TS EAMCET · Maths · Binomial Theorem
If the coefficients of \((2 r+1)^{\text {th }}\) term and \((r+1)^{\text {th }}\) term in the expansion of \((1+x)^{42}\) are equal then \(r\) can be
- A 12
- B 14
- C 16
- D 20
Answer & Solution
Correct Answer
(B) 14
Step-by-step Solution
Detailed explanation
We have, \((1+x)^{42}\) \[ \begin{gathered} T_{2 r+1}={ }^{42} C_{2 r} x^{2 r} \\ T_{r+1}={ }^{42} C_r x^r \end{gathered} \] Coefficient of \((2 r+1)^{\text {th }}\) and \((r+1)^{\text {th }}\) term are equal…
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 real valued function \(f:[4, \infty) \rightarrow \mathbb{R}\) is defined as \(f(x)=\left(x^2+x+1\right)^{\left(x^2-3 x-4\right)}\), then \(f\) isTS EAMCET 2025 Medium
- \(\int_0^{\pi / 4} \frac{\sec x}{3 \cos x+4 \sin x} d x=\)TS EAMCET 2025 Medium
- If the complex cube roots of are thenTS EAMCET 2019 Hard
- \(y=2 x^3-8 x^2+10 x-4\) is a function defined on \([1,2]\). If the tangent drawn at a point \((a, b)\) on the graph of this function is parallel to \(X\)-axis and \(a \in(1,2)\), then \(a=\)TS EAMCET 2024 Medium
- The tangents drawn from a point \((2,-1)\) touch the circle \(x^2+y^2+4 x-2 y+1=0\) at the points A and B. If C is the centre of the circle, then the area (in sq. units) of the triangle ABC isTS EAMCET 2025 Medium
- A bag contains \(n\) white and \(n\) black balls. Pairs of balls are drawn at random without replacement successively, until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is 14400 , then \(n\) is equal toTS EAMCET 2011 Medium
More PYQs from TS EAMCET
- Match the items given in List A with those of the items of List B
The correct match is \(\begin{array}{llll}A & B & C & D\end{array}\)TS EAMCET 2021 Medium - The number of moles of oxalate ions oxidized by one mole of permanganate ions in acidic medium isTS EAMCET 2025 Medium
- A body of mass \(1 \mathrm{~g}\) and carrying a charge \(10^{-8} \mathrm{C}\) passes from two points \(P\) and \(Q . P\) and \(Q\) are at electric potentials. \(600 \mathrm{~V}\) and \(0 \mathrm{~V}\), respectively. The velocity of the body at \(Q\) is \(20 \mathrm{cms}^{-1}\). It velocity in \(\mathrm{ms}^{-1}\) at \(P\) isTS EAMCET 2002 Medium
- The points \(A(2,1), B(3,-2)\) and \(C(a, b)\) are vertices of the rectangle \(A B C D\). If the point \(P(3,4)\) lies on \(C D\) produced, then \(5 a+10 b=\)TS EAMCET 2020 Easy
- The additional energy that should be given to an electron to reduce its de-Broglie wavelength from \(1 \mathrm{~nm}\) to \(0.5 \mathrm{~nm}\) isTS EAMCET 2023 Medium
- The correct order of rate of acid mediated dehydration reaction of the following compounds is
TS EAMCET 2022 Medium