WBJEE · Maths · Binomial Theorem
If \(\mathrm{c}_{0}, \mathrm{c}_{1}, \mathrm{c}_{2}, \ldots \ldots \mathrm{c}{15}\) are the Binomial co-efficients in the expansion of \((1+\mathrm{x})^{15}\), then the value of \(\frac{\mathrm{C}{1}}{\mathrm{c}{0}}+2 \frac{\mathrm{C}{2}}{\mathrm{c}{1}}+3 \frac{\mathrm{c}{3}}{\mathrm{c}{2}}+\ldots \ldots+15 \frac{\mathrm{c}{15}}{\mathrm{c}{14}}\) is
- A 1240
- B 120
- C 124
- D 140
Answer & Solution
Correct Answer
(B) 120
Step-by-step Solution
Detailed explanation
Hint: \(S_{n}=\sum_{r=1}^{15} r \frac{{ }^{15} C_{r}}{{ }^{15} c_{r-1}}=\sum_{r=1}^{15}(15-r+1)=16 \times 15-\frac{15 \times 16}{2}=120\)
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
- If \(x \frac{d y}{d x}+y=x \frac{f(x y)}{f^{\prime}(x y)}\), then \(|f(x y)|\) is equal toWBJEE 2022 Easy
- The points representing the complex number z for which arg \(\left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}\) lie onWBJEE 2012 Medium
- On the set \(R\) of real numbers, the relation \(\rho\) is defined by \(x \rho y,(x, y) \in R\)WBJEE 2018 Easy
- The equation of the plane, which bisects the line joining the points (1,2,3) and (3,4,5) at right angles isWBJEE 2019 Medium
- Let \(f: R \rightarrow R\) be defined by \(f(x)=x^{2}-\frac{x^{2}}{1+x^{2}}\) for all \(x \in R\). Then,WBJEE 2019 Easy
- Let \(Q=\left(\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)\) and\(x=\left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right)\) then \(Q^{3} x\) is equal toWBJEE 2016 Medium
More PYQs from WBJEE
- Which of the following solutions will turn violet when a drop of lime juice is added to it?WBJEE 2017 Easy
- A wooden block is floating on water kept in a beaker. \(40 \%\) of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to \(g / 2\). The block will thenWBJEE 2014 Medium
- If \(\alpha, \beta\) be the roots of the quadratic equation \(\mathrm{x}^2+\mathrm{x}+1=0\) then the equation whose roots are \(\alpha^{19}, \beta^7\) isWBJEE 2010 Hard
- The locus of the center of a variable circle which always touches two given circles externally isWBJEE 2021 Easy
-
In the given circuit, the binary inputs at \(A\) and \(B\) are both 1 in one case and both 0 in the next case. The respective outputs at \(Y\) in these two cases will beWBJEE 2017 Easy - In the bandgap between valence band and conduction band in a material is \(5.0 \mathrm{eV},\) then the material isWBJEE 2014 Easy