WBJEE · Maths · Binomial Theorem
If \(\mathrm{n} > 1\) is an integer and \(\mathrm{x} \neq 0\), then \((1+\mathrm{x})^{\mathrm{n}}-\mathrm{nx}-1\) is divisible by
- A \(\mathrm{nx}^3\)
- B \(\mathrm{n}^3 \mathrm{x}\)
- C \(\mathrm{x}\)
- D \(\mathrm{nx}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{x}\)
Step-by-step Solution
Detailed explanation
\begin{array}{r}\text {Hints: } (1+\mathrm{x})^n={ }^n C_0+{ }^n C_1 x+{ }^n C_2 x^2+{ }^n C_3 \mathrm{x} 3+\ldots \ldots . \\ =1+\mathrm{nx}+\mathrm{x}^2\left({ }^n C_2+{ }^n C_3 \mathrm{x}+\ldots \ldots . .\right) \\…
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
- Let \(z_{1}\) and \(z_{2}\) be two imaginary roots of \(z^{2}+p z+q=0\), where \(p\) and \(q\) are real. The points \(z_{1}, z_{2}\) and origin form an equilateral triangle ifWBJEE 2020 Medium
- Let \(f_{1}(x)=e^{x}, f_{2}(x)=e^{f_{1}(x)} \ldots \ldots\)
\(f_{n+1}(x)=c^{f n(x)}\) for all \(n \geq 1 .\) Then for any fixed
\(n \cdot \frac{d}{d x} f_{n}(x)\) isWBJEE 2018 Hard - The unit vector in ZOX plane, making angles \(45^{\circ}\) and \(60^{\circ}\) respectively with \(\vec{\alpha}=2 \hat{i}+2 \hat{j}-\hat{k}\) and \(\vec{\beta}=j-\hat{k}\) isWBJEE 2020 Medium
- The greatest integer which divides \((p+1)(p+2)(p+3) \ldots(p+q)\) for all
\(p \in N\) and fixed \(q \in N\) isWBJEE 2017 Easy - If \(\left(1-x+x^2\right)^n=a_0+a_1 x+\ldots . .+a_{2 n} x^{2 n}\), then the value of \(a_0+a_2+a_4+\ldots \ldots .+a_{2 n}\) isWBJEE 2010 Hard
- The value of ' \(a\) ' for which the scalar triple product formed by the vectors \(\vec{a}=\hat{i}+a \hat{j}+\hat{k}, \vec{\beta}=\hat{j}+a \hat{k}\) and \(\vec{\gamma}=a \hat{i}+\hat{k}\) is maximum, isWBJEE 2023 Easy
More PYQs from WBJEE
- What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?WBJEE 2019 Easy
- The resistance \(\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}\) where \(\mathrm{V}=(25 \pm 0.4)\) Volt and \(\mathrm{I}=(200 \pm 3)\) Ampere. The percentage error in ' R ' isWBJEE 2025 Medium
- The length of the chord of the parabola \(y^{2}=4 a x(a>0)\) which passes through the vertex and makes an acute angle \(\alpha\) with the axis of the parabola isWBJEE 2020 Medium
- \(\cos \frac{2 \pi}{7}+\cos \frac{4 \pi}{7}+\cos \frac{6 \pi}{7}\)WBJEE 2014 Medium
- If the function
\(f(x)= \begin{cases}\frac{x^2-(A+2) x+A}{x-2} & \text { for } x \neq 2 \\ 2 & \text { for } x=2\end{cases}\)
is continuous at \(x=2\), thenWBJEE 2011 Easy - A ray of light strikes a glass plate at an angle of \(60^{\circ}\). If the reflected and refracted rays are perpendicular to each other, the refractive index of glass isWBJEE 2016 Medium