AP EAMCET · Maths · Binomial Theorem
If \(C_j={ }^n C_j\), then \(C_0 C_r+C_1 C_{r+1}+C_2 C_{r+2}+\ldots+C_{n-r} C_n=\)
- A \(\frac{(2 n) !}{(n-2 r) !(n+2 r) !}\)
- B \(\frac{(2 n) !}{(n-r) !(n+r) !}\)
- C \(2 \mathrm{n}_{\mathrm{C}_{\mathrm{r}}}\)
- D \(2 n_{C_{r+1}}\)
Answer & Solution
Correct Answer
(B) \(\frac{(2 n) !}{(n-r) !(n+r) !}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Since }(1+x)^{2 n}=(1+x)^n(x+1)^n \\ & \Rightarrow(1+x)^{2 n}=\left(C_0+C_1 x+C_2 x^2+\ldots+C_n x^n\right) \\ & \left(C_0 x^n+C_1 x^{n-1}+C_2 x^{n-2}+\ldots+C_n\right) \end{aligned}\) Now equation co-efficient of \(x^{n-r}\) on both side…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The equation \(\sin ^4 x+\cos ^4 x=a\) has real solutions, thenAP EAMCET 2021 Medium
- Let \(A=\{-4,-2,-1,0,3,5\}\) and \(f: \mathrm{A} \rightarrow \mathbf{R}\) be defined by \(f(x)=\left\{\begin{array}{ccc}3 x-1 & \text { for } & x>3 \\ x^2+1 & \text { for } & -3 \leq x \leq 3 \\ 2 x-3 & \text { for } & x < -3\end{array}\right.\) Then the range of \(f\) isAP EAMCET 2017 Easy
- Area of the triangle formed by the lines \(3 x^2-4 x y+y^2=0,2 x-y=6\) isAP EAMCET 2004 Medium
- \(\int_0^{\frac{\pi}{4}} \frac{\sin x+\cos x}{3+\sin 2 x} d x\) is equal toAP EAMCET 2015 Medium
- In a triangle \(\mathrm{ABC}\) if \(2 r_1=3 r_2=r_3\) then \(\mathrm{a}: \mathrm{b}: \mathrm{c}=\)AP EAMCET 2017 Medium
- If the circle \(x^2+y^2+4 x-6 y+c=0\) bisects the circumference of the circle \(x^2+y^2-6 x+4 y-12=0\), then \(c\) is equal toAP EAMCET 2013 Hard
More PYQs from AP EAMCET
- \(1^2+\left(1^2+2^2\right)+\left(1^2+2^2+3^2\right)+\ldots+\)
\(\left(1^2+2^2+\ldots+n^2\right)=\)AP EAMCET 2019 Easy - The transition metal in which of the following compound has zero oxidation state.AP EAMCET 2021 Easy
- If the order and degree of the differential equation \(x \frac{d^2 y}{d x^2}=\left(1+\left(\frac{d^2 y}{d x^2}\right)^2\right)^{-1 / 2}\) are k and \(l\) respectively, then \(\mathrm{k}, l\) are the roots ofAP EAMCET 2025 Medium
- At \(25^{\circ} \mathrm{C}\), the solubility product of \(\mathrm{MCl}\) is \(1 \times 10^{-10}\). What is its molar solubility in \(0.1 \mathrm{M}\) \(\mathrm{NaCl}\) solution at same temperature?AP EAMCET 2022 Medium
- Which of the following is not an analgesic?AP EAMCET 2019 Easy
- Which one of the following coordination complexes exhibit the lowest value of magnetic moment (in BM)?AP EAMCET 2019 Medium