AIEEE 2005 | Mathematical Induction Question 1 | Mathematics

This chapter is currently out of syllabus

AIEEE 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

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

$${A^n} = nA - \left( {n - 1} \right){\rm I}$$

$${A^n} = {2^{n - 1}}A - \left( {n - 1} \right){\rm I}$$

$${A^n} = nA + \left( {n - 1} \right){\rm I}$$

$${A^n} = {2^{n - 1}}A + \left( {n - 1} \right){\rm I}$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Out of Syllabus

Let $$S(K)$$ $$ = 1 + 3 + 5... + \left( {2K - 1} \right) = 3 + {K^2}.$$ Then which of the following is true

Principle of mathematical induction can be used to prove the formula

$$S\left( K \right) \Rightarrow S\left( {K + 1} \right)$$

$$S\left( K \right) \ne S\left( {K + 1} \right)$$

$$S\left( 1 \right)$$ is correct

AIEEE 2002

MCQ (Single Correct Answer)

-1

Out of Syllabus

If $${a_n} = \sqrt {7 + \sqrt {7 + \sqrt {7 + .......} } } $$ having $$n$$ radical signs then by methods of mathematical induction which is true

$${a_n} > 7\,\,\forall \,\,n \ge 1$$

$${a_n} < 7\,\,\forall \,\,n \ge 1$$

$${a_n} < 4\,\,\forall \,\,n \ge 1$$

$${a_n} > 3\,\,\forall \,\,n \ge 1$$

JEE Main Subjects