Download App

BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
If n is the positive integer, then $2^{3n} - 7n - 1$ is divisible by.
  • A
    7
  • B
    10
  • ✓
    49
  • D
    81
✓

Answer

Correct option: C.
49
  1. 49
Solution:
Given: $2^{3 n}-7 n-1$. It can also be written as $8^n-7 n-1$
Let $8^n-7 n-1=0$
So, $8^n=7 n+1$
$8^n=(1+7)^n$
By applying binomial theorem, we get
$8 n-1-7 n=49$ (or) $2^{3 n}-7 n-1=49$
Hence, $2^{3 n}-7 n-1$ is divisible by 49 .

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 BINOMIAL THEOREM→BINOMIAL THEOREM — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The area of the triangle enclosed by the straight lines $x = 0,$ $y = 0\,$ and $x + 2y + 3 = 0$ in sq. unit is
→
If A is the null set and B is an infinite set, then what is A × B?
→
The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is:
→
If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}, then A - B is:
→
The equation of the circle passing through the point $(-2, 4)$ and through the points of intersection of the circle ${x^2} + {y^2} - 2x - 6y + 6 = 0$ and the line $3x + 2y - 5 = 0$, is
→
If the line $y = mx + 1$ meets the circle $x^2 + y^2 + 3x = 0$ in two points equidistant from and on opposite sides of $x-$  axis, then
→
A class contains $b$ boys and $g$ girls. If the number of ways of selecting $3$ boys and $2$ girls from the class is $168$, then $b +3\,g$ is equal to.
→
Given a sequence of $4$ numbers, first three of which are in $G.P.$ and the last three are in $A.P$. with common difference six. If first and last terms in this sequence are equal, then the last term is
→
$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $
→
The value of $\mathop {\lim }\limits_{x \to 0} \,\left( {\frac{{\int_0^{{x^2}} {{{\sec }^2}\,t\,dt} }}{{x\,\sin x}}} \right)\,$ is
→