JEE Mains · Maths · STD 11 - 7. binomial theoram
Suppose \(2-p, p, 2-\alpha, \alpha\) are the coefficient of four consecutive terms in the expansion of \((1+x)^n\). Then the value of \(p^2-\alpha^2+6 \alpha+2 p\) equals
- A \(4\)
- B \(10\)
- C \(8\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(2-p, p, 2-\alpha, \alpha\) Binomial coefficients are…
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 \(O \) be the vertex and \(Q\) be any point on the parabola \({x^2} = 8y\) .If the point \(P\) divides the line segment \(OQ\) internally in the ratio \( 1:3\) , then locus of \(P\) is :JEE Mains 2015 Hard
- Let \([t]\) denote the greatest integer \(\leq t\). The number of points where the function \(f(x)=[x]\left|x^{2}-1\right|+\sin \left(\frac{\pi}{[x]+3}\right)-[x+1], x \in(-2,2)\) is not continuous is ..... .JEE Mains 2021 Hard
- The equation of the plane containing the line \(2x- 5y+ z = 3; x +y+ 4z = 5,\) and parallel to the plane, \(x + 3y+ 6z = 1,\) is:JEE Mains 2015 Medium
- Let \(P\) be the point \((10,-2,-1)\) and \(Q\) be the foot of the perpendicular drawn from the point \(\mathrm{R}(1,7,6)\) on the line passing through the points \((2,-5,11)\) and \((-6,7,-5)\). Then the length of the line segment \(\mathrm{PQ}\) is equal to ..........JEE Mains 2024 Medium
- Let \(\alpha = 3\sin^{-1}\left(\dfrac{6}{11}\right)\) and \(\beta = 3\cos^{-1}\left(\dfrac{4}{9}\right)\), where inverse trigonometric functions take only the principal values.
Given below are two statements:
Statement I: \(\cos(\alpha+\beta) > 0\).
Statement II: \(\cos(\alpha) < 0\).
In the light of the above statements, choose the correct answer from the options given below:JEE Mains 2026 Medium - If \(\left(\frac{1}{\alpha+1}+\frac{1}{\alpha+2}+\ldots+\frac{1}{\alpha+1012}\right) \) \( -\left(\frac{1}{2 \cdot 1}+\frac{1}{4 \cdot 3}+\frac{1}{6 \cdot 5}+\ldots+\frac{1}{2024 \cdot 2023}\right) \) \( =\frac{1}{2024}, \) then \(\alpha\) is equal to-JEE Mains 2024 Hard
More PYQs from JEE Mains
- If \(z =2+3 i\), then \(z ^{5}+(\overline{ z })^{5}\) is equal to.JEE Mains 2022 Medium
- If the solution of the differential equation \((2 x+3 y-2) d x+(4 x+6 y-7) d y=0, y(0)=3\), is \(\alpha x+\beta y+3 \log _e|2 x+3 y-\gamma|=6\), then \(\alpha+2 \beta+3 \gamma\) is equal toJEE Mains 2024 Hard
- If \(f(x)=\left\{\begin{array}{cl}x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.\), thenJEE Mains 2024 Hard
- Let the lines \(\frac{x-1}{\lambda}=\frac{y-2}{1}=\frac{z-3}{2}\) and \(\frac{ x +26}{-2}=\frac{ y +18}{3}=\frac{ z +28}{\lambda}\) be coplanar and \(P\) be the plane containing these two lines. Then which of the following points does \(NOT\) lies on \(P\)?JEE Mains 2022 Hard
- The sum of all rational terms in the expansion of \(\left(1+2^{1 / 3}+3^{1 / 2}\right)^6\) is equal toJEE Mains 2025 Easy
- If a variable line drawn through the intersection of the lines \(\frac{x}{3} + \frac{y}{4} = 1\) and \(\frac{x}{4} + \frac{y}{3} = 1\) , meets the coordinate axes at \(A\) and \(B,\) \((A \ne B),\) then the locus of the midpoint of \(AB\) isJEE Mains 2016 Hard