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MCQ on Expressions using Letter Numbers Class 7
Expressions using Letter Numbers MCQ Class 7
Class 7 Maths MCQ Chapter 4 Expressions using Letter Numbers
Multiple Choice Questions
Question 1.
6a equals
(a) 6 + a
(b) 6 × a
(c) a × a × a × a × a × a
(d) 6 ÷ a
Answer:
(b) 6 × a
Question 2.
11 more than three times the number x can be represented as
(a) 11 + x + 3
(b) 11x – 3
(c) 3x + 11
(d) 11x + 3
Answer:
(c) 3x + 11
Question 3.
If each match box contains 40 matchsticks, the number of matchsticks required to fill n such boxes is
(a) 40 + n
(b) 40n
(c) 40 ÷ n
(d) 40 – n
Answer:
(b) 40n
Question 4.
If the length of each side of a regular hexagon is x metres, then the perimeter of given hexagon is
(a) (x + 6) metres
(b) (x + 6) metres
(c) (x – 6) metres
(d) (6 × x) metres
Answer:
(d) (6 × x) metres
Question 5.
‘Three times a numbers added to 5’ is
(a) 5 + x
(b) 3x + 5
(c) 5x + 3
(d) 15x
Answer:
(b) 3x + 5
Question 6.
9p equals
(a) 9 + p
(b) 9 – p
(c) 9 × p
(d) 9 ÷ p
Answer:
(c) 9 × p
Question 7.
‘p is subtracted from the sum of s and 9′ is written as
(a) (s + 9) – p
(b) p – (s + 9)
(c) p – (s – 9)
(d) p + (s + 9)
Answer:
(a) (s + 9) – p
Question 8.
Geeta earns ₹ x per month and saves ₹ y per month. Her monthly expenditure (in ₹) is
(a) x + y
(b) x ÷ y
(c) x × y
(d) x – y
Answer:
(d) x – y
Question 9.
Jayant drives x km in one hour. How much distance does he cover in 3 hours 40 minutes?
(a) 3x + \(\frac{2}{3}\)
(b) \(\frac{2}{3}\)x + 3
(c) \(\frac{11}{3}\)x
(d) \(\frac{11}{3}\) + x
Answer:
(c) \(\frac{11}{3}\)x
Question 10.
The perimeter of a regular decagon having side length x units, is
(a) 10 x units
(b) 11 x units
(c) 12 x units
(d) 7 x units
Answer:
(a) 10 x units
Question 11.
If Mukesh has 2 notes of ₹ 100, 5 notes of ₹ 20 and 6 notes of ₹ 5, then the correct expression representing his amount is
(a) 2 × 100 + 20 × 6 + 5 × 5
(b) 20 × 2 + 100 × 6 + 5 × 5
(c) 100 × 2 + 5 × 20 + 6 × 5
(d) 5 × 100 + 20 × 5 + 6 × 5
Answer:
(c) 100 × 2 + 5 × 20 + 6 × 5
Question 12.
The subtraction of 5 times of y from x is
(a) 5x – y
(b) y – 5x
(c) x – 5y
(d) 5y – x
Answer:
(c) x – 5y
Question 13.
Neha owns a flour mill. It takes 20 seconds for the roller mill to start running. Once it is running, each kg of grain takes 16 seconds to grind into power. What will be an arithmetic expression which describes the time taken to grind 6 kg of grain, assuming the machine is off initially?
(a) 2 + 16 × 6 + 10
(b) 16 + 20 × 6
(c) 20 + 16 × 6
(d) 6 + 20 × 16
Answer:
(c) 20 + 16 × 6
Question 14.
The value of 32 – (64 + 16) + 3 × 6 is
(a) 31
(b) -32
(c) -30
(d) 30
Answer:
(c) -30
Question 15.
If j = 3, then value of 5 j + 10 is
(a) 15
(b) 25
(c) 65
(d) 30
Answer:
(b) 25
Question 16.
If the price per pencil is ₹ c and price per eraser is ₹ d. Then, the algebraic expression representing the price of 2 pencils and 6 erasers is (in ₹)
(a) 6 + 2 + c + d
(b) cd + 6 + 2
(c) 6c + 2d
(d) 2c + 6d
Answer:
(d) 2c + 6d
Question 17.
The value of 3(x+y) – 3(x-y) is equal to
(a) 6 x
(b) 0
(c) 6 y
(d) 3 x
Answer:
(c) 6 y
Question 18.
The value of p + p + q + q – p – q is equal to
(a) 2p + 2q
(b) p + q
(c) 2p
(d) 2q
Answer:
(b) p + q
Question 19.
Let Ram uses two matchsticks to make a ‘V’-shaped structure. He uses four matchsticks to make two ‘V-shaped structures and six matchsticks for making three. Then, the number of matchsticks used by Ram to make r’ V-shaped structures, is
(a) 2 + r
(b) 2 r
(c) r + 1
(d) 3 r
Answer:
(b) 2 r
Assertion (A) & Reason (R)
Question 1.
A statement of Assertion (A) is followed by a statement of Reason (R).
Assertion (A): The perimeter of an equilateral triangle, if side of the triangle is m is 4m.
Reason (R): In an equilateral triangle, each side length is equal.
Choose the correct option as:
(a) Both assertion and reason are true and the reason is the correct explanation of assertion.
(b) Both assertion and reason are true but the reason is not the correct explanation of the assertion.
(c) Assertion is true and the reason is false.
(d) Assertion is false and the reason is true.
Answer:
(d) Assertion is false and the reason is true.
Question 2.
Assertion (A) The expression 5(a+2) sirfplifies to 5 a + 2.
Reason (R) Distributive property means multiplying the number with terms inside the bracket.
Which of the following is true?
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(d) Assertion is false but Reason is true.
Question 3.
Assertion (A) If Vikas is x years old now, then after 5 years, he will be (x+5) years.
Reason (R) To find future age, we subtract years from the present age.
Which of the following is true?
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(c) Assertion is true but Reason is false.
Question 4.
Assertion (A) The perimeter of a square of side 4 cm is 16 cm .
Reason (R) The perimeter of a regular n-polygon of side length m units is nm units.
Which of the following is true?
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
Answer:
(a) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.
Fill in the blanks:
1. ‘x exceeds by 9’ can be expressed as _________.
Answer:
x + 9
2. The number of days in w week is _________.
Answer:
7w
3. The letter-number used in expression 4x + 8 is _________.
Answer:
x
4. The simplest form of 3x + 4y – 7 + x – 2y is _________.
Answer:
4x + 2y – 7
5. Expression for total cost if “a pencil costs x and a pen costs 5x” is _________.
Answer:
6x
6. 20 + 8 × ( 16 – 6) = ____________ .
Answer:
100
7. 4x + 1 and 4(x + 1) are ____________ .
Answer:
unequal
8. The 11th term in the sequence 4, 8, 12, 16, 20, ____________ is ___________
Answer:
44
9. The expression (40x – 45y) + ( – x – 5y) is simplified to ____________.
Answer:
39x – 50y
10. The sum of (- 6f + 17 – 4g) and (- 7 + 11f + 7g) is ____________ .
Answer:
5f + 3g + 10
11. The perimeter of a regular polygon with n number of sides and having side length n units is _____ units.
Answer:
n × n or n2
12. The algebraic expression for ‘ 3 more than a number’ is _____ by assuming the number letter to be x.
Answer:
3 + x
13. If f=2, g=1, then 2 f-2 g = _____.
Answer:
2
14. 35 × 5 + 5 × 5 + 3 + 2 – 3 × 2 = _____.
Answer:
199
15. The perimeter of a rectangle having length 6 m and width 3 m is _____ m.
Answer:
18
16. (40x + 75y) + (-5x – 10y) = _____.
Answer:
35x + 65y
17. Sum or difference of two like terms is a _____ term.
Answer:
like
18. Like terms in the expression n(6+1) + 6(n-1) are _____ and _____.
Answer:
6n, n, 6n
State whether the given statements are true or false.
1. The area of a square having each side x is 4x.
Answer:
False
2. The expression obtained when x is multiplied by 2 and then subtracted from 3 is 3 – 2x.
Answer:
True
3. Savita has p pencils in her box. She puts q more pencils in the box. The total number of pencils with her is p + q.
Answer:
True
4. The letter-number in the expression 2p + 3 is 2 and 3.
Answer:
False
5. t minutes are equal to 60/ seconds.
Answer:
True
6. ‘Twice a number y decreased by 7’ is written as 2(y – 7).
Answer:
False
7. ‘One-fourth of a number x added to one-third of the four times of x’ is written as \(\frac{x}{3}\) + \(\frac{x}{4}\).
Answer:
False
8. If a side of a regular pentagon is m cm, then its perimeter is (m + 5).
Answer:
False
9. If f = 3, g = 1, then 3g – f = 0
Answer:
True
10. [8 h – (5 + 7 h) + 6] is simplified to h + 1.
Answer:
True
11. The value of the algebraic expression depends on the value of letter-numbers from which the expression is formed.
Answer:
True
12. 3 u and 3 u-3 are equal for both u = 0 and u = 1.
Answer:
False
13. Sum of 2 and p is 2p.
Answer:
False
14. The simplest form of 3(r + 4p + 3n) is 12p – 3r + 9 n.
Answer:
False
15. The terms which involve the same letter-numbers are called as like terms.
Answer:
True
16. 13 x can be described as 13 more than a number x.
Answer:
False
Match the following:
Question 1.
If Ritika’s present age be x years. Match the statements with the expression.
| Situation | Expression |
| (a) Her brother is 4 years younger than her. | (i) x + 27 |
| (b) Her father’s age exceeds her age by 30 years. | (ii) 9x |
| (c) Mother’s age is 3 years less than that of her father. | (iii) 9x – 4 |
| (d) Her grandfather’s age is 9 times of her age. | (iv) x + 30 |
| (e) Her grandmother’s age is 4 years less than her grandfather. | (v) x – 4 |
Answer:
| Situation | Expression |
| (a) Her brother is 4 years younger than her. | (v) x – 4 |
| (b) Her father’s age exceeds her age by 30 years. | (iv) x + 30 |
| (c) Mother’s age is 3 years less than that of her father. | (i) x + 27 |
| (d) Her grandfather’s age is 9 times of her age. | (ii) 9x |
| (e) Her grandmother’s age is 4 years less than her grandfather. | (iii) 9x – 4 |
Question 2.
Match the Column A to Column B.
| Column A | Column B |
| (i) (w + 2) + 7 × 4 | (a) 4w + 36 |
| (ii) ((w + 2) + 7) × 4 | (b) -13 |
| (iii) (30x – 20y) + (30 + 20) × x + y | (c) 21x + 3y |
| (iv) 15x + 8x – 2x + 3y | (d) w + 30 |
| (v) The value of 3 x + 2 y is, if x = -3, y = -2 | (e) 80x – 19y |
Answer:
| Column A | Column B |
| (i) (w + 2) + 7 × 4 | (d) w + 30 |
| (ii) ((w + 2) + 7) × 4 | (a) 4w + 36 |
| (iii) (30x – 20y) + (30 + 20) × x + y | (e) 80x – 19y |
| (iv) 15x + 8x – 2x + 3y | (c) 21x + 3y |
| (v) The value of 3 x + 2 y is, if x = -3, y = -2 | (b) -13 |
Case-Based Question
Question 1.
A teacher asked two students, Aarav and Neha to list the materials needed for a craft project.
- Aarav wrote: 3x + 2y, where x represents coloured paper sheets and v represents glue sticks.
- Neha wrote: 5x – y, with the same meanings for x and y.
Based on the above information, answer the following question:
(a) To avoid duplication, the teacher decides to combine the two lists. What is the combined list of materials in algebraic expression form?
Answer:
8x + y
(b) If Neha decides to remove her list from the total, what will the expression be?
Answer:
3x + 2y
(c) If 1 sheet of coloured paper costs ₹ 2 and 1 glue stick costs ₹ 5, what is the cost of the combined materials list?
Answer:
₹21
Question 2.
Mandvi works for an NGO which helps the poor students by providing them the stationery kits. She prepares kits for 6 students. Each kit consists of 2 pencils, 1 pen, 1 sharpner, 1 eraser and 1 notebook. The cost of a pencil is 2 more than three times a number, the cost of a pen is 1 less than 4 times that number, the cost of a sharpner is 1 less than 3 times that number, the cost of 1 eraser is 5 more than that number and the cost of a notebook is 5 times that number.
Now, she is struggling with a few questions.
(i) Write an expression for the total cost of 1 kits.
(ii) Simplify the expression for 1 kit.
(iii) Write an expression for the cost of 6 kits.
(iv) Simplify the total cost of 6 kits.
(v) If that number is 5, then find the total cost of the 6 kits.
Answer:
Let the letter-number to be x.
Then, the cost of a pencil = ₹(3 x+2), the cost of a pen = ₹(4 x-1), the cost of a sharpner = ₹(3 x-1) the cost of an eraser = ₹(5+x) and the cost of a notebook = ₹ 5 x.
(i) The expression for the total cost of 1 kit is ₹(3x + 2) + (4x – 1) + (3x – 1) + (5 + x) + (5x).
(ii) We have,
(3x + 2)+(4x – 1) + (3x – 1) + (5 + x) + 5 x
= (3x + 4x + 3x + x + 5x) + (2 – 1 – 1 + 5)
= 16x + 5
(iii) The expression for the cost of 6 kits is 6 × (16x + 5).
(iv) We have, 6 × (16x + 5) = 96 x+30
∴ Total cost for 6 kits = ₹(96 x+30)
(v) If x = 5, then total cost of 6 kits = ₹ 96 × 5 + 30
= ₹ 510
Answer the following:
Question 1.
What is the area of a square whose side is m cm?
Answer:
m × m square cm
Question 2.
Write the rule for formula of perimeter (P) of a triangle where a, b and c are the sides of the triangle.
Answer:
P = a + b + c
Question 3.
On my last birthday, I weighed 40 kg. If I put on m kg of weight after a year, what is my present weight?
Answer:
(40 + m)kg
Question 4.
Observe the following patterns and find a rule:
Answer:
Question 5.
Subtract 2x + y from the sum of (x – 2xy + y) and (3x + 2xy – 2y).
Answer:
2(x – y)
Subjective Exercise
Question 1.
Think of a number x. Multiply it by 3, add 5 to the product and subtract y subsequently. Find the resulting number.
Answer:
3x + 5 – y
Question 2.
Write an algebraic expression for the statement “The selling price (S) of an article is equal to the sum of its cost price (C) and the profit (P) earned.”
Answer:
S = C + P
Question 3.
If x = 3, y = 1 and z = 0, then find the value of z (x + 2y).
Answer:
0
Question 4.
Add the expressions:
(i) 8a – 14b + 5 and 5b – (a – 9)
(ii) 13x – 7 – 3y and 3x – 2y + 7
Answer:
(i) 7a – 9b + 14
(ii) 16x – 5y
Question 5.
Subtract the expressions:
(i) 10x + 2 – 5y from – 5x + 8 + 5y
(ii) 9m + 31 – 6n from 6m + 3 – 5n
Answer:
(i) – 15x + 10y + 6
(ii) – 3m + n – 28
Practice Questions Set 1
Question 1.
A man’s monthly salary is ₹ 35,000. Find his savings when his expenditure is
(i) ₹ 22,000
(ii) ₹ 30,500
(iii) ₹ x
Answer:
(i) ₹ 13,000
(ii) ₹ 4,500
(iii) ₹ (35,000 – x)
Question 2.
Mr. Amrit Pal is 5 cm taller than his wife. Find the height of Mr. Amrit Pal, if the height of his wife is
(i) 160 cm
(ii) 158 cm
(iii) h cm.
Answer:
(i) 165 cm
(ii) 163 cm
(iii) (h + 5) cm
Question 3.
Find the number of days in
(i) 3 weeks
(ii) 10 weeks
(iii) p weeks.
Answer:
(i) 21 days
(ii) 70 days
(iii) 7p days
Question 4.
In a test, the marks obtained by Smriti is three-fourth that of Sushma. Find the Smriti’s marks if Sushma’s marks are
(i) 60
(ii) 80
(iii) p
Answer:
(i) 45 marks
(ii) 60 marks
(iii) 3/4 p marks
Question 5.
The time taken by an aeroplane to travel from City A to City B is 10 minutes more than one-eighth of the time taken by a train.
Find the time taken by the aeroplane if the time taken by the train is
(i) 12 hours
(ii) t hours.
Answer:
(i) 1 hour 40 minutes
(ii) (t/8 + 1/6) hours
Question 6.
Write algebraic expression using letter number of your choice:
(i) 12 more than a number
(ii) 5 less than a number
(iii) 3 more than twice a number
(iv) 4 less than 5 times a number.
Answer:
(i) x + 12
(ii) y – 5
(iii) 2x + 3
(iv) 5m – 4
Question 7.
Write algebraic expression for the perimeter of
(i) an equilateral triangle
(ii) a square
(iii) a regular hexagon.
Answer:
(i) Perimeter = 3s, where each side has length ‘s’
(ii) Perimeter = 4l, where each side has length ‘l’
(iii) Perimeter = 6p, where each side has length ‘p’
Question 8.
Simplify the following:
(i) m × 5
(ii) 2p ÷ q
(iii) 6x × 5y
(iv) 12x ÷ 4y
(v) t ÷ 7 + 1 × s
Answer:
(i) 5m
(ii) 2p/q
(iii) 30xy
(iv) 3x/y
(v) t/7 + s
Question 9.
Express the following word statements algebraically:
(i) 10 more than the number x
(ii) 5 less than twice the number y
(iii) 4 more than the sum of x and y
(iv) 2 less than the quotient of 3a by 7.
Answer:
(i) x + 10
(ii) 2y – 5
(iii) (x + y) + 4
(i) 3a/7 – 2
Question 10.
Express the following word statements algebraically:
(i) Add 7 to the product of x and y
(ii) Subtract 12 from the sum of 2a and 3b
(iii) Divide the sum of p and 2q by 4r
(iv) Add the product of p and q to 7.
Answer:
(i) xy + 7
(ii) (2a + 3b) – 12
(iii) (p + 2q)/4r
(iv) 7 + pq
Question 11.
The mass of Book A is 760 g and the mass of Book B is 550 g. Find the total mass of
(i) 3 copies of Book A and 5 copies of Book B.
(ii) m copies of Book A and n copies of Book B.
Answer:
(i) (3 × 760 + 5 × 550) g,
i.e., 5030 g
(ii) (m × 760 + n × 550) g,
i.e., ( 760m + 55 n) g
Question 12.
Mr. Ashwani goes to a movie with his family. He has 2 free tickets. Find the amount he has to pay for the tickets if
(i) there are 5 family members and each ticket costs ₹ 75
(ii) there are n family members and each ticket costs ₹ p.
Answer:
(i) ₹ (75 × 3), i.e., ₹ 225
(ii) ₹ [p × (n – 2)]
Question 13.
Describe a real-life situation that could be represented by the algebraic expression
(i) 2x + 3
(ii) 4m + 3n
Answer:
(i) If the age of person A is 3 years more
than twice the age of another person B. Find the age of A when the age of B is x years.
(ii) The price of a table is ₹ m and that of a chair is ₹ n. Find the total price of 4 tables and 3 chairs.
Question 14.
Suppose you take 5 in a minute. How many breaths do you take in
(i) an hour?
(ii) a day?
Answer:
(i) 60 s breaths
(ii) 1440 s breaths
Question 15.
What does the following represent?
(i) 3x + 4y
(ii) (x + 2y) × 4
(iii) (a – 3b) ÷ 2
(iv) t/8 – 1/6
Answer:
(i) three times of x is added to four times of y
(ii) Sum of x and 2y is multiplied by 4
(iii) The difference of a and 2b is divided by 2
(iv) one – eighth of t minus one-sixth
Question 16.
Some simplifications are shown below where the letter-numbers are replaced by numbers and the value of the expression is obtained. Observe each of them and identify the wrong ones. For each wrong ones, find the correct value of the expression.
(i) If x = 3, then x + 3 = 6
(ii) If m = 5, then 3 – m = 2
(iii) If t = 6, then 3/t = 2
(iv) If p = 10, then 5p – 2 = 13
(v) If x = 3 and y = 1, then x + 2y = 5
(vi) If p = 10 and q = 5, then 5pq + 1 = 21
Answer:
The wrong simplifications are:
(ii) If m = 5, then 3 – m = 2
Correct simplification is 3 – m = -2
(iii) If t = 6, then 3/t = 2
Correct simplification is 3/t = 1/2
(iv) If p = 10, then 5p – 2= 13
Correct simplification is 5p – 2 = 48
(v) If p = 10 and q = 5 , then 5pq + 1 = 21
Correct simplification is 5pq + 1 = 251
Practice Questions Set 2
Question 1.
Simplify:
(i) 3x + 5x
(ii) 3x + (- 5x)
(iii) – 3x + 5x
(iv) – 3x + (- 5x)
(v) 5x – 3x
(vi) 5x – (- 3x)
(vii) – 3x -5x
(viii) – 3x – (-5x)
Answer:
(i) 8x
(ii) -2x
(iii) 2x
(iv) -8x
(v) 2x
(vi) 8x
(vii) -8x
(viii) 2x
Question 2.
Simplify the following:
(i) x + y + x – y
(ii) x + y – x + y
(iii) x + y – (x + y)
(iv) 3p – p – p – p
(v) 3p – p – (p – 2p)
(vi) 3p – q – p – q
(vii) 3p – (p + p) – 3p
(viii) p + 4 + 6p – 3p – 2
(ix) – 1m – 2n – 6n – 4m
(x) 3x – 2y + z – x + 6y – 6z
Answer:
(i) 2x
(ii) 2y
(iii) 0
(iv) 0
(v) 3p
(vi) 2p – 2q
(vii) – 2p
(viii) 4p + 2
(ix) – 13 m – 8n
(x) 2x + 4y – 5z
Question 3.
Simplify the following:
(i) (5x + 8y) – (3x – y)
(ii) (5x + 8y) + (3x – y)
(iii) (x + 3y) – ( 2x + 4y) + (5x – y)
Answer:
(i) 2x + 9y
(ii) 8x – 7y
(iii) 4x – 2y
Question 4.
Are the expressions 5x – 2 and 5(x – 2) equal to each other?
Answer:
Expressions 5x – 2 and 5(x – 2) are not equal to each other.
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