KCET · Maths · Binomial Theorem
The total number of terms in the expansion of \((x+y)^{100}+(x-y)^{100}\) after simplification is
- A 51
- B 202
- C 100
- D 50
Answer & Solution
Correct Answer
(A) 51
Step-by-step Solution
Detailed explanation
Let \(f(x)=(x+y)^{100}+(x-y)^{100}\)
Here, \(\mathrm{n}=100\), which is even.
\(\therefore\) Total number of terms
\[
\begin{aligned}
&=\frac{\mathrm{n}+2}{2}=\frac{100+2}{2} \\
&=51
\end{aligned}
\]
Here, \(\mathrm{n}=100\), which is even.
\(\therefore\) Total number of terms
\[
\begin{aligned}
&=\frac{\mathrm{n}+2}{2}=\frac{100+2}{2} \\
&=51
\end{aligned}
\]
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 \(x^{3}-2 x^{2}-9 x+18=0\) and \(A=\left|\begin{array}{lll}1 & 2 & 3 \\ 4 & x & 6 \\ 7 & 8 & 9\end{array}\right|\), then the maximum value of \(A\) isKCET 2021 Hard
- The local minimum value of the function \(f^{\prime}\) given by \(f(x)=3+|x|\), \(x \in R\) is.KCET 2014 Medium
- \( \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \), then \( A, B \),
C are respectivelyKCET 2019 Hard - The area of the triangle formed by the lines joining the vertex of the parabola \( x^{2}=12 y \) to the
ends of Latus rectum isKCET 2014 Hard - The three points \(A(2, 4, 3), B(4, a, 9)\) and \(C(10, -1, 7)\) form a right-angled triangle with \(\angle B = 90^\circ\), then the value of "a" isKCET 2026 Medium
- The perimeter of a sector is a constant. If its area is to be maximum, then the sectorial angle isKCET 2012 Hard
More PYQs from KCET
- Identify the statement/s given below that does not correspond to the functions of cortisol
(i) Maintains cardiovascular system and kidney functions
(ii) Produces anti-inflammatory reactions
(iii) Maintains electrolyte balance, osmosis and blood pressure
(iv) Suppresses immune response
(v) Stimulates RBC productionKCET 2025 Hard - For sustained interference fringes in double slit experiment, essential condition/s is/are
1. sources must be coherent.
2. the intensities of the two sources must be equal.
Here, the correct option/s is/areKCET 2012 Easy - In the situation shown in the diagram, magnitude, if \(q<<|Q|\) and \(r \gg a\). The net force on the free charge \(-q\) and net torque on it about \(O\) at the instant shown are respectively. ( \(p=2 a Q\) is the dipole moment)
KCET 2023 Medium - The given diagram represents
KCET 2022 Hard - The equilibrium constant of a reaction is \(0.008\) at \(298 \mathrm{~K}\). The standard free energy change of the reaction at the same temperature isKCET 2012 Medium
- If the function \( f(x) \) satisfies \( \lim _{x \rightarrow 1} \frac{f(x)-2}{x^{2}-1}=\pi \) then \( \lim _{x \rightarrow 1} f(x)= \)KCET 2014 Medium