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

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-5is 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.

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\}

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 – (………)

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