is greater than
Q37. Which of the following is equivalent to
1 Mark
Ans: 3. Solu on: Given ra onal number is So, equivalent ra onal number [Mul pying numerator and denominator by 4] Note: If the numerator and denominator of a ra onal number is mul plied/divided by a non-zero integer, then the result we get, is equivalent ra onal number.
Q38. The product is equal to:
1 Mark
Ans: 3. Solu on:
Hence, the correct answer is op on (c).
Q39. Which of the following ra onal numbers is equal to its reciprocal?
1 Mark
− −12^17 17 − 12
⇒ x = −2 3 −^34
− 12
2
− 2 5 − 2 −
2 −
−3×−12×1^ = −2 3
∴ −2×53×5 = −10 15 −4×35×3 = −12 15
2 −
− 5
4 (^516) (^2516) (^2015) 25 16 20
= 4×45×
3 × 17 × 1 56 × 1 25 × 1 111
3 17 × 1 56 × 1 25 × 1 111
= 227 × 116 × 75 ×^1211
= 22×11×7×27×6×5×11 ( ab × cd = b×da×c)
= 8×5+4 5
Ans: 1. Solu on:
- Reciparocal of
- Reciparocal of
- Reciparocal of
- Reciparocal of Note: 1 is the only number, which is equal its recprocal.
Q40. Which is greater number in the following?
1 Mark
Ans: 3. Solu on: (c) Obviously, is greater, since this is ony number which is on the rightmost side of the number line among others.
Q41. Which of the following pairs of ra onal numbers are on the opposite side of the zero on the number line?
None of these.
1 Mark
Ans: 3. Solu on: The ra onal numbers are posi ve ra onal numbers. We know that every posi ve ra onal number is greater than 0, so both the ra onal numbers are represented by points on the right of the zero on the number line. The ra onal numbers are nega ve ra onal numbers. We know that every nega ve ra onal number is less than 0, so both the ra onal numbers are represented by points on the le of the zero on the number line. The ra onal numbers is a posi ve ra onal number whereas the ra onal number is a nega ve ra onal numbers. We know that every nega ve ra onal number is less than 0 and every posi ve ra onal number is greater than 0, so the ra onal number is represented by point on the right of the zero and is represented by point on the le of the zero on the number line. Thus, the ra onal numbers are on the opposite side of the zero on the number line. Hence, the correct answer is op on (c).
Q42. Mark against the correct answer in the following:
None of these.
1 Mark
Ans: 1. Solu on:
Q43. Mark against the correct answer in the following: 1 Mark
1 2
2
1 −
1 2
1 2 1 2
37 and 125
− 37 and −5 12
37 and −5 12
37 and −5 12
37 and 125
37 and 125
− 37 and −5 12
37 and 125
3 7
− (^12 ) −5^7 12
− 37 and −5 12
78 34 ÷ 2 12 =?
78 34 ÷ 2 12 = 3154 ÷^52
= 3154 ×^25
Hence, the correct answer is op on (d).
Q47. Mark against the correct answer in the following:
1 Mark
Ans: (^) 1. Solu on:
Q48. Mark against the correct answer in the following: Reciprocal of -6 is:
None of these.
1 Mark
Ans: (^) 3. Solu on: The correct op on is (c). Reciprocal of
Q49. A ra onal number equal to is:
None of these.
1 Mark
Ans: 2. Solu on: We know that two ra onal numbers are equal if they have the same standard form. The ra onal number is in its standard form. Consider the ra onal number This ra onal numbner can be expressed in standerd form as follows: (Mul plying numerator and denominator by -1 to make denominator posi ve) HCF of 10 and 15 = 5 Dividing the numeator and denominator of by 5, We have:
Thus, the standard form of is which is same as the given ra onal number. So, the ra onal number equal to is Let us check why op ons (a) and (c) are not correct. The standard form of HCF of 10 and 25 = 5
= 21 +^79
= 2×9+7×1 9
−3 14 ×? = 125
− 3518 (^187) (^3) − 3 − 18
? = 125 ÷ (−3) 14
= 125 × (−3)^14
= −36^70
= −18×−135×−
1 (^6) − 6
− 6
−6 is −1 6
− −10^3 (^2510) −15− 6
10 −
− (^3 ) −
−15^10 =^ −15×(−1)10×(−1) = −10 15
− 15
−10 15 = −10÷515÷5 = −2 3
−
− −2^3 3
− 15
−10 25 is −2 5
Dividing the numerator and denominator of by 5, We have:
The standard form of HCF of 6 and 9 = 3 Dividing the numerator and denominator of by 3, We have:
Hence, the correct answer is op on (b)
Q50. Mark against the correct answer in the following:
1 Mark
Ans: 2. Solu on:
Q51. In the standard form of a ra onal number, the common factor of numerator and denominator is always:
- 0
- 1
- 2
1 Mark
Ans: 2. 1 Solu on: (b) By defini on, in the standard form of a ra onal number, the common factor of numerator and denominator is always1. Note: Common factor means, a number which divides both the given two numbers.
Q52. Mark against the correct answer in the following: Which is greater between and
Both are equal.
1 Mark
Ans: 2. Solu on: The correct op on is (b). is greater than LCM of 9 and 12 is 36
Q53. In the standard form of a ra onal number, the denominator is always a:
- 0
- Nega ve integer.
- Posi ve integer.
- 1
1 Mark
Ans: 3. Posi ve integer. Solu on: (c) By defini on, a ra onal number is said to be in the standard form, if its denominator is a posi ve integer.
−10 25 = −10÷525÷5 = −2 5
−9 6 is −3 2
− 3
−9 6 = −9÷36÷2 = −3 2
1 ÷ 12 =?
1 2
1 ÷ 12
= 1 × 21
−
− −4^12 −5^9 12
− 12
− 12
− 9
−5×312×3 = −15 36
−4×412×4 = −16 36
(Dividing both sides by -2)
Hence, the correct answer is op on (b).
Q58.
None of these.
1 Mark
Ans: 4. None of these. Solu on:
(LCM of 13 and 15 = 195)
Hence, the correct answer is op on (d).
Q59. If is expressed as a ra onal number with denominator 5, then the numerator is:
- 3
- 6
1 Mark
Ans: 2. - Solu on: In order to express as a ra onal number with denominator 5, firstly find a number which gives 5 when -45 is divided by it. This number is Dividing the numerator and denominator of by -9, We have:
Thus, the numerator is -3. Hence, the correct answer is op on (b).
Q60. is standard form is:
None of these
1 Mark
Ans: 2. Solu on: The denominator of is naga ve. Hence, the correct answer is op on (b).
Q61. What is the addi ve iden ty element in the set of whole numbers?
- 0
- 1
- None of these.
1 Mark
Ans: 1. 0 Solu on: If a is a whole number then a + 0 = a = 0 + a. Therefore, 0 is the addi ve iden ty element for addi on of whole number because it does not change the iden ty or value of the whole number during the opera on of addi on.
⇒ −2x = 12
⇒ −2x−2 = −2^12
⇒ x = −
29 (^195) − 195
= −7 13 + 158 [ − ( −8 15 ) = 158 ]
= −7×15+8×13 195
27 −
27 −
−45 ÷ 5 = −
27 −
−45^27 =^ −45÷(−9)27÷(−9) = −3 5
44 −77 (^4) −
44 −
Hence, the correct answer is op on (a).
Q62. Mark against the correct answer in the following:
- Not defined
1 Mark
Ans: 3. Solu on:
Q63. Mark against the correct answer in the following: What should be added to to get 1?
1 Mark
Ans: 3. Solu on: The correct op on is (c). should be added to to get 1.
Let the required number be x.
Q64. Mark against the correct answer in the following: in standard form is:
None of these.
1 Mark
Ans: 1. Solu on:
H.C.F. of 55 and 66 is 11
is the standard from.
0 ÷ −7 5 =?
− 7
5 7
0 ÷ −7 5 =?
− 4 9 (^9) − 149 −14^9 9 14 9
14 9
− 9
x + ( −5 9 ) = 1x
= 1 − (−5) 9 = 9+5 9 =^149
55 −66 (^5) −6 − −55^6 66
5 −
= −66^55 = −66×(−1)55×(−1) = −55 66
= 55÷1166÷11 = −5 6
