Download App

BINOMIAL THEOREM — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSBINOMIAL THEOREM1 Mark
MCQ
For $2\leq\text{r}\leq\text{n},$ $\Big(\frac{\text{n}+1}{\text{r}}\Big)+\Big(\frac{\text{n}}{\text{r}-1}\Big)+\Big(\frac{\text{n}}{\text{r}-2}\Big)$is equal to-
  • A
    $\Big(\frac{\text{n}+1}{\text{r}}\Big)$
  • B
    $2\Big(\frac{\text{n}+1}{\text{r}-1}\Big)$
  • C
    $2\Big(\frac{\text{n}+2}{\text{r}}\Big)$
  • ✓
    $\Big(\frac{\text{n}+2}{\text{r}}\Big)$
✓

Answer

Correct option: D.
$\Big(\frac{\text{n}+2}{\text{r}}\Big)$
  1. $\Big(\frac{\text{n}+2}{\text{r}}\Big)$
Solution:
${ }^{n+1} C_r+{ }^n C_{r-1}+{ }^n C_{r-2}$
$={ }^{n+1} C_r+{ }^{n+1} C_{r-1}$
$={ }^{n+2} C_r$

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 "MCQ" 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

Let $A$,$B$ and $C$ be three events such that $P\left( {A \cap \bar B \cap \bar C} \right) = 0.6$, $P\left( A \right) = 0.8$ and $P\left( {\bar A \cap B \cap C} \right) = 0.1$, then the value of $P$(atleast two among $A$,$B$ and $C$ ) equals
→
An ellipse, with foci at $(0, 2)$ and $(0, -2)$ and minor axis of length $4$, passes through which of the following points?
→
Which of the following is incorrect?
→
In geometry, we take a point, a line and a plane as undefined terms:
→
Let P(n) be the statement representing the sum of next three successive natural numbers of n, $\forall\text{n}\in\text{N},$ then the smallest value of n to which P(n) is divisible by 9 is:
→
Consider the statement: “P(n) : n2 – n + 41 is prime.” Then which one of the following is true?
→
At the point of intersection of the rectangular hyperbola $ xy = c^2 $ and the parabola $y^2 = 4ax$  tangents to the rectangular hyperbola and the parabola make an angle $ \theta $ and $ \phi $ respectively with the axis of $X$, then
→
If $(1 + \sin A)(1 + \sin B)(1 + \sin C)$$ = (1 - \sin A)(1 - \sin B)(1 - \sin C),$ then each side is equal to
→
The total number of $4-$digit numbers whose greatest common divisor with $54$ is $2$ , is $..........$.
→
$P$  is a point on the hyperbola $\frac{{{x^2}}}{{{a^2}}} - \frac{{{y^2}}}{{{b^2}}}$ $= 1, N $ is the foot of the perpendicular from $P$  on the transverse axis. The tangent to the hyperbola at $P$  meets the transverse axis at $ T$  . If $O$ is the centre of the hyperbola, the $OT. ON$  is equal to :
→