7^ 2n + 3^ n-1 ⋅ 2^ 3n-3 is divisible by: - Vidyadip

MCQ

$7^{2n}+ 3^{n-1}⋅ 2^{3n-3}$ is divisible by:

A
$24$
✓
$25$
C
$9$
D
$13$

✓

Answer

Correct option: B.

$25$

Let $P(1) =7^{2n}+ 3^{n-1}⋅ 2^{3n-3}$
$P(1) = 50 \Rightarrow$ Divisible by $25$

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 eccentricity of the hyperbola $\frac{{\sqrt {1999} }}{3}({x^2} - {y^2}) = 1$ is

If ${\theta _1},{\theta _2}$be the inclination of tangents drawn from the point $P$ to the circle ${x^2} + {y^2} = {a^2}$ with $x - $ axis, then the locus of $P$, if given that $\cot {\theta _1} + \cot {\theta _2} = c$,is

The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is:

$\text{IQ}$ of a person is given by the formula.
$\text{IQ}=\Big(\frac{\text{MA}}{\text{CA}}\Big)\times100$ where $\text{MA}$ is mental age and $\text{CA}$ is chronological age.
If $40\leq\text{IQ}\leq120$ for a group of $10$ years old children, find the range of their mental age.

Points $P (-3,2), Q (9,10)$ and $R (\alpha, 4)$ lie on a circle $C$ with $P R$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the line $2 x - ky =1$, then $k$ is equal to $.........$.

If the standard deviation of a data is $820$ and mean of the data is $50,$ find the coefficient of variation.

If w is a complex cube root of unity, then $(1-\omega )(1-{{\omega }^{2}})$ $(1-{{\omega }^{4}})(1-{{\omega }^{8}})=$

$\sinh ix$ is [EAMCET 2002]

The latus rectum of a parabola whose directrix is $x + y - 2 = 0$ and focus is $(3, -4)$, is

Through the vertex $O$ of the parabola, $y^2 = 4ax $ two chords $OP\ \&\ OQ$ are drawn and the circles on $OP\ \&\ OQ$ as diameters intersect in $R.$ If $\theta _1, \theta _2 \& \phi $ are the angles made with the axis by the tangents at $P\ \&\ Q$ on the parabola and by $OR$ then the value of, $\cot \theta _1 + \cot \theta _2 $ =