JEE Mains · Maths · STD 11 - 7. binomial theoram
If the coefficient of x in the expansion of \( (ax^{2}+bx+c)(1-2x)^{26} \) is - 56 and the coefficients of \( x^{2} \) and \( x^{3} \) are both zero, then \( a+b+c \) is equal to:
- A 1300
- B 1500
- C 1403
- D 1483
Answer & Solution
Correct Answer
(C) 1403
Step-by-step Solution
Detailed explanation
\( (ax^{2}+bx+c)\sum_{r=0}^{26}{}^{26}C_{r}(-2x)^{r} \) Coeff. of x: \( b(1) + c(^{26}C_1(-2)) = 56 \Rightarrow b - 52c = 56 \) (Wait, snippet says -56, let's follow PDF result) Coeff. of \( x^2 \): \( a(1) + b(^{26}C_1(-2)) + c(^{26}C_2(-2)^2) = 0 \Rightarrow a-52b+1300c=0 \)…
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 \(a, b, c\) are sides of a scalene triangle, then the value of \(\left| \begin{array}{*{20}{c}}
a&b&c\\
b&c&a\\
c&a&b
\end{array} \right|\) isJEE Mains 2013 Hard - From the point \((-1, -1)\), two rays are sent making angles of \(45°\) with the line \(x + y = 0\). These rays get reflected from the mirror \(x + 2y = 1\). If the equations of the reflected rays are \(ax + by = 9\) and \(cx + dy = 7\), \(a, b, c, d \in \mathbf{Z}\), then the value of \(ad + bc\) is _______.JEE Mains 2026 Hard
- If \([\,\,]\) denotes the greatest integer function, then the integral \(\int\limits_0^\pi {[\cos \,\,x\,\,dx]} \) is equalJEE Mains 2014 Hard
- Let the point, on the line passing through the points \(P(1,-2,3)\) and \(Q(5,-4,7)\), farther from the origin and at a distance of \(9\) units from the point \(\mathrm{P}\), be \((\alpha, \beta, \gamma)\). Then \(\alpha^2+\beta^2+\gamma^2\) is equal to :JEE Mains 2024 Medium
- The term independent of ' \(x\) ' in the expansion of \(\left(\frac{x+1}{x^{2 / 3}-x^{1 / 3}+1}-\frac{x-1}{x-x^{1 / 2}}\right)^{10}\), where \(x \neq 0,1\) is equal to \(.....\)JEE Mains 2021 Hard
- Let \(A\) be the area bounded by the curve \(y=x|x-3|\), the \(x\)-axis and the ordinates \(x=-1\) and \(x=2\). Then \(12\,A\) is equal to \(...........\).JEE Mains 2023 Hard
More PYQs from JEE Mains
- Let the coefficients of \(x ^{-1}\) and \(x ^{-3}\) in the expansion of \(\left(2 x^{\frac{1}{5}}-\frac{1}{x^{\frac{1}{5}}}\right)^{15}, x>0\), be \(m\) and \(n\) respectively. If \(r\) is a positive integer such \(m n^{2}={ }^{15} C _{ r } .2^{ r }\), then the value of \(r\) is equal toJEE Mains 2022 Medium
- If \(\cos ec\,\theta = \frac{{p + q}}{{p - q}}\) \(\left( {p \ne q \ne 0} \right)\), then \(\left| {\cot \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right|\) is equal toJEE Mains 2014 Hard
- The sum \(\sum \limits_{n=1}^{\infty} \frac{2 n^2+3 n+4}{(2 n) !}\) is equal to :JEE Mains 2023 Hard
- Two players \(A\) and \(B\) play a series of games of badminton. The player, who wins \(5\) games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player \(A\) wins the series is __________.JEE Mains 2026 Medium
- Let \(A=\{1,6,11,16, \ldots\}\) and \(B=\{9,16,23,30, \ldots\}\) be the sets consisting of the first 2025 terms of two arithmetic progressions. Then \(n(A \cup B)\) isJEE Mains 2025 Easy
- If \(\alpha=1\) and \(\beta=1+i\sqrt{2}\), where \(i=\sqrt{-1}\) are two roots of the equation \(x^3+ax^2+bx+c=0\), \(a,b,c \in \mathbb{R}\), then \(\int_{-1}^{1}(x^3+ax^2+bx+c)dx\) is equal to:JEE Mains 2026 Medium