example-1Multiple choice
4a equals
- (A)4 + a
- (B)4 × a
- (C)a × a × a × a
- (D)4 ÷ a
Show solution
Solution: Correct answer is (B).
Chapter 7 – Algebra
Class 6 Mathematics · 99 questions · 66 with answers
Solved examples
example-2Multiple choice
8 more than three times the number x can be represented
- (A)8 + x + 3
- (B)3 x – 8
- (C)3 x + 8
- (D)8 x + 3
Show solution
Solution: Correct answer is (C). 11.4.2018 UNIT-7
example-3Multiple choice
Which of the following is an equation?
- (A)x + 7
- (B)2y +3 = 7
- (C)2p < 10
- (D)12x
Show solution
Solution: Correct answer is (B)
example-4Fill in the blanks
Fill in the blanks to make it a true statement: 7 times of y subtracted from 50 can be expressed as ________
Show solution
Solution: 50 – 7y
example-5True / False
State true or false: x = 5 is a solution of the equation 3 – x = 8
Show solution
Solution: False Give an expression for each of the examples 6 to 8:
example-6Short answer
13 subtracted from thrice of a number.
Show solution
Solution: Let the number be x. Thrice of the number is 3x. 13 subtracted from it is the expression 3x – 13.
example-7Short answer
Megha’s age (in years) is 2 more than 5 times her daughter’s age.
Show solution
Solution: Let the daughter’s age be m years. 5 times of m is 5m.
example-8Short answer
Anagha, Sushant and Faizal are climbing the steps to a hill top. Anagha is at the step p. Sushant is 10 steps ahead and Faizal is 6 steps behind Anagha. Where are Sushant and Faizal? The total number of steps to the hill top is 3 steps less than 8 times what Anagha has reached. Express the total number of steps using p.
Show solution
Solution: Anagha is at step p. Sushant is 10 steps ahead of Anagha. That is, he is at the step p + 10. 11.4.2018 MATHEMATICS Faizal is 6 steps behind Anagha. That is, he is at step p – 6. 8 times of p = 8p
example-9Short answer
Cost of a pencil is Rs x. A pen costs Rs 6x.
Show solution
Solution: Cost of a pen is 6 times the cost of a pencil.
example-10Short answer
Manisha is z years old. Her uncle is 5z years old and her aunt is (5z – 4) years old.
Show solution
Solution: Manisha’s uncle is five times of Manisha’s age. Her aunt is 4 years younger than her uncle.
Questions
Q2Short answer
more than 5m is the expression 5m + 2. The age of Megha (in years) is (5m + 2).
Show answer
(C)
Q3Short answer
less than 8p = 8p – 3 So, the total number of steps = 8 p – 3 In examples 9 and 10, change the statements, converting expressions into statements in ordinary language.
Show answer
(A)
Q1Multiple choice
If each match box contains 50 matchsticks, the number of matchsticks required to fill n such boxes is
- (A)50 + n
- (B)50n
- (C)50 ÷ n
- (D)50 – n
Show answer
(B) 50n
Q2Multiple choice
Amulya is x years of age now. 5 years ago her age was
- (A)(5 – x) years
- (B)(5 + x) years
- (C)(x – 5) years
- (D)(5 ÷ x) years
Show answer
(C) (x – 5) years
Q3Multiple choice
Which of the following represents 6 × x
- (A)6x
- (B)
- (C)6 + x
- (D)6 – x
Show answer
(A) 6x
Q4Multiple choice
Which of the following is an equation?
- (A)x + 1
- (B)x – 1
- (C)x – 1 = 0
- (D)x + 1 > 0
Show answer
(C) x – 1 = 0
Q5Multiple choice
If x takes the value 2, then the value of x + 10 is
- (A)20
- (B)12
- (C)5
- (D)8 ALGEBRA 107 11.4.2018 UNIT-7
Show answer
(B) 12
Q6Multiple choice
If the perimeter of a regular hexagon is x metres, then the length of each of its sides is
- (A)(x + 6) metres
- (B)(x ÷ 6) metres
- (C)(x – 6) metres
- (D)(6 ÷ x) metres
Show answer
(B) (x ÷ 6) metres
Q7Multiple choice
Which of the following equations has x = 2 as a solution?
- (A)x + 2 = 5
- (B)x – 2 = 0
- (C)2x + 1 = 0
- (D)x + 3 = 6
Show answer
(B) x – 2 = 0
Q8Multiple choice
For any two integers x and y, which of the following suggests that operation of addition is commutative ?
- (A)x + y = y + x
- (B)x + y > x
- (C)x – y = y – x
- (D)x × y = y × x
Show answer
(A) x + y = y + x
Q9Multiple choice
Which of the following equations does not have a solution in integers?
- (A)x + 1 = 1
- (B)x – 1 = 3
- (C)2x + 1 = 6
- (D)1 – x = 5
Show answer
(C) 2x + 1 = 6
Q10Multiple choice
In algebra, a × b means ab, but in arithmetic 3 × 5 is
- (A)35
- (B)53
- (C)15
- (D)8
Show answer
(C) 15
Q11Multiple choice
In algebra, letters may stand for
- (A)known quantities
- (B)unknown quantities
- (C)fixed numbers
- (D)none of these
Show answer
(B) unknown quantities
Q12Multiple choice
“Variable” means that it
- (A)can take different values
- (B)has a fixed value
- (C)can take only 2 values
- (D)can take only three values
Show answer
(A) can take different values
Q13Multiple choice
10 – x means
- (A)10 is subtracted x times
- (B)x is subtracted 10 times
- (C)x is subtracted from 10
- (D)10 is subtracted from x
Show answer
(C) x is subtracted from 10
Q14Multiple choice
Savitri has a sum of Rs x. She spent Rs 1000 on grocery, Rs 500 on clothes and Rs 400 on education, and received Rs 200 as a gift. How much money (in Rs) is left with her?
- (A)x – 1700
- (B)x – 1900
- (C)x + 200
- (D)x – 2100 11.4.2018
Show answer
(A) x – 1700
Q15Multiple choice
The perimeter of the triangle shown in Fig. 7.1 is x x Fig. 7.1
This question refers to a figure in the original PDF.
- (A)2x + y
- (B)x + 2y
- (C)x + y
- (D)2x – y
Show answer
(A) 2x + y
Q16Multiple choice
The area of a square having each side x is
- (A)x × x
- (B)4x
- (C)x + x
- (D)4 + x
Show answer
(A) x × x
Q17Multiple choice
The expression obtained when x is multipled by 2 and then subtracted from 3 is
- (A)2x – 3
- (B)2x + 3
- (C)3 – 2x
- (D)3x – 2
Show answer
(C) 3 – 2x
Q18Multiple choice
= 3 has a solution
- (A)6
- (B)8
- (C)3
- (D)2
Show answer
(A) 6
Q19Multiple choice
x – 4 = – 2 has a solution
- (A)6
- (B)2
- (C)– 6
- (D)– 2
Show answer
(B) 2
Q20Multiple choice
= 2 denotes a
- (A)numerical equation
- (B)algebraic expression
- (C)equation with a variable
- (D)false statement
Show answer
(A) numerical equation
Q21Multiple choice
Kanta has p pencils in her box. She puts q more pencils in the box. The total number of pencils with her are
- (A)p + q
- (B)pq
- (C)p – q p
- (D)
Show answer
(A) p + q
Q22Multiple choice
The equation 4x = 16 is satisfied by the following value of x
- (A)4
- (B)2
- (C)12
- (D)–12
Show answer
(A) 4
Q23Multiple choice
I think of a number and on adding 13 to it, I get 27. The equation for this is
- (A)x – 27 = 13
- (B)x – 13 = 27
- (C)x + 27 = 13
- (D)x + 13 = 27 11.4.2018 UNIT-7 In question 24 to 40, fill in the blanks to make the statements true:
Show answer
(D) x + 13 = 27 11.4.2018 UNIT-7 In question 24 to 40, fill in the blanks to make the statements true:
Q24Fill in the blanks
The distance (in km) travelled in h hours at a constant speed of 40km per hour is __________.
Show answer
40h
Q25Fill in the blanks
p kg of potatoes are bought for Rs 70. Cost of 1kg of potatoes (in Rs) is __________.
Q26Fill in the blanks
An auto rickshaw charges Rs 10 for the first kilometre then Rs 8 for each such subsequent kilometre. The total charge (in Rs) for d kilometres is __________.
Show answer
8d + 2
Q27Fill in the blanks
If 7x + 4 = 25, then the value of x is __________.
Show answer
3
Q28Fill in the blanks
The solution of the equation 3x + 7 = –20 is __________.
Show answer
– 9
Q29Fill in the blanks
‘x exceeds y by 7’ can be expressed as __________.
Show answer
x = y + 7
Q30Fill in the blanks
‘8 more than three times the number x’ can be written as __________.
Show answer
3x + 8
Q31Fill in the blanks
Number of pencils bought for Rs x at the rate of Rs 2 per pencil is __________.
Q32Fill in the blanks
The number of days in w weeks is __________.
Show answer
7w
Q33Fill in the blanks
Annual salary at r rupees per month alongwith a festival bonus of Rs 2000 is __________.
Show answer
12x + 2000
Q34Fill in the blanks
The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is __________.
Show answer
10t + u
Q35Fill in the blanks
The variable used in the equation 2p + 8 = 18 is __________.
Show answer
p
Q36Fill in the blanks
x metres = __________ centimetres
Show answer
100x
Q37Fill in the blanks
p litres = __________ millilitres
Show answer
1000p
Q38Fill in the blanks
r rupees = __________ paise
Show answer
100x
Q39Fill in the blanks
If the present age of Ramandeep is n years, then her age after 7 years will be __________.
Show answer
n+7
Q40Fill in the blanks
If I spend f rupees from 100 rupees, the money left with me is __________ rupees. 11.4.2018 MATHEMATICS In question 41 to 45, state whether the statements are true or false.
Show answer
100 – f
Q41Short answer
0 is a solution of the equation x + 1 = 0
Show answer
F
Q42Short answer
The equations x + 1 = 0 and 2x + 2 = 0 have the same solution.
Show answer
T
Q43Short answer
If m is a whole number, then 2m denotes a multiple of 2.
Show answer
T
Q44Short answer
The additive inverse of an integer x is 2x.
Show answer
F
Q45Short answer
If x is a negative integer, – x is a positive integer.
Show answer
T
Q46Short answer
2x – 5 > 11 is an equation.
Show answer
F
Q47Short answer
In an equation, the LHS is equal to the RHS.
Show answer
T
Q48Short answer
In the equation 7k – 7 = 7, the variable is 7.
Show answer
F
Q49Short answer
a = 3 is a solution of the equation 2a – 1 = 5
Show answer
T
Q50Short answer
The distance between New Delhi and Bhopal is not a variable.
Show answer
T
Q51Short answer
t minutes are equal to 60t seconds.
Show answer
T
Q52Short answer
x = 5 is the solution of the equation 3x + 2 = 20
Show answer
F
Q53Short answer
‘One third of a number added to itself gives 8’, can be expressed as +8=x
Show answer
F
Q54Short answer
The difference between the ages of two sisters Leela and Yamini is a variable.
Show answer
F
Q55Short answer
The number of lines that can be drawn through a point is a variable. In questions 56 to 74, choose a letter x, y, z, p etc...., wherever necessary, for the unknown (variable) and write the corresponding expressions:
Show answer
F
Q56Short answer
One more than twice the number.
Show answer
2x + 1
Q57Short answer
20oC less than the present temperature.
Show answer
t – 20
Q58Short answer
The successor of an integer.
Show answer
n + 1
Q59Short answer
The perimeter of an equilateral triangle, if side of the triangle is m.
Show answer
3m
Q60Short answer
Area of the rectangle with length k units and breadth n units.
Show answer
kn
Q61Short answer
Omar helps his mother 1 hour more than his sister does. ALGEBRA 111 11.4.2018 UNIT-7
Show answer
x + 1
Q62Short answer
Two consecutive odd integers.
Show answer
2n + 1 and 2n + 3
Q63Short answer
Two consecutive even integers.
Show answer
2m and 2m + 2
Q64Short answer
Multiple of 5.
Show answer
5n
Q65Short answer
The denominator of a fraction is 1 more than its numerator.
Show answer
x +1
Q66Short answer
The height of Mount Everest is 20 times the height of Empire State building.
Show answer
20y, where y is height of Empire State Building.67. 2p + 3 68. 13 – (–3) z (=13+3z) 69. 10 + 70. 3x + 1 71. 10 – 6 q 72. 3y + 4 = 10, 2x – 3 = 1 73. 2t + 3 = 3 74. x + 1 = 0 OOLRLPNOV k_rfck_rgaq 75. The cost of pen is 5 times the cost of a pencil. 76. Amount left with Leela is Rs 10,000 more than the amount she contributed towards Prime Minister’s Relief fund. 77. Age of Kartik’s Father is seven times the age of Kartik. 78. The difference between maximum and minimum temperature on a day in Delhi was 10°C. 79. Last year Jay planted 10 more plants than twice the number of plants planted by John. 80. Sharad reduced the consumption of tea per day by 5 cups after having some health problem. 81. The number of students dropping out this year is 30 less than the number of students dropped last year. 82. The price of petrol per liter decreased this month by Rs 5 than its price last month. 83. Khader’s monthly salary increased by Rs 1000 in the year 2006 than in 2005. 84. The number of girls enrolled this year was 10 less than 3 times the girls enrolled last year. x 2x x 85. (a) 2x – 13 = 3 (b) = x – 5 (c) = 12 (d) 2x + 9 = 13 (e) –1=1 5 3 3 86. (a) p = 3a (b) d = 2r (c) s = c + p (d) a = p + i 87. (i) x – 2 (ii) x + 35 (iii) x + 32 (iv) 8 x 88. m 0 1 2 3 4 Solution is m = 2 2m – 5 –5 –3 –1 1 3 89. 50 p – 1800 90. 8 x + 100L 91. m × m sq cm. 92. The perimeter of a triangle is the sum of all its sides. 93. The perimeter of a rectangle is twice the sum of its length and breadth. 94. (m + 40)kg 95. (i) 2 (r + t) + 10 (ii)15x (iii) (8rt + 4000)sq cm (iv) Rs 23x ANSWERS 161 OOLRLPNOV _lqucpq 96. (i) Sunita : x + 4, Geeta : 2 x + 4, where x is the present age (in years) of Sunita. (ii) Sunita : x – 3, Geeta : 2x – 3 97. (i) – (B), (ii) – (E), (iii) – (C), (iv) – (C), (v) – (A)
Q67Short answer
If a note book costs Rs p and a pencil costs Rs 3, then the total cost (in Rs) of two note books and one pencil.
Q68Short answer
z is multiplied by –3 and the result is subtracted from 13.
Q69Short answer
p is divided by 11 and the result is added to 10.
Q70Short answer
x times of 3 is added to the smallest natural number.
Q71Short answer
6 times q is subtracted from the smallest two digit number.
Q72Short answer
Write two equations for which 2 is the solution.
Q73Short answer
Write an equation for which 0 is a solution.
Q74Short answer
Write an equation whose solution is not a whole number. In questions 75 to 84, change the statements, converting expressions into statements in ordinary language:
Q75Short answer
A pencil costs Rs p and a pen costs Rs 5p.
Q76Short answer
Leela contributed Rs y towards the Prime Minister’s Relief Fund. Leela is now left with Rs (y + 10000).
Q77Short answer
Kartik is n years old. His father is 7n years old.
Q78Short answer
The maximum temperature on a day in Delhi was poC. The minimum temperature was (p – 10)oC.
Q79Short answer
John planted t plants last year. His friend Jay planted 2t + 10 plants that year.
Q80Short answer
Sharad used to take p cups tea a day. After having some health problem, he takes p – 5 cups of tea a day.
Q81Short answer
The number of students dropping out of school last year was m. Number of students dropping out of school this year is m – 30. 11.4.2018 MATHEMATICS
Q82Short answer
Price of petrol was Rs p per litre last month. Price of petrol now is Rs (p – 5) per litre.
Q83Short answer
Khader’s monthly salary was Rs P in the year 2005. His salary in 2006 was Rs (P + 1000).
Q84Short answer
The number of girls enrolled in a school last year was g. The number of girls enrolled this year in the school is 3g – 10.
Q85Multiple choice
Translate each of the following statements into an equation, using x as the variable:
- (a)13 subtracted from twice a number gives 3.
- (b)One fifth of a number is 5 less than that number.
- (c)Two-third of number is 12.
- (d)9 added to twice a number gives 13. (e) 1 subtracted from one-third of a number gives 1.
Q86Multiple choice
Translate each of the following statements into an equation:
- (a)The perimeter (p) of an equilateral triangle is three times of its side (a).
- (b)The diameter
- (c)The selling price (s) of an item is equal to the sum of the cost price (c) of an item and the profit (p) earned. (d) Amount (a) is equal to the sum of principal (p) and interest (i).
- (d)of a circle is twice its radius (r).
Q87Multiple choice
Let Kanika’s present age be x years. Complete the following table, showing ages of her relatives: Situation (described in ordinary language) Expressions
- (i)Her brother is 2 years younger. ________________
- (ii)Her father’s age exceeds her age by 35 years. ________________
- (iii)Mother’s age is 3 years less than that of her father. ________________
- (iv)Her grand father’s age is 8 times of her age. ________________ ALGEBRA 113 11.4.2018 UNIT-7
Q88Short answer
If m is a whole number less than 5, complete the table and by inspection of the table, find the solution of the equation 2m – 5 = – 1 : 2m –5
Q89Short answer
A class with p students has planned a picnic. Rs 50 per student is collected, out of which Rs 1800 is paid in advance for transport. How much money is left with them to spend on other items?
Q90Short answer
In a village, there are 8 water tanks to collect rain water. On a particular day, x litres of rain water is collected per tank. If 100 litres of water was already there in one of the tanks, what is the total amount of water in the tanks on that day?
Q91Short answer
What is the area of a square whose side is m cm?
Q92Short answer
Perimeter of a triangle is found by using the formula P = a + b + c, where a, b and c are the sides of the triangle. Write the rule that is expressed by this formula in words.
Q93Short answer
Perimeter of a rectangle is found by using the formula P = 2 ( l + w), where l and w are respectively the length and breadth of the rectangle. Write the rule that is expressed by this formula in words.
Q94Short answer
On my last birthday, I weighed 40kg. If I put on m kg of weight after a year, what is my present weight?
Q95Multiple choice
Length and breadth of a bulletin board are r cm and t cm, respectively.
- (i)What will be the length (in cm) of the aluminium strip required to frame the board, if 10cm extra strip is required to fix it properly.
- (ii)If x nails are used to repair one board, how many nails will be required to repair 15 such boards?
- (iii)If 500sqcm extra cloth per board is required to cover the edges, what will be the total area of the cloth required to cover 8 such boards?
- (iv)What will be the expenditure for making 23 boards, if the carpenter charges Rs x per board. 11.4.2018
Q96Multiple choice
Sunita is half the age of her mother Geeta. Find their ages
- (i)after 4 years?
- (ii)before 3 years?
Q97Multiple choice
Match the items of Column I with that of Column II: Column I Column II (i) The number of corners of a quadrilateral
- (A)= (ii) The variable in the equation 2p + 3 = 5
- (B)constant (iii) The solution of the equation x + 2 = 3
- (C)+1 (iv) solution of the equation 2p + 3 = 5
- (D)–1 (v) A sign used in an equation (E) p (F) x Activity 1: Observe the following patterns and find a rule: (i) Perimeter Number of unit shapes 1 1 3 1 1 4 2 1 1 5 3 1 1 1 1 1 1 6 4 1 1 Rule : Perimeter = Number of unit shapes + 2 = k + 2, where k is the number of unit shapes (triangles). 11.4.2018 UNIT-7 (ii) 1 1 4 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 Rule : (iii) 1 1 1 1 5 1 11 1 1 111 1 1 1 11 1 Rule : (iv) 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11 Rule : 11.4.2018