RBSE Class 7 Maths Important Questions Chapter 12 Algebraic Expressions

Rajasthan Board RBSE Class 7 Maths Important Questions Chapter 12 Algebraic Expressions Important Questions and Answers.

RBSE Class 7 Maths Chapter 12 Important Questions Algebraic Expressions

Multiple Choice Questions

Question 1.
Number of terms in the expression 3x²y - 2y²z - z²x + 5 is :
(a) 2
(b) 3
(c) 4
(d) 5
Answer:
(c) 4

Question 2.
Coefficient of x in - 9xy²z is :
(a) 9yz
(b) - 9yz
(c) 9y²z
(d) -9y²z
Answer:
(d) -9y²z

Question 3.
Which of the following is a pair of like terms?
(a) - 7xy²z, - 7x2yz
(b) - 10xyz², 3xyz²
(c) 3xyz, 3x²y²z²
(d) 4xyz², 4x²yz
Answer:
(b) - 10xyz², 3xyz²

Question 4.
The sum of x⁴ - xy + 2y² and - x⁴ + xy + 2y² is:
(a) 4y²
(b) - 8y²
(c) 2xy
(d) - 2y²
Answer:
(a) 4y²

Question 5.
The subtraction of 5 times ofy from x is:
(a) 5x - y
(b) y - 5x
(c) x - 5y
(d) 5y - x
Answer:
(b) y - 5x

Question 6.
123x²2y - 138x²y is a like term of:
(a) 10xy
(b) - 15xy
(c) - 15xy²
(d) 10x²y
Answer:
(d) 10x²y

Question 7.
The value of 3x² - 5x + 3 when x = 1 is :
(a) 1
(b) 0
(c) - 1
(d) 11
Answer:
(a) 1

Fill in the Blanks

Question 1.
3a²b and - 76a² are __________ terms.
Answer:
like

Question 2.
Number of terms in a monomial is __________
Answer:
one

Question 3.
Like terms in the expression n(n + 1) + 6 (n - 1) are __________
Answer:
n and 6n

Question 4.
3x + 23x² + 6y² + 2x + y² + __________ = 5x + 7y².
Answer:
- 23x²

Question 5.
If Rohit has 5ry toffees and Shantanu has 20yx toffees. Shantanu has more toffees.
Answer:
15xy

State whether True or False

Question 1.
Sum of x andy is x +y.
Answer:
True

Question 2.
A trinomial has exactly three terms.
Answer:
True

Question 3.
4p is the numerical coefficient of q² in - 4pq².
Answer:
False

Question 4.
If we add a monomial and binomial, then answer can never be monomial.
Answer:
False

Question 5.
If we subtract a monomial from a binomial, then answer is always binomial.
Answer:
False

Very Short Answer Type Questions

Question 1.
Write the coefficient of x² in the following:
(i) x² - x + 4
(ii) x³ - 2x² + 3x + 1
(iii) 1 + 2x + 3x² + 4x³
(iv) y + y²x + y³x² + y⁴x³
Answer:
(i) Coefficient of x² = 1
(ii) Coefficient of x² = - 2
(iii) Coefficient of x² = 3
(iv) Coefficient of x² = y³

Question 2.
Add 3x + 11 + 7x - 5.
Answer:
3x + 11 + 7x - 5
= 3x + 7x + 11 - 5 = 10x + 6.

Question 3.
If n - - 2 then find the value of 5n - 2.
Answer:
Put n = - 2 in 5n - 2
= 5 (- 2) - 2 = - 10 - 2 = - 12

Question 4.
Draw a tree diagram of terms and factors of 1 + x + x².
Answer:

Question 5.
Find the number of terms in 4p²qr - 4pq².
Answer:
Two.

Short Answer Type Questions

Question 1.
Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial:
(a) 3x²yz² - 3xy²z + x²yz² + 7xy²z
Answer:
3x²y²z - 3xy²z + x²yz² + 7xy²z
= (3x²yz² + x²yz²) + (- 3xy²z + 7xy²z)
= 4x²yz² + 4xy²z
As, the expression has two terms, therefore it is a binomial.

(b) x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y²
Answer:
x⁴ + 3x³y + 3x²y² - 3x³y - 3xy³ + y⁴ - 3x²y²
= x⁴ + (3x³y - 3x³y) + (3x²y² - 3x²y²) - 3xy³ + y⁴
= x⁴ + 0 + 0 - 3xy³ + y⁴
= x⁴ - 3xy³ + y⁴
As, the expression has three terms, therefore it is a trinomial.

Question 2.
Find the value of polynomials for m = 1, n = - 1 and p = 1:
(a) m + n +p
(b) m² + n² + p²
(c) m³ + n³ +p³ - 3mnp
(d) m²n² + n²p² + p²m²
Answer:
(a) m + n+ p = 1 - 1 + 1 = 0 + 1 = 1
(b) m² + n² + p² = (1)² + (- 1)² + (1)² - 1 + 1 + 1 = 3
(c) m³ + n³ + p³ - 3mnp = (1)³ + (- 1)³ + (1)³ -3 × 1 × -1 × 1 = 1 -1 + 1 + 3 = 0 + 1 + 3 = 4
(d) m²n² + n²p² + p²m² = (1)² × (- 1)² + (- 1)² × (1)² + (1)² × (1)²
= 1 × 1 + 1 × 1 + 1 × 1 = 1 + 1 + 1 = 3