MCQ
The difference between an integer and its cube is divisible by
  • A
    $4$
  • $6$
  • C
    $9$
  • D
    None of these

Answer

Correct option: B.
$6$
b
(b) It can easily proved by putting $n = 2,\;3,\;4........$.

The difference between an integar and its cube is divisible by $6$.

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

Similar questions

Total number of terms in the expansion of $\left[ {{{\left( {1 + x} \right)}^{100}} + {{\left( {1 + {x^2}} \right)}^{100}}{{\left( {1 + {x^3}} \right)}^{100}}} \right]$ is
Two numbers $a$ and $b$ are chosen at random from the set of first $30$ natural numbers. The probability that ${a^2} - {b^2}$ is divisible by $3$ is
If $x = a{\rm{ }}\left( {\cos t + \log \tan {t \over 2}} \right)\,,y = a\sin t,$ then ${{dy} \over {dx}} = $
If $\vec a = \vec i + 2\vec j + 3\vec k$ , $\vec b = 2\vec i + 3\vec j + \vec k$ , $\vec c = 3\vec i + \vec j + 2\vec k$ and $\alpha \vec a + \beta \vec b + \gamma \vec c =  - 3\left( {\hat i - \hat k} \right)$ . Then the triplet $\left( {\alpha ,\beta ,\gamma } \right)$ is
${11^2} + {12^2} + {13^2} + {.......20^2} = $
Two tangents are drawn from a point $P$ on radical axis to the two circles touching at $Q$ and $R$ respectively then triangle formed by joining $PQR$ is
If the sum of the coefficients in the expansion of ${(x + y)^n}$ is $1024$, then the value of the greatest coefficient in the expansion is
${11^2} + {12^2} + {13^2} + {.......20^2} = $
The equations of the sides $AB , BC$ and $CA$ of a triangle $ABC$ are: $2 x + y =0, x + py =21 a ,( a \neq 0)$ and $x-y=3$ respectively. Let $P(2, a)$ be the centroid of $\triangle ABC$. Then $( BC )^2$ is equal to $........$
If the shortest distance between the lines $\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}$ and $\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}$ is $\frac{38}{3 \sqrt{5}} \mathrm{k}$ and $\int_0^{\mathrm{k}}\left[\mathrm{x}^2\right] \mathrm{dx}=\alpha-\sqrt{\alpha}$, where $[\mathrm{x}]$ denotes the greatest integer function, then $6 \alpha^3$ is equal to ............................