AP EAMCET · Maths · Binomial Theorem

If ${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$, then find $k$

Verified Solution

Answer & Solution

Correct Answer

(D) 4

Step-by-step Solution

Detailed explanation

It is given that, \[ { }^{12} C_{2 k-1}={ }^{12} C_{k+1} \] So, either $2 k-1=k+1$ or…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

In a Binomial distribution, if $p=q$ and $n \geq 4$, then $2^n P(X=5)=$

AP EAMCET 2022 Medium
If $f^{"} (x)$ is a positive function for all $x \in R, f^{'} (3) = 0$ and $g (x) = f (\tan^{2} (x) - 2 \tan (x) +$ $4)$ for $0 < x < \frac{π}{2}$ , then the interval in which $g (x)$ is increasing is

AP EAMCET 2021 Medium
a,b,c are three vectors such that $|\mathbf{a}|=\mathbf{l},|\mathbf{b}|=2,|\mathbf{c}|=3$ and $\mathbf{b}. \mathbf{c}=\mathbf{0}$. If the projection of $\mathbf{b}$ along $\mathbf{a}$ is equal to the projection of $\mathbf{c}$ along $\mathbf{a}$, then $|2 \mathbf{a}+3 \mathbf{b}-3 \mathbf{c}|=$

AP EAMCET 2019 Easy
Let $D$ be the domain of a twice differentiable function $f$. For all $x \in D, f^{\prime \prime}(x)+f(x)=0$ and $f(x)=\int g(x) d x+$ constant. If $h(x)=\{\mathrm{f}(x)\}^2+\{g(x)\}^2$ and $h(0)=5$, then $h(2015)-h(2014)$ is equal to

AP EAMCET 2015 Hard
Which of the following points lie on the plane passing through $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}, 3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ ?

AP EAMCET 2021 Easy
The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta),(b \sin \theta,-b \cos \theta)$ and $(1,0)$ is (here, $\theta$ is a parameter)

AP EAMCET 2014 Medium

Explore more questions on app

From AP EAMCET

$\int \frac{d x}{x\left(x^2+1\right)^3}=$

AP EAMCET 2017 Hard
Which of the following sets is correct?

AP EAMCET 2023 Medium
Assertion (A) The angle between acceleration and velocity of a body is one-dimensional motion is always zero. Reason (R) One-dimensional motion is along a straight line.

AP EAMCET 2018 Easy
If $\lim _{n \rightarrow \infty} x_n$ exists and is finite, $x_1=2, x_{n+1}=\frac{a+b x_n}{b+c x_n} \forall n \in N$ and $\mathrm{c}>\mathrm{b}>\mathrm{a}>\mathrm{o}$ then $\lim _{n \rightarrow \infty} x_n=$

AP EAMCET 2022 Medium
$In Δ A B C, a^{3} \cos (B - C) + b^{3} \cos (C - A) + c^{3} \cos (A - B) =$

AP EAMCET 2018 Medium
If $α, β$ are the real roots of $x^{2} + p x + q = 0$ and $α^{4}, β^{4}$ are the roots of $x^{2} - r x + s = 0,$ then the equation $x^{2} - 4 q x + 2 q^{2} - r = 0$ has always

AP EAMCET 2019 Easy

Explore more questions on app

If \({ }^{12} C_{2 k-1}={ }^{12} C_{k+1}\), then find \(k\)

Answer & Solution

Step-by-step Solution

See the Complete Solution