✔ ⋂ ⋃ ф ܓ ⋎ ∈ ≤ ≥ ∉ ⇒ → ∞ ⊙ ⊄ ⊂ ∴ ∵ ≠ ± ∀ ✕❌ △ ≌ ∠ ॥ π ₹ θ √ ⊥ 𝛂 β ܓ ⋎ λ ∃ ⇔🇽 RESOURCE CENTRE Lab Activities Mathematics 10+1 Activity-3 , Solution: The equation of the given circle is x^2 + y^2 + 8x - 16y + 64 = 0 ⇒ x 2 + 8 x + 16 + ( y 2 − 16 y + 64 ) = 16 \Rightarrow x^2 + 8x + 16 + (y^2 - 16y + 64) = 16 ⇒ ( x + 4 ) 2 + ( y − 8 ) 2 = 4 2 \Rightarrow (x + 4)^2 + (y - 8)^2 = 4^2 ⇒ { x − ( − 4 ) } 2 + ( y − 8 ) 2 = 4 2 \Rightarrow \{ x - (-4) \}^2 + (y - 8)^2 = 4^2 Clearly, the center of the circle is ( − 4 , 8 ) (-4, 8) ( − 4 , 8 ) and its radius is 4. The image of the center after reflection in the line x = 0 x = 0 x = 0 is ( 4 , 8 ) (4, 8) ( 4 , 8 ) . So, the equation of the reflected circle is ( x − 4 ) 2 + ( y − 8 ) 2 = 4 2 (x - 4)^2 + (y - 8)^2 = 4^2 Expanding the equation: x 2 − 8 x + y 2 − 16 y + 64 = 0 x^2 - 8x + y^2 - 16y + 64 = 0 Thus, the equation of the reflected circle is x 2 − 8 x + y 2 − 16 y + 64 = 0...
Math Assignment Class VIII | Exponents & Redicals Ch-3
Mathematics Assignment Class VIII
Exponents & Redicals
Important extra questions on Exponents and Redicals class VIII strictly according to the DAV board and CBSE Board, necessary for board examinations.
Assignment chapter - 3
Question 1 :
(i) Evaluate: (2/7)y = 1
Ans. y = 0
(ii) Evaluate : (0.000064)5/6.
Ans. 0.00032
(iii) Evaluate : 22x-1 = 8x-3.
Ans. x = 8
^{1/3}\right]^{1/3})
(iv) Evaluate: (5o + 6o + 7o + 8o)1/2.
Ans. 2
(v) Evaluate: (3o + 4-1) x 22.
Ans. 5
(vi) Simplify : ^{6/5}\div(27)^{1/5})
Ans. 27
(vii) Evaluate :
Ans. 3
(viii) Find x if (16)245 = (32)x.
Ans. x = 196
^{-2/3}\times(625)^{5/4}}{\left(\frac{1}{5}\right)^{-3}})
^{2}\right]^{3/8}\div\left(\frac{-5}{6}\right)^{7/6}=\left(\frac{-5}{6}\right)^{7-x})
Question 2 :
(i) Simplify : (-2)k+1 x (-2)3 = (-2)7.
Ans. k = 3
(ii) Find the value of x if : 2(3x – 3x-1) = 324
Ans. x = 5
(iii) Find the value of x if x3 = (100)-4 x 100
Ans. 1/100
^{-1/2}\right\}^{-1/4}\right]^{2})
(iv) Simplify :
Ans.
(v) Evaluate:
Ans. 4
Question 3 :
Evauate: ^{-1/2})
Ans. 1/10
Question 4 :
Evaluate : (6-1 – 8-1)-1 + (2-1 – 3-1)-1.
Ans. 30
Question 5 :
(i) If 4x + 4x = 32, then find the value of x.
Ans. x = 2
(ii) If 4x - 4x-1 = 24, then find the value of x.
Ans. x = 5/2
(iii) Find the value of \div(4^{x-1}-4^{x+1}))
Ans. -17/15
Question 6 :
(i) Find the value of x if 5x + 5x-1 = 750
Ans. x = 4
(ii) Find the value of x if 5x - 5x-1 = 100
Ans. x = 3
(iii) If 5x-1 + 5x+1 = 130, find the value of x3.
Ans. x = 2, x3 = 8
(iv) If 6(5x – 5x-1) = 120, then find the value of x
Ans. x = 2
(v) Find the value of x if 5x + 5x+1 = 53 ✕ 30.
Ans. x = 4
(vi) If 
, then find the the value of x.
Ans. x = 2
Question 7 :
Find the value of p in 
Ans. P = 2/3
Question 8 :
Evaluate: ^{-2/3}}+\frac{1}{(256)^{-3/4}}+\frac{1}{(243)^{-1/5}})
Ans. 103
Question 9 :
Find the value of x if ^{x}=\frac{625}{576})
Ans. x = 2
Question 10 :
(i) Evaluate: ^{3}\right]^{1/4})
Ans. 7
(ii) Evaluate : ^{1/3}+(125)^{1/3}\right\}^{2}\right]^{1/3})
Ans. 7
Question 11 :
Find the value of the square root of x if
Ans.
Question 12 :
Find the value of : ^{-2}+\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2})
Ans. 29
Question 13 :
If 
, then find x.
Ans. x = 25
Question 14 :
Find the value of ^{-2/3}+\frac{1}{\left(\frac{256}{625}\right)^{1/4}}+\frac{\sqrt{25}}{\sqrt[3]{64}})
Ans. 65/16
Question 15 :
Simplify : 
Ans. 125/7
Question 16 : Simplify : 
Ans. x/y
Question 17 :
(i) Evaluate : ^{-1/2}\times\left[(81)^{1/2}+(81)^{3/2}\right])
Ans. 328
(ii) Evaluate: ^{-1/2}\left[(64)^{1/2}+(64)^{3/2}\right])
Ans. 325
(iii) Evaluate: ^{-1/2}\times\left[(0.064)^{1/3}+(0.0625)^{1/4}\right])
Ans. 4
Question 18 :
(i) Simplify :
Ans. 42
(ii) Evaluate:
Ans. 1
Question 19 :
(i) If ^{-5}\times\left(\frac{1}{3}\right)^{7}=\left(\frac{1}{3}\right)^{2x-1})
then find the value of x
Ans. x = 3/2
(ii) Evaluate : ^{-2}-\left(\frac{1}{2}\right)^{-3}\right\}\div\left(\frac{1}{4}\right)^{-2})
Ans. 1/16
Question 20 :
Ans. x = 2
Question 21 :
(i) Evaluate : ^{3/2}\times(8)^{-4/3}\times(36)^{-1/2}}{(125)^{2/3}\times(27)^{-2/3}})
Ans. 15/32
(ii) Evaluate: ^{2}\times(5^{6})^{1/3}\times(7^{-3})^{2}}{(3^{-2})^{3}\times(25)^{1/2}\times(7^{-2})^{3}})
Ans. 45
(iii) Evaluate: ^{-1/6}\times(216)^{-1/3}\times(81)^{1/4}}{(512)^{-1/3}\times(16)^{1/4}\times(9)^{-1/2}})
Ans. 9/2
(iv) Evaluate: ^{3/4}\times(216)^{-2/3}\times(125)^{1/3}}{(64)^{1/6}\times(243)^{-2/5}\times(343)^{1/3}})
Ans. 135/56
(v) Evaluate: ^{-1/4}\times(36)^{-1/2}\times(81)^{1/4}}{(216)^{-1/3}\times(512)^{-1/3}\times(16)^{1/4}})
Ans. 3
Question 22 : Find the value of x
Ans. 89 / 12
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