Selina solutions concise mathematics class 6 icse Solutions for Chapter 20 substitution including use of brackets as grouping symbols

Exercises in Chapter 20 substitution including use of brackets as grouping symbols Grade 6

Exercise 20(A)

Exercise 20(B)

Exercise 20(C)

Revision Exercise

Questions in Exercise 20(A)

Q1)Fill in the following blanks, when :

x = 3,y = 6, z = 18, a = 2, b = 8, c = 32 and d = 0.

(i) $x+y=$ ..........

(ii) $y-x=$ ..........

(iii) $\frac{y}{x}=$ ..........

(iv) $c\div b=\$ ..........

(v) $z\div x=$ ..........

(vi) $y\ \times d=$ ...........

(vii) $d\div x=$ ..........

(viii) $ab\ +y=$ ..........

(ix) $a+b+x=$ ..........

(x) $b+z-d=$ ..........

(xi) $a-b+y=$ ..........

(xii) $z-a-b=$ ..........

(xiii) $d-a+x=$ ..........

(xiv) $xy-bd=$ ...........

(xv) $xz+cd=$ ...........

Q2)Find the value of :

(i) $p+2q+3r$ , when p=1, q=5 and r=2

(ii) $2a+4b+5c$ , when a=5, b=10 and c=20

(iii) $3a-2b$ , when a=8 and b=10

(iv) $2p-3q+4r-8s$ , when p=10, q=8, r=6 and s=2

(vi) $6m-2n-5p-3q$ , when m=20, n=10, p=2 and q=9

Q3)Find the value of :

(i) $4pq\times2r$ , when p=5, q=3 and r= 1/2

(ii) $\frac{yx}{z}$ , when x=8, y=4 and z=16

(iii) $\frac{a+b-c}{2a}$ , when a=5, b=7 and c=2

Q4)If a = 3, b = 0, c = 2 and d = 1, find the value of :

(i) $3a+2b-6c+4d$

(ii) $6a-3b-4c-2d$

(iii) $ab-bc+cd-da$

(iv) $abc-bcd+cda$

(v) $a^2+2b^2-3c^2$

(vi) $a^2+b^2-c^2+d^2$

(vii) $2a^2-3b^2+4c^2-5d^2$

Q5)Find the value of $5x^2-3x+2$ , when x=2.

Q6)Find the value of $3x^3-4x^2+5x-6$ , when x=-1.

Q7)Show that the value of $x^3-8x^2+12x-5$ is zero, when x = 1.

Q8)State true and false :

(i) The value of x + 5 = 6, when x = 1

(ii) The value of 2x – 3 = 1, when x = 0

(iii) $\frac{2x-4}{x+1}=-1$ , when x=1

Q9)If x = 2, y = 5 and z = 4, find the value of each of the following :

(i) $\frac{x}{2x^2}$

(ii) $\frac{xz}{yz}$

(iii) $z^x$

(iv) $y^x$

(v) $\frac{x^2y^2z^2}{xz}$

(vi) $\frac{5x^4y^2z^2}{2x^2}$

(vii) $xy\div y^2z$

(viii) $\frac{x^2y^x}{x}$

Q10)If a = 3, find the values of $a^2$ and $2^a$ .

Q11)If m = 2, find the difference between the values of $4m^3$ and $3m^4$ .

Questions in Exercise 20(B)

Q1)Evaluate :

(i) (23 – 15) + 4

(ii) 5x + (3x + 7x)

(iii) 6m – (4m – m)

(iv) (9a – 3a) + 4a

(v) 35b – (16b + 9b)

(vi) (3y + 8y) – 5y

Q2)Simplify :

(i) 12x - (5x + 2x)

(ii) 10m + (4n - 3n) - 5n

(iii) (15b - 6b) - (8b + 4b)

(iv) -(-4a - 8a)

(v) x - (x - y) - (-x + y)

(vi) p + (-q -r -s) - (p -q -r)

(vii) (a + b) - (c + d) - (e - f)

(viii) 3x + ( 8x - 5x ) - (7x - x )

(ix) a - (a - b - c)

(x) $6a^2+\left(2a^2-a^2\right)-\left(a^2-b^2\right)$

(xi) 2m - ( 3m + 2n - 6n)

(xii) -m -n - (-m) -m

(xiii) $x+y-\left(x+\overline{y-x}\right)$

(xiv) 25y - (5x - 10y + 6x - 3y)

(xv) $3x+\left(2x-\overline{x+2}\right)$

(xvi) $a-\left(2a-\overline{4a+3a}\right)$

(xvii) $5x^2-\left(3x-\overline{x^2-4}\right)$

(xviii) $-\left(y-x\right)-\left(x+y-\overline{2x+y}\right)$

Q3)Simplify :

(i) x - (y - z) + x + (y - z) + y -(z + x)

(ii) $x-\left[y+\left\{x-\left(y+x\right)\right\}\right]$

(iii) 4x+3 (2x - 5y)

(iv) 2 (3a-b) - 5(a - 3b)

(v) $p+2\left(q-\overline{r+p}\right)$

(vi) $a-\left[-\left\{-\left(a-\overline{b-c}\right)\right\}\right]$

(vii) $3x-\left[5y-\left\{6y+2\left(10y-x\right)\right\}\right]$

(viii) $5\left\{a^2-a\left(a-\overline{a-2}\right)\right\}$

Questions in Exercise 20(C)

Q1)Fill in the blanks :

(i) 2a + b - c = 2a + (.......)

(ii) 3x - z + y = 3x - (.......)

(iii) 6p - 5x + q = 6p - (.......)

(iv) a + b - c + d = a + (.......)

(v) 5a + 4b + 4x - 2c = 4x - (.......)

(vi) 7x + 2z + 4y - 3 = -3 + 4y + (.......)

(vii) 3m - 2n + 6 = 6 - (.......)

(viii) 2t + r - p - q + s = 2t + r - (.......)

Q2)Insert the bracket as indicated :

(i) x - 2y = - (.........)

(ii) m + n - p = - (.........)

(iii) a + 4b - 4c = a + (.........)

(iv) a - 3b + 5c = a - (.........)

(v) $x^2-y^2=z^2=x^2-\left(...........\right)$

(vi) $m^2+x^2-p^2=-\left(..........\right)$

(vii) 2x - y + 2z = 2z - (.........)

(viii) ab + 2bc - 3ac = 2bc - (.........)

Questions in Revision Exercise

Q1)Find the value of 3ab + 10bc – 2abc when a = 2, b = 5 and c = 8.

Q2)If x = 2, y = 3 and z = 4, find the value of $3x^2-4y^2+2z^2$ .

Q3)If x = 3, y = 2 and z = 1; find the value of:

(i) $x^y$

(ii) $y^x$

(iii) $3x^2-5y^2$

(iv) $2x-3y+4z+5$

(v) $y^2-x^2+6z^2$

(vi) $xy+y^2z-4zx$

Q4)If P= $-12x^2-10xy+5y^2$ , Q= $7x^2+6xy+2y^2$ and R= $5x^2+2xy+4y^2$ ; find :

(i) P – Q

(ii) Q + P

(iii) P – Q + R

(iv) P + Q + R

Q5)If x = $a^2-bc$ , y= $b^2-ca$ and $z=c^2-ab$ ; find the value of :

(i) ax + by + cz

(ii)ay – bx + cz

Q6)Multiply and then evaluate :

(i) (4x + y) and (x - 2y); when x = 2 and y = 1.

(ii) $\left(x^2-y\right)$ and $\left(xy-y^2\right)$ ; when x = 1 and y = 2.

(iii) (x - 2y + z) and (x -3z); when x = -2, y = -1 and z = 1

Q7)Simplify :

(i) 5 (x + 3y) – 2 (3x – 4y)

(ii) 3x – 8 (5x – 10)

(iii) 6 {3x – 8 (5x – 10)}

(iv) 3x – 6 {3x – 8 (5x – 10)}

(v) $2(3x^2-4x-8)-(3-5x-2x^2)$

(vi) 8x – (3x – 2x−3)

(vii) $8x-\left(3x-\overline{2x-3}\right)$

$12x^2-(7x-\overline{3x^2+15})$

Q8) If x = -3, find the value of :

$2x^3+8x^2-15$

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Chapters in this book

Number System (Consolidating the Sense of Numberness)

Estimation

Numbers in India and International System (With Comparison)

Place Value

Natural Numbers and Whole Numbers (Including Patterns)

Negative Numbers and Integers

Number Line

HCF and LCM

Playing with Numbers

Sets

Ratio

Proportion (Including Word Problems)

Unitary Method

Fractions

Decimal Fractions

Percent (Percentage)

Idea of Speed, Distance and Time

Fundamental Concepts (Algebra)

Fundamental Operations (Related to Algebraic Expressions)

Substitution (Including Use of Brackets as Grouping Symbols)

Framing Algebraic Expressions (Including Evaluation)

Simple (Linear) Equations (Including Word Problems)

Fundamental Concepts (Geometry)

Angles (With their Types)

Properties of Angles and Lines (Including Parallel Lines)

Triangles (Including Types, Properties and Construction)

Quadrilateral

Polygons

The Circle

Revision Exercise on Symmetry (Including Constructions on Symmetry)

Recognition of Solids

Perimeter and Area of Plane Figures

Data Handling (Including Pictograph and Bar Graph)

Mean and Median