COMEDK · Maths · 7. Binomial Theorem
If \(4^n+15 n+P\) is divisible by 9 for all \(n \in N\), then the least negative integral value of \(P\) is
- A -1
- B -2
- C -3
- D -4
Answer & Solution
Correct Answer
(A) -1
Step-by-step Solution
Detailed explanation
Let \(f(n) = 4^n + 15n + P\). We are given that \(f(n)\) is divisible by 9 for all \(n \in N\). For \(n=1\), \(f(1) = 4^1 + 15(1) + P = 19 + P\). Since \(f(1)\) is divisible by 9, \(19 + P = 9k\) for some integer \(k\). For \(n=2\),…
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
- A number n is chosen at random from \(s = \{1, 2, 3, \dots, 50\}\). Let A = {\(n \in s : n \text{ is a prime}\)}, B = {\(n \in s : n \text{ is a square}\)} and C = {\(n \in s : n \text{ is a cube}\)}. Then, correct order of their probabilities isCOMEDK 2023 Easy
- If \(0 \leq x \leq \pi\) and \(81^{\sin ^{2} x}+81^{\cos ^{2} x}=30\) then \(x\) is equal toCOMEDK 2013 Easy
- If \(\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)\), where \(x\) and \(y\) are real, then the ordered pair \((2 x, 2 y)\) isCOMEDK 2023 Medium
- Three vertices are chosen randomly from the nine vertices of a regular 9 -sided polygon. The probability that they form the vertices of an isosceles triangle, isCOMEDK 2023 Easy
- \(\int \dfrac{1}{\sqrt{9+8 x-x^2}} d x=\varphi(x)+c\) then \(\varphi(x)=\)COMEDK 2025 Medium
- If \(A=\left[\begin{array}{ll}1 & 2 \\ 0 & 1\end{array}\right]\), then \(A^{n}\) isCOMEDK 2018 Easy
More PYQs from COMEDK
- Area bounded by the \(Y\)-axis, \(y=\cos x, y=\sin x\), when \(0 \leq x \leq \frac{\pi}{2}\) isCOMEDK 2015 Easy
- \(\int \dfrac{2 x}{\left(x^2+1\right)\left(x^2+2\right)^2} d x=\)COMEDK 2025 Medium
- The equivalent resistance of the circuit between \(A\) and \(B\) is
COMEDK 2014 Medium - The specific conductivity of a solution containing \(1.0 \mathrm{~g}\) of anhydrous \(\mathrm{BaCl}_{2}\) in \(200 \mathrm{~cm}^{3}\) of the solution has been found to be \(0.0058 \mathrm{Scm}^{-1}\). The molar and equivalent conductivity of the solution respectively areCOMEDK 2021 Medium
- The locus of the mid-point of the intercept of the line \(x \cos \alpha+y \sin \alpha=p\) between the coordinate axes isCOMEDK 2018 Easy
- The sides of a parallelogram are represented by vectors \(\mathbf{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) Then, the area of the parallelogram isCOMEDK 2023 Easy