( * 20 c n 0 ) + 2 , ( * 20 c n 1 ) + 2^2 ( * 20 c n 2 ) + ..... … - Vidyadip

MCQ

$\left( {\begin{array}{*{20}{c}}n\\0\end{array}} \right) + 2\,\left( {\begin{array}{*{20}{c}}n\\1\end{array}} \right) + {2^2}\left( {\begin{array}{*{20}{c}}n\\2\end{array}} \right) + ..... + {2^n}\left( {\begin{array}{*{20}{c}}n\\n\end{array}} \right)$ is equal to

A
${2^n}$
B
$0$
✓
${3^n}$
D
None of these

✓

Answer

Correct option: C.

${3^n}$

c
(c) ${(1 + x)^n} = {}^n{C_0} + x.{}^n{C_1} + {x^2}.{}^n{C_2} + .... + {x^n}.{}^n{C_n}$

Put $x = 2$

==> ${3^n} = {}^n{C_0} + 2.{}^n{C_1} + {2^2}.{}^n{C_2} + {2^3}.{}^n{C_3} + .... + {2^n}{.^n}{C_n}$.

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 "M.C.Q (1 Marks)" from STD 11 - 7. binomial theoram→STD 11 - 7. binomial theoram — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

The equation of circle passing through the points $(1, \sqrt 2 ), (7,\sqrt 2 )$ and $(1, 3)$ is

The value of the limit $\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - {e^{ - x}} - 2x}}{{x - \sin \,x}}$ is

If the points $( - 5,\,1),\,(p,\,5)$ and $(10,\,7)$ are collinear, then the value of $p$ will be

If the line $ax + y = c,$ touches both the curves $x^2 + y^2 = 1$ and $y^2 - 4\sqrt 2 x ,$ then $|c|$ is equal to

$^n{C_r} + {2^n}{C_{r - 1}}{ + ^n}{C_{r - 2}} = $

If $\text{cosec x}+\cot\text{x}=\frac{11}{2},$ then $\tan\text{x}=$

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac {1}{2}$ each and the remaining $10$ items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac {4}{3}$ then $\left| d \right|$ equals

A card is drawn from a pack of $52$ cards. If $A =$ card is of diamond, $B =$ card is an ace and $A \cap B = $ card is ace of diamond, then events $A$ and $B$ are

The sum of the first four terms of an $A.P.$ is $56$. The sum of the last four terms is $112$. If its first term is $11$, the number of terms is

If $2x - 4y = 9$ and $6x - 12y + 7 = 0$ are the tangents of same circle, then its radius will be