Download App

Principle of Mathematical Induction — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical Induction1 Mark
MCQ
For all $n \in N, 3n^5+ 5n^3+ 7n$ is divisible by:
  • A
    $5$
  • ✓
    $15$
  • C
    $10$
  • D
    $3$
✓

Answer

Correct option: B.
$15$
Given number $= 3n^5+ 5n^3+ 7n$
Let $n = 1, 2, 3, 4, ……..$
$3n^5+ 5n^3+ 7n$
$= 3 \times 1^2+ 5 \times 1^3+ 7 \times 1$
$= 3 + 5 + 7 $
$= 15$
$3n^5+ 5n^3+ 7n$
$= 3 \times 2^5+ 5 \times 2^3+ 7 \times 2$
$= 3 \times 32 + 5 \times 8 + 7 \times 2$
$= 96 + 40 + 14$
$= 15 \times 10$
$= 150$
$3n^5+ 5n^3+ 7n$
$= 3 \times 3^5+ 5 \times 3^3+ 7 \times 3$
$= 3 \times 243 + 5 \times 27 + 7 \times 3$
$= 729 + 135 + 21$
$= 15 \times 59$
​​​​​​​$= 885$
Since, all these numbers are divisible by $15$ for $n = 1, 2, 3, …..$
So, the given number is divisible by $1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Principle of Mathematical Induction→Principle of Mathematical Induction — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The roots of $|x - 2{|^2} + |x - 2| - 6 = 0$are
→
Choose the correct answer. $\lim\limits_{\text{x} \rightarrow \pi}\frac{\text{x}^{2}\cos\text{x}}{1-\cos\text{x}}$ is equal to:
→
Let $m$ and $n$ be two positive integers greater than $1$ . If

$\lim _{\alpha \rightarrow 0}\left(\frac{e^{\cos \left(\alpha^n\right)}-e}{\alpha^m}\right)=-\left(\frac{e}{2}\right)$

then the value of $\frac{m}{n}$ is

→
$n (n+1) (n+5)$ is a multiple of $3$ is true for
→
Number of integral tems in the expansion of  $\left\{7^{\left(\frac{1}{2}\right)}+11^{\left(\frac{1}{6}\right)}\right\}^{824}$  is equal to..................
→
If the roots of the equation $a{x^2} + bx + c = 0$be $\alpha $and $\beta $, then the roots of the equation $c{x^2} + bx + a = 0$ are
→
If $x + y + z = {180^o},$ then $\cos 2x + \cos 2y - \cos 2z$ is equal to
→
A bag contains $8$ black and $7$ white balls. Two balls are drawn at random. Then for which the probability is more
→
If ${x^2} - 3x + 2$ be a factor of ${x^4} - p{x^2} + q,$ then $(p,q) = $
→
Solution of $\bigg|\text{x}+\frac{1}{\text{x}}\bigg|<4$ is:
→