Download App

Model Paper 1 — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsModel Paper 11 Mark
MCQ
$\left\{C_0+2 C_1+3 C_2+\ldots+(n+1) C_n\right\}=?$
  • A
    $( n +1). 2^{ n }$
  • B
    $( n +2) . 2^{ n +1}$
  • ✓
    $( n +2). 2^{ n -1}$
  • D
    $n . 2^{ n -1}$
✓

Answer

Correct option: C.
$( n +2). 2^{ n -1}$
Here, $C _0+2 C _1+3 C _2+\ldots+( n +1) C _{ n }$
$=\left(C_0+C_1+C_2+\ldots+C_n\right)+\left(C_1+2 C_2+3 C_3+\ldots+n C_n\right)$
$=2^n+n \cdot 2^{n-1}$
$=(n+2) \cdot 2^{n-1}$

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 1→Model Paper 1 — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Let $P(2,3)$ , $Q(6,0)$ and $R(\alpha ,\beta )$ be three points in $x-y$ plane such that
$|PR + QR| + |PR -QR|$ is minimum then the value of $(\alpha  -2\beta )$ is
→
The range of values of $'a'$ such that the angle $\theta$ between the pair of tangents drawn from the point $(a, 0)$ to the circle $x^2 + y^2 = 1$ satisfies $\frac{\pi }{2} < \theta < \pi$ is :
→
A series can also be denoted by symbol $.........$
→
Let $S$ be the set of all passwords which are six to eight characters long, where each character is either an alphabet from $\{ A , B , C , D , E \}$ or a number from $\{1,2,3,4,5\}$ with the repetition of characters allowed. If the number of passwords in $S$ whose at least one character is a number from $\{1,2,3,4,5\}$ is $\alpha \times 5^{6}$, then $\alpha$ is equal to $.......$
→
The equation of the circle passing through the origin and cutting intercepts of length $3$ and $4$ units from the positive axes, is
→
The number of solutions for the equations $|z - 1| = |z - 2| = $ $|z - i|$ is
→
What is the value of the $\lim_\limits{\text{x} \rightarrow 5}\frac{32\text{x}+1}{\text{x}^2-5\text{x}}?$
→
Mark the correct answer for $3 i^{34}+5 i^{27}-2 i^{38}+5 i^{41}=$ ?
→
If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is 
→
If $x$ be real, the least value of ${x^2} - 6x + 10$ is
→