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1.

If and are whole numbers such that = 121, the value of ( - 1) is:

Answer» We know that 112 = 121. Putting m = 11 and n = 2, we get: (m - 1)n + 1 = (11 - 1)(2 + 1) = 103 = 1000.
Discussion
2.

If 3 = 27 and 3 = 243, then is equal to:

Answer» 3x - y = 27 = 33       x - y = 3 ....(i) 3x + y = 243 = 35       x + y = 5 ....(ii) On solving (i) and (ii), we get x = 4.
Discussion
3.

(17) x (17) = 17

Answer» Let (17)3.5 x (17)x = 178. Then, (17)3.5 + x = 178. 3.5 + x = 8 x = (8 - 3.5) x = 4.5
Discussion
4.

Given that 10 = , 10 = and = , then the value of is close to:

Answer» xz = y2       10(0.48z) = 10(2 x 0.70) = 101.40 0.48z = 1.40 z = 140 = 35 = 2.9 (approx.) 48 12
Discussion
5.

If 5 = 3125, then the value of 5 is:

Answer» 5a = 3125       5a = 55 a = 5. 5(a - 3) = 5(5 - 3) = 52 = 25.
Discussion
6.

The value of [(10) ÷ (10)]

Answer» (10)150 ÷ (10)146 = 10150 10146    = 10150 - 146    = 104    = 10000.
Discussion
7.

(25) x (5) ÷ (125) = 5

Answer» Let (25)7.5 x (5)2.5 ÷ (125)1.5 = 5x. Then, (52)7.5 x (5)2.5 = 5x (53)1.5 5(2 x 7.5) x 52.5 = 5x 5(3 x 1.5) 515 x 52.5 = 5x 54.5 5x = 5(15 + 2.5 - 4.5) 5x = 513 x = 13.
Discussion
8.

(0.04) = ?

Answer» (0.04)-1.5 = 4 -1.5 100    = 1 -(3/2) 25    = (25)(3/2)    = (52)(3/2)    = (5)2 x (3/2)    = 53    = 125.
Discussion
9.

(256) x (256) = ?

Answer» (256)0.16 x (256)0.09 = (256)(0.16 + 0.09)    = (256)0.25    = (256)(25/100)    = (256)(1/4)    = (44)(1/4)    = 44(1/4)    = 41    = 4
Discussion