JEE Mains · Maths · STD 11 - 7. binomial theoram
The remainder when \((11)^{1011}+(1011)^{11}\) is divided by \(9\) is
- A \(1\)
- B \(4\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Re}\left(\frac{(11)^{1011}+(1011)^{11}}{9}\right)=\operatorname{Re}\left(\frac{2^{1011}+3^{11}}{9}\right)\) For \(\operatorname{Re}\left(\frac{2^{1011}}{9}\right)\) \(2^{1011}=(9-1)^{337}={ }^{337} C_{0} 9^{337}(-1)^{0}\) \(+{ }^{337} C_{1} 9^{336}(-1)^{1}\)…
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
- Bag \(A\) contains \(3\) white, \(7\) red balls and bag \(B\) contains \(3\) white, \(2\) red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag \(\mathrm{A}\), if the ball drawn in white, is :JEE Mains 2024 Medium
- The mean and standard deviation of \(15\) observations were found to be \(12\) and \(3\) respectively. On rechecking it was found that an observation was read as \(10\) in place of \(12\) . If \(\mu\) and \(\sigma^2\) denote the mean and variance of the correct observations respectively, then \(15\left(\mu+\mu^2+\sigma^2\right)\) is equal to ...........JEE Mains 2024 Hard
- The number of solutions of \(sin \,3x\, = cos\, 2x\) , in the interval \(\left( {\frac{\pi }{2},\pi } \right)\) isJEE Mains 2018 Hard
- The set of all values of \(k\) for which \(\left(\tan ^{-1} x \right)^{3}+\left(\cot ^{-1} x \right)^{3}= k \pi^{3}, x \in R\), is the intervalJEE Mains 2022 Hard
- Let \(x =\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\) and \(A =\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right]\). For \(k \in N\), if \(X ^{\prime} A ^{ k } X =33\), then \(k\) is equal to.JEE Mains 2022 Hard
- The integer \('k'\), for which the inequality \(x^{2}-2(3 k-1) x+8 k^{2}-7>0\) is valid for every \(x\) in \(R ,\) isJEE Mains 2021 Medium
More PYQs from JEE Mains
- Let \(\vec{a}\) and \(\overrightarrow{ b }\) be two non-zero vectors perpendicular to each other and \(|\overrightarrow{ a }|=|\overrightarrow{ b }| .\) If \(|\overrightarrow{ a } \times \overrightarrow{ b }|=|\overrightarrow{ a }|,\) then the angle between the vectors \((\vec{a}+\vec{b}+(\vec{a} \times \vec{b}))\) and \(\vec{a}\) is equal toJEE Mains 2021 Hard
- Let \(A\) be a \(3 \times 3\) matrix having entries from. the set \(\{-1,0,1\}\). The number of all such matrices A having sum of all the entries equal to \(5\) , isJEE Mains 2022 Hard
- If the shortest distance between the lines \(\frac{x+2}{2}=\frac{y+3}{3}=\frac{z-5}{4}\) and \(\frac{x-3}{1}=\frac{y-2}{-3}=\frac{z+4}{2}\) is \(\frac{38}{3 \sqrt{5}} \mathrm{k}\) and \(\int_0^{\mathrm{k}}\left[\mathrm{x}^2\right] \mathrm{dx}=\alpha-\sqrt{\alpha}\), where \([\mathrm{x}]\) denotes the greatest integer function, then \(6 \alpha^3\) is equal to ...........JEE Mains 2024 Hard
- Let \(\mathrm{E}_1: \frac{x^2}{9}+\frac{y^2}{4}=1\) be an ellipse. Ellipses \(\mathrm{E}_1\) 's are constructed such that their centres and eccentricities are same as that of \(E_1\), and the length of minor axis of \(E_i\) is the length of major axis of \(E_{i+1}(i \geq 1)\). If \(A_i\) is the area of the ellipse \(E_i\), then \(\frac{5}{\pi}\left(\sum_{i=1}^{\infty} A_i\right)\), is equal toJEE Mains 2025 Hard
- \(\lim\limits_{x \rightarrow 0}\left(\frac{3 x^{2}+2}{7 x^{2}+2}\right)^{\frac{1}{x^{2}}}\) is equal toJEE Mains 2020 Hard
- In an increasing geometric progression ol positive terms, the sum of the second and sixth terms is \(\frac{70}{3}\) and the product of the third and fifth terms is \(49\). Then the sum of the \(4^{\text {th }}, 6^{\text {th }}\) and \(8^{\text {th }}\) terms is :-JEE Mains 2024 Hard