Download App

BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM2 Marks
Question
Prove that ${\sum\limits_{r=0}^n3^r\;^nC_r=4^n}$
✓

Answer

$\sum_{r=0}^n\;^nC_ra^{n-r}b^r=\;\left(a\;+b\right)^n\;.........\left(1\right)$
$Now,\sum_{r=0}^n3^r\;^nC_r\;=\overset n{\underset{r=0}{\sum\nolimits}}\;^nC_r\;(1)^{n-r}.3^r\;=\;(1+3)^n\;\;\;\;(by\;(1)$
$\;\;\;=\;4^n$

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 "(Each question 2 marks)" 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

Find the number of different signals that can be generated by arranging at least 2 flags in order (one below the other) on a vertical staff, if five different flags are available.
→
Find the derivative of function (x + a) (it is to be understood that a, b, c, d, p, q, r, and s are fixed non-zero constants and m and n are integers).
→
How many different five-digit number licence plates can be made if.
  1. First digit cannot be zero and the repetition of digits is not allowed.
  2. The first-digit cannot be zero, but the repetition of digits is allowed?
→
Given below are two statements p : 25 is a multiple of 5. q : 25 is a multiple of 8. Write the compound statements connecting these two statements with “And” and “Or”. In both cases check the validity of the compound statement.
→
Find the equation of the parabola that satisfies the given conditions: Focus (6, 0) directrix x = -6
→
Find the equation of the line which satisfy the given conditions:
Passing through $(2,2 \sqrt{3})$ and inclined with the x-axis at an angle of $75^o$.
→
From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow0}\frac{\log\text{(a}+\text{x})-\log\text{a}}{\text{x}}$
→
Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment.
→
Find the derivative of function $\frac{a}{{{x^4}}} - \frac{b}{{{x^2}}} + \cos x$ (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers).
→