Mathematical Induction

Appeared 3 times across 3 years of JEE Main papers — about 1.0 questions a year. Every one of them is below, with a full worked solution.

Questions per year

1’02

1’04

1’05

01Easy3×since 2002Q4305

{a_n} = \sqrt {7 + \sqrt {7 + \sqrt {7 + .......} } }

having

n

radical signs then by methods of mathematical induction which is true

02Medium3×since 2002Q4306

Let

S(K)

= 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.

Then which of the following is true

03Medium3×since 2002Q4307

A = \left[ {\matrix{ 1 & 0 \cr 1 & 1 \cr } } \right]

and

I = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],

then which one of the following holds for all

n \ge 1,

by the principle of mathematical induction?

Mathematical Induction — previous year questions · Alror

Mathematics