NCERT Exemplar Class 6 Maths Algebra Solution: NCERT Exemplar Solution Class 6 Maths Chapter 7 Algebra Full Explanation. NCERT Exemplar Class 6 Maths – Chapter 7 Algebra. NCERT Exemplar Class 6 Maths Algebra Solution by Expert.
NCERT Exemplar Class 6 Maths Algebra Solution
In questions 1 to 23, out of the four given options, only one is correct. Write the correct answer.
Question 1:
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
Solution: Answer is B
1 match box contain 50 match sticks then n match box contains 50n match sticks.
Question 2:
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
Solution: Answer is C
Presents age of Amulya is x years 5 year ago her age is (X – 5) years.
Question 3:
Which of the following represents 6 × x
(A) 6x
(B) x/6
(C) 6 + x
(D) 6 – x
Solution: Answer is A
6x represent the 6 × x
Question 4:
Which of the following is an equation?
(A) x + 1
(B) x – 1
(C) x – 1 = 0
(D) x + 1 > 0
Solution: Answer is C
Option no (c) x – 1 = 0 this option writes in equation form.
Question 5:
If x takes the value 2, then the value of x + 10 is
(A) 20
(B) 12
(C) 5
(D) 8
Solution: Answer is B
If x = 2 then x + 10 = 2 + 10 = 12.
Question 6:
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
Solution: Answer is B
Perimeter of regular hexagon is x meter and sides = 6 length of each side is x/6 = (x ÷ 6) metres
Question 7:
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
Solution: Answer is B
When we put x = 2 in equation x – 2 = 0, 2 – 2 = 0, 0 = 0 x = 2 values satisfied this equation.
Question 8:
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
Solution: Answer is A.
x + y = y + x suggest that operation of addition is cumulative for any two-integer x and y.
Question 9:
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
Solution: Answer is A.
2x + 1 = 6
2x = 6 – 1
2x = 5
X = (5)/2 This equation close not have solution in integers.
Question 10:
In algebra, a × b means ab, but in arithmetic 3 × 5 is
(A) 35
(B) 53
(C) 15
(D) 8
Solution: Answer is C.
3 x 5 = 15
Question 11:
In algebra, letters may stand for
(A) known quantities
(B) unknown quantities
(C) fixed numbers
(D) none of these
Solution: Answer is B.
In algebra latter may stand for unknown quantities.
Question 12:
“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
Solution: Answer is A.
Can take different value, ‘’ variable “means that it can take different value.
Question 13:
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
Solution: Answer is C.
10 – x means x subtracted from 10
Question 14:
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
Solution: Answer is B.
Savitri has a sum of Rs x.
X – 1700 money is left with her.
Question 15:
The perimeter of the triangle shown in Fig. 7.1 is
(A) 2x + y
(B) x + 2y
(C) x + y
(D) 2x – y
Solution: Answer is A
Given triangle have two side equal in length and one different like that
Hence perimeter of 2x + y.
Question 16:
The area of a square having each side x is
(A) x * x
(B) 4x
(C) x + x
(D) 4 + x
Solution: Answer is A.
Each side of square is same each side square is x.
Hence the area of square is X * X.
Question 17:
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
Solution: Answer is C.
X is multiplied by 2 = 2x then subtracted from 3 = 3 – 2x
Question 18:
q/2 = 3 has a solution
(A) 6
(B) 8
(C) 3
(D) 2
Solution: Answer is A.
9/2 = 3 has a solution 6 like that
9 = 3 × 2
9 = 6
Question 19:
x – 4 = – 2 has a solution
(A) 6
(B) 2
(C) – 6
(D) – 2
Solution: Answer is B.
X – 4 = -2 has a solution 2.
After solving x = -2 + 4
X = 2
Question 20:
4/2 = 2 2 denotes a
(A) numerical equation
(B) algebraic expression
(C) equation with a variable
(D) false statement
Solution: Answer is A.
4/2 = 2 denote numerical equation.
Question 21:
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
(D) p/q
Solution: Answer is A.
Kanta has p pencil in her box she puts q more pencils in box means q add in p = p + q.
Question 22:
The equation 4x = 16 is satisfied by the following value of x
(A) 4
(B) 2
(C) 12
(D) –12
Solution: Answer is A.
When we put x = 4
4x = 16
4 x 4 = 16 means x = 4 satisfied given equation.
Question 23:
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
Solution: Answer is D.
The unknown number is x by assuming
This unknown number adding with 13. Get 27 this equation write in the form x + 13 = 27.
In question 24 to 40, fill in the blanks to make the statements true:
Question 24:
The distance (in km) travelled in h hours at a constant speed of 40km per hour is ______.
Solution: The distance (in km) travelled in h hours at a constant speed of 40km per hour is 40h.
Question 25:
p kg of potatoes are bought for Rs 70. Cost of 1kg of potatoes (in Rs) is ______.
Solution: p kg of potatoes are bought for Rs 70. Cost of 1kg of potatoes (in Rs) is 70/p.
Question 26:
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 ______.
Solution: 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 8d + 2.
Question 27:
If 7x + 4 = 25, then the value of x is ______.
Solution: If 7x + 4 = 25, then the value of x is 3.
Question 28:
The solution of the equation 3x + 7 = –20 is _______.
Solution: The solution of the equation 3x + 7 = –20 is -9.
Question 29:
‘x exceeds y by 7’ can be expressed as __________.
Solution: ‘x exceeds y by 7’ can be expressed as x = y + 7.
Question 30:
‘8 more than three times the number x’ can be written as __________.
Solution: ‘8 more than three times the number x’ can be written as 3x + 8.
Question 31:
Number of pencils bought for Rs x at the rate of Rs 2 per pencil is __________.
Solution: Number of pencils bought for Rs x at the rate of Rs 2 per pencil is (x )/2.
Question 32:
The number of days in w weeks is __________.
Solution: The number of days in w weeks is 7w.
Question 33:
Annual salary at r rupees per month along with a festival bonus of Rs 2000 is __________.
Solution: Annual salary at r rupees per month along with a festival bonus of Rs 2000 is 12x + 2000.
Question 34:
The two digit number whose ten’s digit is ‘t’ and units’s digit is ‘u’ is ______.
Solution: The two digit number whose ten’s digit is ‘t’ and unit’s digit is ‘u’ is 10t + u.
Question 35:
The variable used in the equation 2p + 8 = 18 is ________.
Solution: The variable used in the equation 2p + 8 = 18 is p.
Question 36:
x metres = _______ centimetres
Solution: x metres = 100x centimetres
Question 37:
p litres = _______ millilitres
Solution: p litres = 1000p millilitres
Question 38:
r rupees = __________ paise
Solution: r rupees = 100x paise
Question 39:
If the present age of Ramandeep is n years, then her age after 7 years will be ______.
Solution: If the present age of Ramandeep is n years, then her age after 7 years will be n + 7.
Question 40:
If I spend f rupees from 100 rupees, the money left with me is ________ rupees.
Solution: If I spend f rupees from 100 rupees, the money left with me is 100 – f rupees.
In question 41 to 45, state whether the statements are true or false.
Question 41:
0 is a solution of the equation x + 1 = 0
Solution: False
Because -1 is the solution of the equation x + 1 = 0.
Question 42:
The equations x + 1 = 0 and 2x + 2 = 0 have the same solution.
Solution: The statement is true.
Question 43:
If m is a whole number, then 2m denotes a multiple of 2.
Solution: The statement is true.
Question 44:
The additive inverse of an integer x is 2x.
Solution: False
The additive inverse of an integer x is not 2x.
Question 45:
If x is a negative integer, – x is a positive integer.
Solution: The statement is true.
Question 46:
2x – 5 > 11 is an equation.
Solution: False
2x – 5 = 11 is an equation.
But 2x – 5 > 11 is not an equation.
Question 47:
In an equation, the LHS is equal to the RHS.
Solution: The statement is true.
Question 48:
In the equation 7k – 7 = 7, the variable is 7.
Solution: False
In the equation 7k – 7 = 7, the variable is K.
Question 49:
a = 3 is a solution of the equation 2a – 1 = 5
Solution: The statement is true.
Question 50:
The distance between New Delhi and Bhopal is not a variable.
Solution: The statement is true.
Question 51:
t minutes are equal to 60t seconds.
Solution: The statement is true.
Question 52:
x = 5 is the solution of the equation 3x + 2 = 20
Solution: False
Because x = 5 is not the solution of the equation 3x + 2 = 20.
X = 6 is the solution 3x + 2 = 20
3x = 20 – 2
X = 18/3
X = 6
Question 53:
‘One third of a number added to itself gives 8’, can be expressed as x/3 + 8 = x
Solution: False
One third of a number added to itself gives 8 + x = 8
Question 54:
The difference between the ages of two sisters Leela and Yamini is a variable.
Solution: The difference between the ages of two sisters Leela and Yamini is a Number.
Question 55:
The number of lines that can be drawn through a point is a variable.
Solution: False
Because The number of lines that can be drawn through a point is not 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:
Question 56:
One more than twice the number.
Solution: We assume y Is that number 2y + 1
Question 57:
20°C less than the present temperature.
Solution: Let assume that temperature is t.
t – 20
Question 58:
The successor of an integer.
Solution: we assume that is q
q + 1
Question 59:
The perimeter of an equilateral triangle, if side of the triangle is m.
Solution: 3m
Question 60:
Area of the rectangle with length k units and breadth n units.
Solution: km
Question 61:
Omar helps his mother 1 hour more than his sister does.
Solution: His sister helping hour is q.
q + 1
Question 62:
Two consecutive odd integers.
Solution: 2n + 5, 2n + 7
Question 63:
Two consecutive even integers.
Solution: –2n + 4, 2n + 6
Question 64:
Multiple of 5.
Solution: 5m
Question 65:
The denominator of a fraction is 1 more than its numerator.
Solution: z/z + 1
Question 66:
The height of Mount Everest is 20 times the height of Empire State building.
Solution: 20 g where g is the height of empire state building.
Question 67:
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
Solution: 2p + 3
Question 68:
z is multiplied by –3 and the result is subtracted from 13.
Solution: 13 – (-3z) = 13 + 3z
Question 69:
p is divided by 11 and the result is added to 10.
Solution: p/11 + 10
Question 70:
x times of 3 is added to the smallest natural number.
Solution: 3x + 1
Question 71:
6 times q is subtracted from the smallest two digit number.
Solution: 10 – 6q
Question 72:
Write two equations for which 2 is the solution.
Solution: 5x + 3 = 7, 3t + 6 = 12
Question 73:
Write an equation for which 0 is a solution.
Solution: 4y + 7 = 7
Question 74:
Write an equation whose solution is not a whole number.
Solution: t + 1 = 0
In questions 75 to 84, change the statements, converting expressions into statements in ordinary language:
Question 75:
A pencil costs Rs p and a pen costs Rs 5p.
Solution: The cost of the pen is 5 times the cost of pencil.
Question 76:
Leela contributed Rs y towards the Prime Minister’s Relief Fund. Leela is now left with Rs (y + 10000).
Solution: Money left with Leela 10,000 more than the amount she contributed towards prime ministers’ relief fund.
Question 77:
Kartik is n years old. His father is 7n years old.
Solution: Kartik’s father 7 time older than Kartik.
Question 78:
The maximum temperature on a day in Delhi was p°C. The minimum temperature was (p – 10)°C.
Solution: The minimum temperature in Delhi is ten less than maximum temperature of Delhi.
Question 79:
John planted t plants last year. His friend Jay planted 2t + 10 plants that year.
Solution: Jay planted a plant 2 time than jay planted and 10 more plants.
Question 80:
Sharad used to take p cups tea a day. After having some health problem, he takes p – 5 cups of tea a day.
Solution: Sharda reduced/lost the consumption of tea per day by 5 cups after having some health problem with him.
Question 81:
The number of students dropping out of school last year was m. Number of students dropping out of school this year is m – 30.
Solution: The number of students dropping out of school this is 30 year is 30 less than the number of students dropping out of school last year.
Question 82:
Price of petrol was Rs p per litre last month. Price of petrol now is Rs (p – 5) per litre.
Solution: Price of petrol is Rs 5 less than the price of the petrol was last month.
Question 83:
Khader’s monthly salary was Rs P in the year 2005. His salary in 2006 was Rs (P + 1000).
Solution: Khader’s monthly salary in 2006 was Rs 1000 more than in monthly salary in 2005.
Question 84:
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.
Solution: The number of girls enrolled in a school this year is 10 less than 3 times of the number girls enrolled in a school last year.
Question 85:
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.
Solution:
2x – 13 = 3
2x + 9 = 13
2x/3 = 12
x/5 = x – 5
x/3 – 1 = 1
Question 86:
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 (d) of a circle is twice its radius (r).
(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).
Solution:
(a) p = 3a a
A side and sides of an equal lateral triangle are equal.
(b) d = 2r, d – diameter, r – radius
(c) s = c + p, s – selling price, c – cost price, p – profit
(d) a = p + I, a – amount, p – principle, I – interest
Question 87:
Let Kanika’s present age be x years. Complete the following table, showing ages of her relatives:
Solution:
Question 88:
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:
Solution:
M = 2 , 2m – 5 = 2 x 2 – 5
= 4 – 5
= -1
Question 89:
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?
Solution: A class with p students means student is assume to be p.
Rs 50 per student is collected Means = 50p out of which Rs 1800 is paid in advance for transports. 50p -1800 money is left with them to spend on another item.
Question 90:
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?
Solution: Number of water tank = 8 to collect rain water Rain water is collected per tank is x litters if 100 litre of water was already there in one of the tanks them 8x + 100 litre amount of water in the tank on that day.
Question 91:
What is the area of a square whose side is m cm?
Solution: m × m sq. cm is the area of a square whose side is m cm.
Question 92:
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.
Solution: Perimeter of a triangle is the sum of all its three sides.
Question 93:
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.
Solution: Perimeter of rectangle is the twice the sum of length and breadth.
Question 94:
On my last birthday, I weighed 40kg. If I put on m kg of weight after a year, what is my present weight?
Solution: last birthday weight is 40kg
If I put on m kg of weight after a year then my present weight is (40 + m) kg.
Question 95:
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.
Solution:
(i) The frame is in rectangular shape length is t cm and breath is t cm. Perimeter of rectangle = 2(r + t) and extra 10cm required them 2(r + t) + 10 will the length of the aluminium strip.
(ii) X nails are used to repair on board 15x nails will be required to repair is such boards
(iii) Area of the length = r t If 500sqcm extra cloth per board is required to cores the edge mean (rt + 500) 8rt + 4000 is the total area of cloth required to cores 8 such boards.
(iv) Carpenter charge x Rs per boards 23x will be the expenditure for making 23 boards.
Question 96:
Sunita is half the age of her mother Geeta. Find their ages
(i) after 4 years?
(ii) before 3 years?
Solution: Sunita ages is half the age of her mother age Gita is her mother. G/2 Sunita present age of Sunita i.e., x years.
2 Sunita = Geeta
2x = Geeta
(i) Subita = x + 4 after 4 years
Geeta = 2x + 4
(ii) Before 2 years
Sunita = x – 3
Geeta = 2x – 3
Question 97:
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 |
Solution:
(i) The number of corners of a quadrilateral is constant —– (B)
(ii) The variable in the equation 2p + 3 = 5 is P————(F)
(iii) The solution of the equation x + 2 = 3 is +1
X + 2 = 3
X = 3 – 2 = 1
(iv) Solution of the equation 2p + 3 = 5 is
2p + 3 = 5
2p = 5 – 3
2/2 = 1
(v) A sign used in an equation =
R ———– (A)
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