The difference between an integer and its cube is divisible by - Vidyadip

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

Explore more

More "MCQ" from 8. sequence and series→8. sequence and series — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Out of $800$ boys in a school, $224$ played cricket, $240$ played hockey and $336$ played basketball. Of the total, $64$ played both basketball and hockey; $80$ played cricket and basketball and $40$ played cricket and hockey; $24$ played all the three games. The number of boys who did not play any game is

An ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ and the parabola $x^2=4(y+b)$ are such that the two foci of the ellipse and the end points of the latusrectum of parabola are the vertices of a square. The eccentricity of the ellipse is

If $\left(\frac{1+i}{1-i}\right)^{\frac{m}{2}}=\left(\frac{1+i}{i-1}\right)^{\frac{n}{3}}=1,(m, n \in N)$ then the greatest common divisor of the least values of $m$ and $n$ is

The ratio in which the line joining the points (1, 2, 3) and (-3, 4, -5) is divided by the xy-plane is:

Let a triangle be bounded by the lines $L _{1}: 2 x +5 y =10$; $L _{2}:-4 x +3 y =12$ and the line $L _{3}$, which passes through the point $P (2,3)$, intersect $L _{2}$ at $A$ and $L _{1}$ at $B$. If the point $P$ divides the line-segment $A B$, internally in the ratio $1: 3$, then the area of the triangle is equal to

The length of latus rectum of the parabola $(x-2 a)^2+y^2=x^2$ is:

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and product of remaining two middle term is $15$, then greatest number of the series will be

The line passing through the points $(3, -4)$ and $(-2, 6)$ and a line passing through $(-3,6)$ and $(9, -18)$ are

Suppose $a_{1}, a_{2}, \ldots, a_{ n }, \ldots$ be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms of the sum of first nine terms of the progression is $5: 17$ and $110< a_{15} < 120$ , then the sum of the first ten terms of the progression is equal to -

If $OB$ is the semi-minor axis of an ellipse, $F_1$ and $F_2$ are its foci and the angle between $F_1B$ and $F_2B$ is a right angle, then the square of the eccentricity of the ellipse is