Download App

Model Paper 2 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 21 Mark
MCQ
$(\sqrt{5}+1)^4+(\sqrt{5}-1)^4$ is
  • A
    an irrational number
  • B
    a negative real number
  • C
    a rational number
  • D
    a negative integer
✓

Answer

(c) a rational number 
Explanation: We have $(a+b)^n+(a-b)^n$
$\begin{array}{l}=\left[{ }^n C_0 a^n+{ }^n C_1 a^{n-1} b+{ }^n C_2 a^{n-2}
b^2+{ }^n C_3 \quad a^{n-3} b^3+\ldots . .+{ }^n C_n b^n\right]+ \\ {\left[{ }^n
C_0 a^n-{ }^n C_1 a^{n-1} b+{ }^n C_2 a^{n-2} b^2-{ }^n C_3 a^{n-3}
b^3+\ldots . .+(-1)^n \cdot{ }^n C_n \quad b^n\right]} \\ =2\left[{ }^n C_0 \quad
a^n+{ }^n C_2 \quad a^{n-2} b^2+\ldots\right]\end{array}$
Let $a =\sqrt{5}$ and $b =1$ and $n =4$
Now we get $(\sqrt{5}+1)^4+(\sqrt{5}-1)^4=2\left[{ }^4 C_0(\sqrt{5})^4+{ }^4
C_2(\sqrt{5})^2 1^2+{ }^4 C_4(\sqrt{5})^0 1^4\right]$
$=2[25+30+1]=112$

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 Model Paper 2→Model Paper 2 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament? 
→
The probability of any sure event is :
→
In any case, the difference of the least and greatest term is:
→
The set of all values of m for which both the roots of the equation x2 − (m + 1) x + m + 4 = 0 are real and negative, is:
→

The value of $\sin(45^\circ+\theta)-\cos(45^\circ-\theta)$ is:

  1. $2\cos\theta$

  2. $2\sin\theta$

  3. 1

  4. 0

→
If (1 + ax)n = 1 + 8x + 24x2 + .... then a × n is:
    →
    The value of $\sum\limits^{\text{n}}_{\text{r}=1}\Big\{\big(2\text{r}-1\big)\text{a}+\frac{1}{\text{b}^\text{r}}\Big\}$ is equal to:
    1. $\text{an}^2+\frac{\text{b}^{\text{n}-1}-1}{\text{b}^{\text{n}-1}(\text{b}-1)}$
    2. $\text{an}^2+\frac{\text{b}^\text{n}-1}{\text{b}^\text{n}(\text{b}-1)}$
    3. $\text{an}^3+\frac{\text{b}^{\text{n}-1}-1}{\text{b}^{\text{n}}(\text{b}-1)}$
    4. none of these.
    →
    The number of irrational terms in the expansion of $\Big(4^{\frac{1}{5}}+7^{\frac{1}{10}}\Big)^{45}$ is:
    →
    The number of subsets of a set containing n elements is
    →
    What is the set of values of p for which the roots of the equation $ 3\text{x}^2 + 2\text{x} + \text{p}(\text{p} – 1) = 0$ are of opposite sign?
    →