NIMCET 2011 — Mathematics PYQ

Topic: Exponents and Powers

Question: Suppose X=2100, Y=3100 and Z=4100. Exactly one of the following is true. Which is it?

Options: (a) X+Y=Z (b) X+Y<Z (c) X+Y>Z (d) XY=Z

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Solution

1. Given values:

2. Comparing X+Y and Z:

3. Analysis: We can rewrite 4100 as:

Now compare:

Since 3>2, then 3100>2100. However, for large exponents:

Comparing 3100 and 4100: As 3<4, then 3100 is significantly smaller than 4100. Even adding a smaller value like 2100 to 3100 will not make it reach 4100.

4. Verification:

Since both (21​)100 and (43​)100 are very small fractions (much less than 0.5):

Correct Option: (b) X+Y<Z