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Q1. Which of the following equations cannot be formed using the equation x = 7? 2x + 1 = 15 7x 1 = 50 x 3 = 4
1 Mark
Ans: 7x 1 = 50 Solution: We have, x = 7 On multiplying both the sides by 7, we get 7 x = 7 7 7x = 49 On adding 1 both the sides, we get 7x + 1 = 49 + 1 7x - 1 = 49 - 1 ⇒ 7x - 1 = 48
Q2. Shifting one term from one side of an equation to another side with a change of sign is known as: Commutativity. Transposition. Distributivity. Associativity.
1 Mark
Ans: Transposition. Solution: Transposition means shifting one term from one side of an equation to another side with a change of sign.
Q3. Mark against the correct answer in the following: If , then x =? 8 16 24 30
1 Mark
Ans: 30 Solution:
Q4. If 2 2n + 5 = 3 3n 10 , then n = 5 3 7 8
1 Mark
Ans: 8 Solution: As, 2 2n + 5 = 3 3n - 10 ⇒ 4n + 10 = 9n - 30 ⇒ 4n - 9n = 10 - 30 By transposing 10 to R.H.S. and 9n to L.H.S.) ⇒ 5n = 40 ⇒ n = 40 - 5 By transposing 5 to R.H.S.)
x 7 − 1 = 0
x 2 − x 3 = 5
x 2 − x 3 = 5
⇒ 3x−2x 6 = 5
⇒ x = 30
Hence, the correct alternative is option (d).
Q5. If then x =
1 Mark
Ans: Solution: As, By transpoing to R.H.S. and 5x to L.H.S.)
By transposing 3 to R.H.S.)
Hence, the correct alternative is option (b).
Q6. If then x =
1 Mark
Ans:
Solution: As, By transposing to R.H.S. and to L.H.S.)
By cross multiplication)
Hence, the correct alternative is option (d).
Q7. Mark against the correct answer in the following: A number when multiplied by 4 is increased by 54. The number is 21 16 18 19
1 Mark
Ans: 18 Solution: Let the number be x. According to the equation, we have: 4x = x + 54 ⇒ 3x = 54 ⇒ x = 18
Q8. Mark against the correct answer in the following: Two supplementary angles differ by 20°. The smaller of the two measures:
1 Mark
∴ n = 8
2x − 32 = 5x + 34 ,
3 4
4 3
2x − 32 = 5x +^34
⇒ 2x − 5x = 34 +^34 − 32
⇒ −3x = 64 +^34
⇒ −3x = 6+3 4
⇒ x = 4×(−3)^9
⇒ x = 4×(−1)^3
⇒ x = −4^3
∴ x = − 34
2x + 53 = 14 x + 4,
3 (^44) 3 4 3
2x + 53 = 14 x + 4
⇒ 2x − 14 x = 4 −^5353 14 x
⇒ 2x 1 − x 4 = 41 −^53
⇒ 8x 4 − x 4 = 123 −^53
⇒ 8x−x 4 = 12−5 3
⇒ 7x 4 =^73
⇒ 7x × 3 = 4 × 7
⇒ 21x = 28
⇒ x = 2821
∴ x = 43
Ans: 18 Solution: As, By transposing to L.H.S. and 4 to R.H.S.)
By transposing 6 to R.H.S.)
Hence, the correct alternative is option (c).
Q12. Mark against the correct answer in the following: If 8 2x - 5 - 6 3x - 7 = 1, then x ?
1 Mark
Ans:
Solution: 8 2x 5 6 3x 7 = 1 ⇒ 16x 40 18x + 42 = 1 ⇒ 2x + 2 = 1 ⇒ 2x = 1 2 = 1
Q13. Mark against the correct answer in the following: A number when multiplied by 5 is increased by 80. The number is: 15 20 25 30
1 Mark
Ans: 20 Solution: Let the number = x According to the condition, 5x = 80 + x ⇒ 5x - x = 80 ⇒ 4x = 80 ⇒ x = 20 Number = 20
Q14. Mark against the correct answer in the following: The sum of two consecutive even numbers is 86. The larger of the two is: 46 36 38 44
1 Mark
Ans: 44 Solution: Let first even number = 2x Then second number = 2x + 2 And sum = 86 2x + 2x + 2 86 ⇒ 4x = 86 2 = 84
x 2 − 4 = x 3 − 1
⇒ x 2 − x 3 = 4 − 1^ x 3
⇒ 3x 6 − 2x 6 = 3
⇒ 3x−2x 6 = 3
⇒ x 6 = 3
⇒ x = 3 × 6
∴ x = 18
1 (^21) 3 1 2
x = 12
⇒ x = 21 Larger even number = 2x + 2 = 2 21 + 2 = 42 + 2 = 44
Q15. Mark against the correct answer in the following: The length of a rectangle is three times its width and its perimeter is 96 m. The length is: 12m 24m 36m 48m
1 Mark
Ans: 36m Solution: Let width of rectangle = xm Then length = 3xm Perimeter = 96m 2 (x + 3x) = 96
⇒ 4x = 48 ⇒ x = 12 Length = 3x = 12 3 = 36m
Q16. Mark against the correct answer in the following: If then x ?
1 Mark
Ans:
Solution:
Q17. Twice a number when increased by 7 gives 25. The number is: 7 9 10 8
1 Mark
Ans: 9 Solution: Let the number be x. As, twice the number when increased by 7 gives 25. ⇒ 2x + 7 = 25 ⇒ 2x = 25 - 7 By transposing 7 to R.H.S.) ⇒ 2x = 18 By transposing 2 to R.H.S.)
So, the number is 9. Hence, the correct alternative is option (b).
Q18. The length of a rectangle is three times its width and its perimeter 56m. The length is: 7m 14m 21m 28m
1 Mark
⇒ x + 3x = 962 = 48
5x − 34 = 2x −^23
1 (^121) 4
1 36 1 36
5x − 34 = 2x −^23
⇒ 5x − 2x = − 23 +^34
⇒ 3x = −8+9 12
⇒ 3x = 121
⇒ x = 12×3^1
⇒ x = 182
∴ x = 9
Given equation is 3x 7 = 20 ⇒ 3x = 20 - 7 [transposing 7 to RHS ⇒ 3x = 27 On dividing the above equation by 3, we get x = 9 Hence, the solution of the given equation is 9.
Q22. Mark against the correct answer in the following: If , then x =?
1 Mark
Ans:
Solution:
Q23. If then x = 9 6 9 4
1 Mark
Ans: 9 Solution: As, By transposing to L.H.S.)
By cross multiplication)
Hence, the correct alternative is option (c).
Q24. The solution of the equation ax + b = 0 is:
1 Mark
Ans: Solution: Given equation is ax + b = 0 [transposing b to RHS [on dividing both sides by a]
Q25. Which of the following is not allowed in a given equation? Adding the same number to both sides of the equation. Subtracting the same number from both sides of the equation. Multiplying both sides of the equation by the same non-zero number. Dividing both sides of the equation by the same number.
1 Mark
2x + 53 = 14 x + 4
3 (^44) 3 4 3
2x + 53 = 14 x + 4
⇒ 2x − 14 x = 4 −^53
⇒ 8x−1x 4 = 12−5 3
⇒ 7x 4 =^73
⇒ 21x = 28
⇒ x = 2821 =^43
x 6 + x 4 = x 2 + 34 ,
x 6 + x 4 = x 2 +^34
⇒ x 6 + x 4 − x 2 =^34 x 2
⇒ 2x 12 + 3x 12 − 6x 12 =^34
⇒ 2x+3x−6x 12 =^34
⇒ −x 12 =^34
⇒ −x × 4 = 3 × 12
⇒ −4x = 36
⇒ x = −4^36
∴ x = −
a b
−b
− ba
b a
− ba
⇒ ax = −b
⇒ x = − ba
Ans: Dividing both sides of the equation by the same number. Solution: Dividing both sides of the equation by the same non-zero number is allowed in a given equation, division of any number by zero is not allowed as set division of number by zero is not defined. Note: If we add same number to both sides of the equation while adding subtracting, then there will be no change in the given equation.
Q26. Mark against the correct answer in the following: If , then x ? 6 7 8 10
1 Mark
Ans: 8 Solution:
Q27. If then x =
1 Mark
Ans: Solution: As, By cross multiplication)
By transposing 2x to L.H.S. and 6 to R.H.S.)
Hence, the correct alternative is option (a).
Q28. If k + 7 = 16, then the value of 8k 72 is: 0 1 112 56
1 Mark
Ans: 0 Solution: Given equation is k + 7 = 6 On transposing 7 to RHS, we get k = 16 - 7 = 9 Put the value of k in the equation 8k - 72 , we get 8 9 - 72 = 72 - 72 = 0
Q29. Mark against the correct answer in the following: Two complementary angles differ by 14°. The larger angle is: 50° 52° 54° 56°
1 Mark
Ans: 52° Solution: Let the two complementary angles be x° and 90 - x)°.
x−1x+1 = 79
x−1x+1 = 79
⇒ 9x − 9 = 7x + 7
⇒ 9x − 7x = 7 + 9
⇒ 2x = 16
⇒ x = 162 = 8
x+2x−2 = 23 ,
4 3
x+2x−2 = 23
⇒ 3(x + 2) = 2(x − 2)
⇒ 3x + 6 = 2x − 4
⇒ 3x − 2x = −6 + 4
∴ x = −
⇒ x - 31 = 81 - x ⇒ x + x = 81 + 31 By transposing -x to L.H.S. and 31 to R.H.S.) ⇒ 2x = 112 By transposing 2 to R.H.S.)
So, the number is 56. Hence, the correct alternative is option (b).
Q34. Mark against the correct answer in the following: Thrice a number when increased by 6 gives 24. The number is: 6 7 8 11
1 Mark
Ans: 6 Solution: Let number = x then 3x + 6 = 24 ⇒ 3x = 24 6 = 18 ⇒ x = 6 Number = 6
Q35. of a number is less than the original number by 20. The number is: 30 40 50 60
1 Mark
Ans: 60 Solution: Let the number be x. As, 23 of the number is less than the original number by 20.
By transposing 3 to R.H.S.)
So, the number is 60. Hence, the correct alternative is option (d).
Q36. If a and b are positive integers, then the solution of the equation ax = b will always be a. Positive number. Negative number. 1 0
1 Mark
Ans: Positive number. Solution: Given equation is ax = b On dividing the equation by a, we get
Now, if a and b are positive integers, then the solution of the equation is also positive number as division of two positive integers is also a positive number.
Q37. The equation having 3 as a solution is: x + 3 = 1 8 + 2x = 3
1 Mark
∴ x = 1122
∴ x = 56
2 3
⇒ x − 23 x = 20
⇒ x 1 − 2x 3 = 20
⇒ 3x 3 − 2x 3 = 20
⇒ 3x−2x 3 = 20
⇒ x 3 = 20
⇒ x = 20 × 3
∴ x = 60
x = ba
10 + 3x = 1 2x + 1 = 3
Ans: 10 + 3x = 1 Solution: Let us solve the equation: Given equation is x + 3 = 1 ⇒ x = 1 - 3 ⇒ x = 2 Given equation is 8 + 2x = 3 ⇒ 2x = 3 - 8 ⇒ 2x = 5
Given equation is 10 + 3x = 1 ⇒ 3x = 1 - 10 ⇒ 3x = 9 ⇒ x = 3 Now, we don't have to solve next equation as we get the answer.
Q38. Two complementary angles differ by 20º. The smaller angle is: 55º 25º 65º 35º
1 Mark
Ans: 35º Solution: Let the smaller angle be x. Then,The larger angle = (x + 20°) As, the sum of the two complementary angles is always 90°. ⇒ x + (x + 20°) = 90° ⇒ 2x + 20° = 90° ⇒ 2x = 90° - 20° ⇒ 2x = 70° By transposing 2 to R.H.S.)
So, the smaller angle is 35°. Hence, the correct alternative is option (d).
Q39. The solution of which of the following equations is neither a positive fraction nor an integer? 2x + 6 = 0 3x 5 0 5x 8 = x + 4 4x + 7 = x +
1 Mark
Ans: 4x + 7 = x + Solution: Let us solve the equation: Given equation is 2x + 6 = 0 [transposing 6 to RHS [dividing both sides by 2 (integer) Given equation is 3x - 5 = 0 [transposing 5 to RHS (fraction) [dividing both sides by 3 Given equation is 5x - 8 = x + 4 [transposing 8 to RHS
[transposing x to LHS
⇒ x = − 52
⇒ x = 70
∘ 2
∴ x = 35∘
⇒ 2x = −
⇒ x = − 62
⇒ x = −
⇒ 3x = 5
⇒ k = 53
⇒ 5x = x + 4 + 8
⇒ 5x = x + 12
⇒ 5x − x = 12
⇒ 4x = 12
⇒ x + (x - 40°) = 180° 2x - 40° = 180° ⇒ 2x = 180° + 40° ⇒ 2x = 220° By transposing 2 to R.H.S.)
So, the measure of the larger angle is 110°. Hence, the correct alternative is option (c).
Q43. Which of the following numbers satisfy the equation 6 + x = 12? 2 6 6 2
1 Mark
Ans: 6 Solution: Let us put the values given in the options in equation 6 + x = 12 Put x = 2 ⇒ 6 + 2 = 2 ⇒ 4 = 12 LHS RHS Put x = 6 ⇒ 6 + 6 = 12 ⇒ 0 = 12 LHS RHS Put x = 6 ⇒ 6 + 6 = 12 ⇒ 6 - 6 = 12 ⇒ 12 = 12 LHS = RHS (satisfied) Now, there is no need to check the next option. Hence, x = 6 satisfied the given equation.
Q44. Mark against the correct answer in the following: Two complementary angles differ by 10°. The larger angle is: 60° 50° 64° 54°
1 Mark
Ans: 50° Solution: Let first angle = x Then second = 90° - x x - 90° - x) = 10 ⇒ x 90° + x = 10° ⇒ 2x = 10° + 90° = 100° x = 50° Second angle = 90° 50° = 40° Larger angle = 50°
Q45. The zero of 3 x + 2 is:
1 Mark
Ans:
Solution:
⇒ x = 220
∘ 2
∴ x = 1106∘
− 2
If 3x + 2 = 0, then 3x = 2 Transposing 2 to R.H.S.)
So, the zero of 3x + 2 is Note: A zero is that number, when put in place of the variable, makes the expression equal to zero. Hence, the correct alternative is option (c).
Q46. Which of the following equations can be formed starting with x = 0? 2x + 1 = 1 3x 1 = 1 3x 1 = 1
1 Mark
Ans: 3x 1 = 1 Solution: We have, x = 0 On multiplying both the sides by 3, we get 3 x = 3 0 ⇒ 3x = 0 On adding 1 both the sides, we get 3x + 1 = 0 + 1 ⇒ 3x - 1 = 1
Q47. Mark against the correct answer in the following: of a number is less than the original number by 10. The original number is: 30 36 45 60
1 Mark
Ans: 30 Solution:
Q48. Mark against the correct answer in the following: The sum of two consecutive odd numbers is 36, the smaller one is: 15 17 19 13
1 Mark
Ans: 17 Solution: Let first odd number = 2x + 1 Second number = 2x + 3 2x + 1 + 2x + 3 = 36 ⇒ 4x + 4 = 36 ⇒ 4x = 36 4 = 32 ⇒ x = 8 Smaller number = 2x + 1 = 2 8 + 1 = 16 + 1 = 17
Q49. If the sum of a number and its two-fifth is 70. The number is: 70 50 60 90
1 Mark
Ans: 50
⇒ x − 23
x 2 + 5 = 7
2 3
∴ 23 x = x − 10
⇒ x − 23 x = 10
⇒ 13 x = 10
⇒ x = 30
So, the smaller number is 21. Hence, the correct alternative is option (a).
Q52. The sum of three consecutive odd numbers is 81. The middle number is: 25 27 31 29
1 Mark
Ans: 27 Solution: Let the three consecutive odd numbers be x, x + 2 and x + 4. As, the sum of the three consecutive numbers is 81. ⇒ x + (x + 2 + (x + 4 = 81 ⇒ 3x + 6 = 81 ⇒ 3x = 81 - 6 By transposing 6 to R.H.S.) ⇒ 3x = 75 By transposing 3 to R.H.S.)
So, the middle number is 27. Hence, the correct alternative is option (b).
Q53. Mark against the correct answer in the following: On adding 9 to the twice of a whole number gives 31 The whole number is: 21 16 17 11
1 Mark
Ans: 11 Solution: Let number = x 2x + 9 = 31 ⇒ 2x = 31 9 = 22 ⇒ x = 11
Q54. Mark against the correct answer in the following: The sum of two consecutive whole numbers is 53. The smaller number is: 25 26 29 23
1 Mark
Ans: 26 Solution: Let first whole number = x Then second number = x + 1 And sum = 53 x + x + 1 = 53 ⇒ 2x = 53 1 ⇒ 2x = 52 ⇒ x = 26 Smaller number = 26
Q55. The sum of two consecutive odd numbers is 36. The larger number is: 17 15 19 21
1 Mark
∴ x = 21
⇒ x = 753
⇒ x = 25
∴ x + 2 = 25 + 2 = 27
Ans: 19 Solution: Let the two consecutive odd numbers be x and x + 2. As, the sum of the two consecutive odd numbers is 36. ⇒ x + (x + 2 = 36 ⇒ 2x + 2 = 36 ⇒ 2x = 36 - 2 ⇒ 2x = 34
⇒ x = 17 x + 2 = 17 + 2 = 19 So, the larger number is 19. Hence, the correct alternative is option (c).
Q56. x Exceeds 3 by 7, can be represented as: x + 3 = 2 x + 7 = 3 x 3 = 7 x 7 = 3
1 Mark
Ans: x 7 = 3 Solution: The given statement means x is 7 more than 3. So, the equation is x 7 = 3 We can also write it as x 3 = 7.
Q57. If 43m = 0.086, then the value of m is: 0. 0. 0. 2
1 Mark
Ans: 0. Solution: Given equation is 43m = 0. On dividing the given equation by 43, we get
If we remove the decimal, we get 1000 in denominator
Q58. Mark against the correct answer in the following: If 2n + 5 = 3 3n - 10 , then n ?
1 Mark
Ans: 5 Solution: 2n + 5 = 3 3n 10 ⇒ 2n + 5 = 9n 30 ⇒ 9n 2n = 5 + 30 ⇒ 7n = 35 ⇒ n = 5
⇒ x = 342
m = 0.086 43
m = 8643 × 10001 = 10001 = 0.
2 (^52) 3
