KCET · Maths · Binomial Theorem
The number of terms in the expansion of \( \left(x^{2}+y^{2}\right)^{25}-\left(x^{2}-y^{2}\right)^{25} \) after simplification is
- A \( 13 \)
- B \( 50 \)
- C \( 00 \)
- D \( 26 \)
Answer & Solution
Correct Answer
(A) \( 13 \)
Step-by-step Solution
Detailed explanation
(A)
\( (a+b)^{n}-(a-b)^{n} \) if \( \mathrm{n} \) is odd
On simplification we get \( \frac{n+1}{2} \) terms i.e., \( \frac{25+1}{2}=13 \) terms
\( (a+b)^{n}-(a-b)^{n} \) if \( \mathrm{n} \) is odd
On simplification we get \( \frac{n+1}{2} \) terms i.e., \( \frac{25+1}{2}=13 \) terms
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
- Which of the following is a subgroup of the group \(G=\left\{2^{n} \mid n \in Z\right\}\) under multiplication?KCET 2012 Medium
- If \(\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=\overrightarrow{\mathbf{a}} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}})=\overrightarrow{\mathbf{a}} \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=1\) then \(\overrightarrow{\mathbf{a}}\) is equal toKCET 2008 Medium
- If \(f(x)=\sin \left[\pi^{2}\right] x+\cos \left[-\pi^{2}\right] x\), then \(f^{\prime}(x)\) is, here \(\left[\pi^{2}\right]\) and \(\left[-\pi^{2}\right]\) greatest integer function not greater than its valueKCET 2012 Medium
- The equation of the normal to the curve \( y\left(1+x^{2}\right)=2-x \) where the tangent crosses \( x \)-axis isKCET 2016 Medium
- The eccentricity of the ellipse \( 9 x^{2}+25 y^{2}=225 \) isKCET 2019 Easy
- The value of \( k \) such that the line \( \frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2} \) lies on the plane \( 2 x-4 y+z=7 \) isKCET 2018 Easy
More PYQs from KCET
- The wave number of the spectral line in the emission spectrum of hydrogen will be equal to \(\frac{8}{9}\) times the Rydberg's constant if the electron jumps fromKCET 2010 Easy
- The standard electrode potential for the half-cell reactions are
\[
\begin{aligned}
&\mathrm{Zn}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Zn} ; \mathrm{E}^{\circ}=-0.76 \mathrm{~V} \\
&\mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{Fe} ; \mathrm{E}^{\circ}=-0.44 \mathrm{~V}
\end{aligned}
\]
The emf of the cell reaction,
\(\mathrm{Fe}^{2+}+\mathrm{Zn} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Fe}\) isKCET 2009 Easy - A dibromo derivative of an alkane reacts with sodium metal to form an alicyclic hydrocarbon. The derivative isKCET 2010 Medium
- Three conductors draw currents of \(1 \mathrm{~A}, 2 \mathrm{~A}\) and 3 A respectively, when connected in turn across a battery. If they are connected in series and the combination is connected across the same battery, the current drawn will beKCET 2013 Medium
- A capacitor of capacitance \(5 \mu \mathrm{~F}\) is charged by a battery of emf 10 V . At an instant of time, the potential difference across the capacitors is 4 V and the time rate of change of potential difference across the capacitor is \(0.6 \mathrm{Vs}^{-1}\). Then, the time rate at which energy is stored in the capacitor at any instant isKCET 2024 Hard
- A student while extracting DNA from Aspergillus fungus __________ enzyme to break open the cell wall.KCET 2019 Medium