TS EAMCET · Maths · Binomial Theorem
If \((1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad\) then \(\sum_{r=1}^{15} r \frac{a_r}{a_r-1}\) is equal to
- A 110
- B 115
- C 120
- D 135
Answer & Solution
Correct Answer
(C) 120
Step-by-step Solution
Detailed explanation
Given that \(\begin{aligned} &(1+x)^{15}=a_0+a_1 x+a_2 x^2+\ldots+a_{15} x^{15} \\ & \Rightarrow \quad{ }^{15} C_0+{ }^{15} C_1 x+{ }^{15} C_2 x^2+\ldots+{ }^{15} C_{15} x^{15} \\ &=a_0+a_1 x+a_2 x^2+\ldots+a_{15} x^{15} \end{aligned}\) Equating the coefficient of various powers…
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 direction cosines of the line passing through \(P(2,3-1)\) and the origin areTS EAMCET 2005 Easy
- The solution of \(\left(y-3 x^2\right) d x+x d y=0\) isTS EAMCET 2017 Easy
- are observations with mean and standard deviation . Match the items of List-I with those of List-II
List - I List - II (a) (i) Median (b) Variance (ii) Coefficient of variation (c) Mean deviation (iiii) Zero (d) Measure used to find the homogeneity of given two series (iv) Mean of the absolute deviations from any measure of central tendency (v) Mean of the squares of the deviations from mean TS EAMCET 2018 Hard - \(\lim _{x \rightarrow-2^{+}}\left([x]^2-[x]-2\right)+\lim _{x \rightarrow-3^{-}}\left([x]^2-4[x]+3\right)=\)TS EAMCET 2023 Easy
- If \(\triangle A B C\) is a non isosceles triangle and \(\angle C=90^{\circ}\), then \(\frac{a^2+b^2}{a^2-b^2} \sin (A-B)=\)TS EAMCET 2020 Hard
- If \(\alpha\) and \(\beta\) are scalar and \(\mathbf{r}=(2+\alpha-3 \beta) \hat{\mathbf{i}}+(\beta-3) \hat{\mathbf{j}}+(2 \alpha-5 \beta-1) \hat{\mathbf{k}}\) is equation of a plane, then that equation in Cartesian form isTS EAMCET 2021 Medium
More PYQs from TS EAMCET
- If a circle touches the ellipse internally, thenTS EAMCET 2021 Medium
- If \((2,3,-3)\) is one end of a diameter of the sphere \(x^2+y^2+z^2-6 x-12 y-2 z+20=0\), then the other end of the diameter isTS EAMCET 2010 Medium
- If \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3+p x^2+q x+r=0\), then \((\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)=\)TS EAMCET 2019 Easy
- If \(\mathrm{f}(\mathrm{x})\) is a function such that \(\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})\) and \(\mathrm{f}(1)\) \(=7\) then \(\sum_{r=1}^n \mathrm{f}(\mathrm{r})=\)TS EAMCET 2023 Easy
- An electron revolves in a circle of radius \(0.4 Å\) with a speed of \(10^6 \mathrm{~m} / \mathrm{s}\) in a hydrogen atom. The magnetic field produced at the centre of the orbit due to the motion of the electron (in Tesla) is : \(\left[\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}\right.\), charge on the electron \(\left.=1.6 \times 10^{-19} \mathrm{C}\right]\)TS EAMCET 2002 Medium
- The term independent of \(x\) in the expansions of \(\left(\sqrt{x}-\frac{2}{\sqrt{x}}\right)^{18}\) isTS EAMCET 2014 Easy