If n is a positive integer, then (3 + 1)2n + 1 + (3 - 1)2n + 1 is… - Vidyadip

MCQ

If n is a positive integer, then ($\sqrt{3}$ + 1)^{2n + 1} + ($\sqrt{3}$ - 1)^{2n + 1} is:

A
an even positive integer
B
a rational number
C
an odd positive integer
D
an irrational number

✓

Answer

an irrational number

Solution:

Since n is a positive integer, assume n = 1

$(\sqrt{3}+1)³ + (\sqrt{3}−1)³$

$ = {3\sqrt{3} + 1 + 3\sqrt{3}(\sqrt{3} + 1)} + {3\sqrt{3} - 1 - 3\sqrt{3}(\sqrt{3} - 1)}$

$ = 3\sqrt{3} + 1 + 9 + 3\sqrt{3} + 3\sqrt{3}- 1 - 9 + 3\sqrt{3}$

= $12\sqrt{3}$, which is an irrational number.

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 Limits and Derivatives→Limits and Derivatives — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If A = (2, -3, 1), B = (3, -4, 6) and C is a point of trisection of AB, then C_y =

The number of real solutions of ∣2x − x²−3∣=1 is:

Choose the correct answers:
Let $\text{f(x)}=\sqrt{1+\text{x}^2}$ then.

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:

If 2x + 1 > 5 then which is true?

The number of subsets of a set containing n elements is:

n
2ⁿ - 1
n²
2ⁿ.

For two sets $\text{A}\cap\text{B = A}$ iff:

$\text{B}\subseteq\text{A}$
$\text{A}\subseteq\text{B}$
$\text{A}\not=\text{B}$
$\text{A}=\text{B}.$

The converse of the statement.

“If sun is not shining, then sky is filled with clouds” is.

If sky is filled with clouds, then the sun is not shining.
If sun is shining, then sky is filled with clouds.
If sky is clear, then sun is shining.
If sun is not shining, then sky is not filled with clouds.

Choose the correct answer.
The distance of point P(3, 4, 5) from the yz-plane is:

Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?

$\frac{1}{16}$
$\frac{16}{25}$
$\frac{1}{645}$
$\frac{1}{25}$