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11. (243)n/5×32n+19n×3n−1=?

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Solution:
GivenExpression=(243)n/5×32n+19n×3n−1=(35)n/5×32n+1(32)n×3n−1=(35×(n/5)×32n+1)(32n×3n−1)=3n×32n+132n×3n−1=3(n+2n+1)3(2n+n−1)=33n+133n−1=3(3n+1−3n+1)=32=9
12. 11+a(n−m)+11+a(m−n)=?

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Solution:
11+a(n−m)+11+a(m−n)=1(1+anam)+1(1+aman)=am(am+an)+an(am+an)=(am+an)(am+an)=1
13. If m and n are whole numbers such that mn = 121, the value of (m - 1)n + 1 is:

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Solution:
We know that 112 = 121.
Putting m = 11 and n = 2, we get:
(m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000
14. (xbxc)(b+c−a).   (xcxa)(c+a−b).   (xaxb)(a+b−c)   = ?

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Solution:
Given Exp.=x(b−c)(b+c−a).x(c−a)(c+a−b).x(a−b)(a+b−c)
  =x(b−c)(b+c)−a(b−c).    x(c−a)(c+a)−b(c−a).   x(a−b)(a+b)−c(a−b)
=x(b2−c2+c2−a2+a2−b2).x−a(b−c)−b(c−a)−c(a−b)=x0.x(−ab+ac−bc+ba−ca+cb)=(x0×x0)=(1×1)=1
15. If x=3+22,    then the value of (x−1x)   is:

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Solution:
(x−1x)2=x+1x−2=(3+22)+1(3+22)−2=(3+22)+1(3+22)×(3−22)(3−22)−2=(3+22)+(3−22)−2=4∴(x−1x)=2
16. Simplify : (32+3−22−32−53)=?

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Solution:
32+3−22−32−53=3(2−3)−2(2+3)(2+3)(2−3)2−53=6−33−4−23(2+3)(2−3)(2−53)=2−532−53=1
17. (8 - 4 - 2) Equals to = ?

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Solution:
(8−4−2)=22−2−2=22−2−2=2(2−1)−2=2−2
18. (64)−23×(14)−2    is equal to ?

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Solution:
64−23×(14)−2=(43)−23×(14)−2=4−2×(14)−2=(14)2×(14)−2=(14)2−2=(14)0=1
19. The value of (92×184316)   is = ?

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Solution:
(92×184316)=92×(9×2)4316=(32)2×(32)4×24316=34×38×24316=3(4+8)×24316=312×24316=243(16−12)=2434=1681
20. [43×54]÷45=?

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Solution:
43×5445=544(5−3)=5442=62516=39.0625

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