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State whether a given pair of terms is of like or unlike terms. (i) 1, 100 (ii) -7x, (5/2)x (iii) – 29x, – 29y (iv) 14xy, 42yx (v) 4m²p, 4mp² (vi) 12xz, 12x²z²

When terms have the same algebraic factors, they are like terms. The terms have different algebraic factors, they are unlike terms. (i) 1, 100... View Article

Classify into monomials, binomials and trinomials. (i) 4y – 7z (ii) y2 (iii) x + y – xy (iv) 100 (v) ab – a – b (vi) 5 – 3t (vii) 4p²q – 4pq² (viii) 7mn (ix) z² – 3z + 8 (x) a² + b² (xi) z² + z (xii) 1 + x + x²

(i) 4y – 7z Answer Binomial. An expression that consists of two unlike terms is called a binomial. (ii) y2 Answer Monomial. An expression... View Article

Identify terms which contain y² and give the coefficient of y². (i) 8 – xy² (ii) 5y²+ 7x (iii) 2x2y – 15xy² + 7y²

Sl.No. Expression Terms Coefficient of y2 (i) 8 – xy2 – xy2 – x (ii) 5y2 + 7x 5y2 5 (iii)... View Article

Identify terms which contain x and give the coefficient of x. (i) y²x + y (ii) 13y² – 8yx (iii) x + y + 2 (iv) 5 + z + zx (v) 1 + x + xy (vi) 12xy² + 25 (vii) 7x + xy²

Solution:- Sl.No. Expression Terms Coefficient of x (i) y2x + y y2x y2 (ii) 13y2 – 8yx – 8yx -8y (iii)... View Article

Identify the numerical coefficients of terms (other than constants) in the following expressions: (i) 5 – 3t² (ii) 1 + t + t² + t₃ (iii) x + 2xy + 3y (iv) 100m + 1000n (v) – p²q² + 7pq (vi) 1.2 a + 0.8 b (vii) 3.14 r² (viii) 2 (l + b) (ix) 0.1 y + 0.01 y²

A coefficient is a number used to multiply a variable (2x means 2 times x, so 2 is a coefficient) Variables on their own (without... View Article

Identify terms and factors in the expressions given below: (a) – 4x + 5 (b) – 4x + 5y (c) 5y + 3y² (d) xy + 2x2y² (e) pq + q (f) 1.2 ab – 2.4 b + 3.6 a (g) ¾ x + ¼ (h) 0.1 p² + 0.2 q²

A coefficient is a number used to multiply a variable (2x means 2 times x, so 2 is a coefficient) Variables on their own (without... View Article

Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams. (a) x – 3 (b) 1 + x + x² (c) y – y₃ (d) 5xy² + 7x2y (e) – ab + 2b² – 3a²

(a) x – 3 Answer Expression: x – 3 Terms: x, -3 Factors: x; -3 (b) 1 + x + x2 Answer Expression: 1 + x + x2 Terms: 1, x,... View Article

Get the algebraic expressions in the following cases using variables, constants and arithmetic operations. (i) Subtraction of z from y. (ii) One-half of the sum of numbers x and y. (iii) The number z multiplied by itself. (iv) One-fourth of the product of numbers p and q. (v) Numbers x and y both squared and added. (vi) Number 5 added to three times the product of numbers m and n. (vii) Product of numbers y and z subtracted from 10. (viii) Sum of numbers a and b subtracted from their product.

(i) Subtraction of z from y. Answer = Y – z (ii) One-half of the sum of numbers x and y. Answer = 1/2 (x + y) = (x + y)/2 (iii)... View Article

Find the area of the quadrilateral ABCD. Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM ⊥ AC, DN ⊥ AC

Given AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM ⊥ AC, DN ⊥ AC Find out We have to determine the area of the quadrilateral... View Article

In the following figures, find the area of the shaded portions:

To determine the area of EFDC, first we have to find the area of ΔAEF, ΔEBC and rectangle ABCD Area of ΔAEF =... View Article

The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find: (i) the area of the whole land (ii) the area of the flower bed (iii) the area of the lawn excluding the area of the flower bed (iv) the circumference of the flower bed.

Given From the given data we get to know that The radius of a circular pipe = 4 cm Side of a square = 4 cm Find out We have to determine... View Article

Pragya wrapped a cord around a circular pipe of radius 4 cm (adjoining figure) and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (π = 3.14)

Given From the given data we get to know that The radius of a circular pipe = 4 cm Side of a square = 4 cm Find out We have to determine if... View Article

Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find (i) the area covered by the roads. (ii) the cost of constructing the roads at the rate of ₹ 110 per m²

Given From the given data we get to know that Length of the field (L) = 90 m Breadth of the field (B) = 60 m Find out We have to determine... View Article

Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.

Given From the given data we get to know that Length of the park (L) = 700 m Breadth of the park (B) = 300 m Find out We have to determine... View Article

A path 1 m wide is built along the border and inside a square garden of side 30 m. Find: (i) the area of the path (ii) the cost of planting grass in the remaining portion of the garden at the rate of ₹ 40 per m²

Given From the given data we get to know that Side of square garden (s) = 30 m Find out (i) the area of the path (ii) the cost of planting... View Article

A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find: (i) the area of the verandah. (ii) the cost of cementing the floor of the verandah at the rate of ₹ 200 per m².

Given From the given data we get to know that Length of the cardboard (L) = 8 cm Breadth of the cardboard (B) = 5 cm Find out (i) the area... View Article

A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.

Given From the given data we get to know that Length of the cardboard (L) = 8 cm Breadth of the cardboard (B) = 5 cm Find out We have to... View Article

A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.

Given From the given data we get to know that Length of the park (L) = 125 m Breadth of the park (B) = 65 m Find out We have to determine... View Article

A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

Given From the given data we get to know that Length of the garden (L) = 90 m Breadth of the garden (B) = 75 m Find out We have to... View Article

The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)

Given From the given details we get to know that Length of the minute hand of the circular clock = 15 cm Find out We have to determine how... View Article