Download App

Principle of Mathematical Induction — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPrinciple of Mathematical Induction1 Mark
MCQ
Let $P(m)$ be the statement $m^2 > 100$, the statement $P(k + 1)$ will be true if:
  • A
    $P(1)$ is true
  • B
    $P(2)$ is true
  • ✓
    $P(k)$ is true
  • D
    none of these
✓

Answer

Correct option: C.
$P(k)$ is true
$P(r)$ is true
$ \Rightarrow r^2>100$
$\Rightarrow r^2+2 r+1>100+2 r+1 $
$ \Rightarrow(r+1)^2>100 $
$ \Rightarrow P(r+1) $ is true as
$r^2+(2 r+1)>r^2>100$
$\Rightarrow P(k+1)$ is true $($say $r=k)$
$P(k + 1)$ is true when every $p(k)$ is
So, In order to prove that $P(k + 1)$ is true.
It is sufficient to consider $P(k)$ is true.

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

What are the values of $k$ if the term independent of $x$ in the expansion of $\Big(\sqrt{\text{x}}+\frac{\text{k}}{\text{x}^{2}}\Big)^{10}$ is $405?$
→
If one root of the equation ${x^2} + px + q = 0$ is $2 + \sqrt 3 $, then values of $p$ and $q$ are
→
The mean of $5$ observations is $5$ and their variance is $124$ . If three of the observations are $1, 2$ and $6$; then the mean deviation from the mean of the data is
→
A person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$, then $n$ equals
→
Let $f(x)=a x^2+b x+c$, where $a, b, c$ are integers, Suppose $f(1)=0,40 < f(6) < 50,60 < f(7) < 70$ and $1000 t < f(50) < 1000(t+1)$ for some integer $t$. Then, the value of $t$ is
→
$\lim_\limits{\text{x} \rightarrow 0}\frac{2\text{x}^2+3\text{x}+4}{2}=$
→
If the cube roots of unity be $1,\omega ,{\omega ^2},$ then the roots of the equation ${(x - 1)^3} + 8 = 0$are
→
Let $A=\left\{n \in N \mid n^{2} \leq n+10,000\right\}, B=\{3 k+1 \mid k \in N\}$ and $C=\{2 k \mid k \in N\}$, then the sum of all the elements of the set $A \cap(B-C)$ is equal to $.....$
→
In a high school, a committee has to be formed from a group of $6$ boys $M _1, M _2, M _3, M _4, M _5, M _6$ and $5$ girls $G _1, G _2, G _3, G _4, G _5$

$(i)$ Let $\alpha_1$ be the total number of ways in which the committee can be formed such that the committee has $5$ members, having exactly $3$ boys and $2$ girls.

$(ii)$ Let $\alpha_2$ be the total number of ways in which the committee can be formed such that the committee has at least $2$ members, and having an equal number of boys and girls.

$(iii)$ Let $\alpha_3$ be the total number of ways in which the committee can be formed such that the committee has $5$ members, at least $2$ of them being girls.

$(iv)$ Let $\alpha_4$ be the total number of ways in which the committee can be formed such that the committee has $4$ members, having at least $2$ girls and such that both $M _1$ and $G _1$ are $NOT$ in the committee together.

 $LIST I $ $LIST I $
$P$ The value of $\alpha_1$ is $1$ $136$
$Q$ The value of $\alpha_2$ is $2$ $189$
$R$ The value of $\alpha_3$ is $3$ $192$
$S$ The value of $\alpha_4$ is $4$ $200$
  $5$ $381$
  $6$ $461$

The correct option is:

→
If $|z - 2|/|z - 3| = 2$ represents a circle, then its radius is equal to
→