TS EAMCET · Maths · Binomial Theorem
The absolute value of the numerically greatest term in the expansion of \((2 x-3 y)^{12}\) when \(x=3\), \(y=2\) is
- A \({ }^{12} \mathrm{C}_5 6^{12}\)
- B \({ }^{12} \mathrm{C}_6 6^{42}\)
- C \({ }^{12} \mathrm{C}_4 6^{12}\)
- D \({ }^{12} \mathrm{C}_9 6^{12}\)
Answer & Solution
Correct Answer
(B) \({ }^{12} \mathrm{C}_6 6^{42}\)
Step-by-step Solution
Detailed explanation
The absolute value of greatest term in \((2 x-3 y)^{12}\) is middle term, so \[ \begin{gathered} T_{\left(\frac{12}{2}\right)}=T_6 \\ \Rightarrow{ }^{12} C_6 \cdot(2 x){ }^6(3 y)^6={ }^{12} C_6 \cdot(2 \cdot 3)^6 \cdot(3 \cdot 2)^6={ }^{12} C_6 \cdot(6)^{12} \end{gathered} \]
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 shortest distance between the lines \(\overline{\mathrm{r}}=(3 \bar{i}-5 \bar{j}+2 \bar{k})+t(4 \bar{i}+3 \bar{j}-\bar{k})\) and \(\overline{\mathrm{r}}=(\bar{i}+2 \bar{j}-4 \bar{k})+s(6 \bar{i}+3 \bar{j}-2 \bar{k})\) isTS EAMCET 2025 Medium
- In a triangle and divide the sides and in the ratio respectively. If is the point of intersection of and then the ratio in which divides isTS EAMCET 2022 Medium
- Equation of a common tangent to the circle \(x^2+y^2=4\) and to the ellipse \(2 x^2+25 y^2=50\) isTS EAMCET 2020 Easy
- If \(\vec{a}, \vec{b}, \vec{c}\) are non-coplanar vector and the points \(\lambda \vec{a}+3 \vec{b}-\vec{c}, \vec{a}-\lambda \vec{b}+3 \vec{c}, 3 \vec{a}+4 \vec{b}-\lambda \vec{c}, \vec{a}-6 \vec{b}+6 \vec{c}\) are coplanar, then one of the values of \(\lambda\) isTS EAMCET 2024 Easy
- If are given vectors, then a vector satisfying the equations and isTS EAMCET 2021 Easy
- \(p\) is non-zero real number. If the equation whose roots are the squares of the roots of the equation \(x^3-p x^2+p x-1=0\) is identical with the given equation, then \(p=\)TS EAMCET 2020 Easy
More PYQs from TS EAMCET
- If the function \(f:[a, b] \rightarrow\left[-\frac{\sqrt{3}}{4}, \frac{1}{2}\right]\) defined by \[ f(x)=\left|\begin{array}{ccc} 1 & 1 & 1 \ 1 & 1+\sin x & 1 \ 1+\cos x & 1 & 1 \end{array}\right| \] is one-one and onto, thenTS EAMCET 2019 Medium
- Let \(\alpha \neq \beta \quad\) satisfy \(\alpha^2+1=6 \alpha, \beta^2+1=6 \beta\). Then, the quadratic equation whose roots are \(\frac{\alpha}{\alpha+1}, \frac{\beta}{\beta+1}\), isTS EAMCET 2015 Easy
- If the radius of the earth becomes \(x\) times its present value, the new period of rotation in hours isTS EAMCET 2023 Easy
- The angle between the lines whose direction cosines satisfy the equations \(l+m+n=0\), \(l^2+m^2-n^2=0\) isTS EAMCET 2009 Easy
- The number of normals that can be drawn through the point \((9,6)\) to the parabola \(y^2=4 x\) isTS EAMCET 2024 Medium
- A load of \(1 \mathrm{~kg}\) weight is a attached to one end of a steel wire of area of cross-section \(3 \mathrm{~mm}^2\) and Young's modulus \(10^{11} \mathrm{~N} / \mathrm{m}^2\). The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position the fractional change in length is \(\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)\)TS EAMCET 2008 Easy