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Correct option is D) 11 ÷ (5 – 6) + 2

Correct option is  A) 1

Correct option is C) y

Literal coefficients are variables (letters) that represent unknown numbers.

Therefore, the literal coefficient of -y is y.

(i) Let the cost of pencil = ₹x 

then the cost of pen = double the cost of pencil = 2 × ₹ x 

∴ The cost of pen = ₹ 2x

(ii) Let the age of Yusuf = a years 

then the age of John = (a + 10) years

(iii) Let the height of Giri = x cm 

then the height of Siri = (x – 15) cm

(iv) Let the breadth = b units then the length of rectangle

= 3 times b + 2 

= (3 ∙ b + 2) units.

8x³

Given:- l = b = h = 2x

Volume of rectangular plot = l × b × h

= 2x × 2x × 2x

= 8x³

Correct option is D) The days in January month

Correct option is C) the product of 10, l, m, n

Algebraic expression, with the same degree are

i) ax² + bx + c .

ii) 4x² – 5x – 1

Correct option is  B) 3

Correct option is A) -3/2

Correct option is A) -3

Numerical coefficients are know numbers which is multiplied to variables.

Therefore, the numerical coefficient of -3z is  -3

Correct option is C) Your height

Yes, the product of two monomials is always a monomial. 

Ex: 2xy × 5y = 10xy is a monomial.

Correct option is  A) 11

Correct option is C) – 1

y + y²x + y³x² + y⁴x³

The coefficient of x² in the given expression is y³.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

1 + 2x + 3x² + 4x³

The coefficient of x² in the given expression is 3.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

Correct option is C) m is multiplied by 3 and 5 is added to the product

Correct option is  A) bx + 5

Correct option is C) 16 is added to m

As per the condition given the question = x² + z³

Therefore, the obtained expression is binomial.

Correct option is B) – 6p

x² – x + 4

The coefficient of x² in the given expression is 1.

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

Correct option is A) 7x – 3

As per the condition given the question = q³ – 2q

Therefore, the obtained expression is binomial.

If (x²y + y² + 3) is subtracted from (3x²y + 2y² + 5), then coefficient of y in the result is 2x².

(x²y + y² + 3) is subtracted from (3x²y + 2y² + 5)

= (3x²y + 2y² + 5) – (x²y + y² + 3)

= 3x²y + 2y² + 5 – x²y – y² – 3

= (3x²y – x²y) + (2y² – y²) + (5 – 3)

= 2x²y + y² + 2

As per the condition given in the question, t³ – s³

Therefore, the obtained expression is binomial.

The products of a and b, b and c and c and a = (a × b) and (b × c) and (c × a)

The, sum products of a and b, b and c and c and a = ab + bc + ca

Therefore, the obtained expression is trinomial.

We know that, area of square = side × side

= x × x

= x²

Therefore, the obtained expression is monomial.

We know that, perimeter of triangle = sum of all sides

= x + x + x

= 3x

Therefore, the obtained expression is monomial.

We know that, area of triangle = ½ × base × height

= ½ × m × n

= ½ mn

Therefore, the obtained expression is monomial.

We know that, perimeter of rectangle = 2 (length + breadth)

= 2 (p + q)

= 2p + 2q

Therefore, the obtained expression is binomial.

Let the sides of triangle are x = a + 3b,

 y = a – b and z = 2a – b 

Perimeter of triangle = x + y + z 

= (a + 3b) + (a – b) + (2a – b) 

= a + 3b + a – b + 2a – b 

= (a + a + 2a) + (3b – b – b) 

= (1 + 1 + 2)a + (3 – 1 – 1)b 

Perimeter of triangle. 

= (4a + b) units.

Given length of rectangle l = 6x + y 

breadth b = 3x – 2y 

Perimeter of Rectangle = 2 (l + b) 

= 2[(6x + y) + (3x – 2y)] 

= 2[6x + y + 3x – 2y] 

= 2[(6 + 3)x + (1 – 2)y] 

= 2[9x + (- 1) y] = 2[9x – 1y] 

= 2 × (9x) – 2 × (1y) 

∴ Perimeter of rectangle = (18x – 2y) units.

Let A = 6m³ + 4m² + 7m – 3 and 

B = 2 m² + 4 

A – B = A + (- B) 

Additive inverse of B is 

– B = – (2m³ + 4) 

= – 2m³ – 4 ∴ A – B = A + (- B) 

= (6m³ + 4m² + 7m – 3) + (- 2m³ – 4) 

= 6m³ + 4m² + 7m – 3 – 2m³ – 4 

= (6m³ – 2m³ ) + 4m² + 7m + (- 3 – 4) 

= (6 – 2)m³ + 4m² + 7m + (- 7) 

∴ A – B = 4m³ + 4m² + 7m – 7

Given 4m² n, n² p, – m² n, m² n²

Like terms: 4m² n, – m² n.

Given a², b², 2a², c²

Like terms: a², 2 a²

The sum of 2pq and 4pq = 2pq + 4pq = 6pq 

According to Sheela’s solution it is 8p²q² .

6pq ≠ 8p²q² 

Sheela’s solution is wrong.

False.

-4 is the numerical coefficient of q² in – 4pq².

i) True. 7x² and 2x have different algebraic factors and terms contain variables with different exponents.

ii) True. pq² and – 4pq² are contain variables with same exponents. So, they are like terms.

iii) False. xy, – 12x² y and 5xy² are contain variables with different exponents. So, they are unlike terms.

(d) – 9y²z

Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.

(i) Given 7x³y + 9yx³

7x³y + 9yx³ 

= (7 + 9) x³y

= 16x³y

(ii) Given

12a²b + 3ba² 

= (12 + 3) a²b

= 15a²b

(i) Given 3x and 7x

3x + 7x = (3 + 7) x

= 10x

(ii) Given -5xy and 9xy

-5xy + 9xy = (-5 + 9) xy

= 4xy

The correct option is 2xy.

9xy – (- 5xy) 

= 9xy + 5xy

= (9+ 5)xy 

= 14xy

The product of 3x (x + y) is 3x² + 3xy.

LHS

(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a)

= (a² – b²) + (b² – c²) + (c² – a²)

= a² – b² + b² – c² + c² – a²

= (a² – a²) + (b² – b²) + (c² – c²)

= 0 + 0 + 0 + 0

= RHS

The value of 10xy + 5xy + y²+ 4y² will be 15xy + 5y².

5xy + 2xz + 3xy + x² + y²

= 5xy + 3xy + 2xz + x² + y²

= 8xy + 2xz + x² + y²

Hence the number of terms = 4