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51. If x=5+35−3   and y=5−35+3   then (x+y)  equals ?

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Solution:
x=5+35−3⇒x=5+35−3×5+35+3⇒x=(5+3)22Similarlyy=5−35+3⇒y=(5−3)22Now, x+y=5+3+215+5+3−2152=162=8
52. Simplified from of [(x−355)−53]5   is = ?

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Solution:
[(x−355)−53]5=[{(x−35)15}−53]5=[(x{(−35)×15})−53]5=[(x−325)−53]5=[x{(−325)×(−53)}]5=(x15)5=x(15×5)=x
53. What will come in place of both the question marks in the following question : (?)2342=5(?)13

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Solution:
Let (x)2342=5(x)13Then,x23.x13=42×5=210⇒x(23+13)=210⇒x=210
54. The value of 514×(125)0.25    is = ?

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Solution:
514×(125)0.25=50.25×(53)0.25=50.25×5(3×0.25)=50.25×50.75=5(0.25+0.75)=51=5
55. 123+5+22    is equal to = ?

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Solution:
123+5+22=12(3+5−22)[(3+5)+22][(3+5)−22]=12(3+5−22)(3+5)2−(22)2=12(3+5−22)9+5+65−8=12(3+5−22)65+6=2(3+5−22)5+1=2(3+5−22)(5−1)(5−1)(5+1)=2(35+5−210−3−5+22)5−1=2(25+22−210+2)4=2×2(5+2−10+1)4=5+2−10+1or,1+5+2−10
56. [8−(4942.2222−2)12]     is equal to = ?

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Solution:
[8−(4942.2222−2)12]=[8−(22×9421+2214)12]=[8−(292.2322×12)12]=[8−(2122)12]=[8−(26×12)]=[8−(23)]=[8−8]=0
57. 326+3−  263+1+  236+2  is equal to = ?

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Solution:
326+3−263+1+236+2
=(326+3×6−36−3 )−      (263+1×3−13−1 )+     (236+2 ×6−26−2 )
=32(6−3)3−    26(3−1)2+   23(6−2)2
=12−6−18+6+18−23=12−23=23−23=0
58. The value of 1(216)−23 +   1(256)−34 +   1(32)−15  is = ?

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Solution:
1(216)−23 + 1(256)−34 + 1(32)−15=1(63)−23 + 1(44)−34 + 1(25)−15=163×(−2)3 + 144×(−3)4+125×(−1)5=16−2 + 14−3 + 12−1=(62+43+21)=(36+64+2)=102
59. (48)−27×(16)−57×(3)−57=?

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Solution:
(48)−27×(16)−57×(3)−57=(16×3)−27×(16)−57×(3)−57=(16)−27×(3)−27×(16)−57×(3)−57=(16)(−27−57)×(3)(−27−57)=(16)(−77)×(3)(−77)=(16)−1×(3)−1=116×13=148
60. If 10x = 12 then 10−8x=?

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Solution:
10−8x=[10x]−8=[12]−8=28=256

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