Let \( K_{1}= \) Total number of ways of selecting of ball from a bag which contains \( n \) bal... VIDEO
Let \( K_{1}= \) Total number of ways of selecting of ball from a bag which contains \( n \) balls of first colour, \( (n+1) \) balls of second colour, \( (n+2) \) balls of third colour,..., \( (2 n-1) \) balls of \( n \) colour.
\( K_{2}= \) number of \( n \)-digit numbers using the digits \( 1,2,3, \ldots, n \) and \( K_{3}= \) number of ways of arranging \( (n+1) \) objects on a circle. The value of \( \lim _{n \rightarrow \infty}\left(\frac{K_{1}}{K_{2}+K_{3}}\right) \) is
(a) \( e \)
(b) 1
(c) 0
(d) does not exist
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions 2022-10-27 If \( \left|f\left(x_{1}\right)-f\left(x_{2}\right)\right| \leq\left(x_{1}-x_{2}\right)^{2}, \fo... 2022-10-27 The tangent to the curve \( y=x-x^{3} \) at a point \( P \) meets the curve again at \( Q \). Pr... 2022-10-27 The slope of the tangent to the curve \( \left(y-x^{5}\right)^{2}=x\left(1+x^{2}\right)^{2} \) a... 2022-10-27 Determine all the curves for which the ratio of the length of the segment intercepted by any tan... 2022-10-27 To find the point of contact \( P \equiv\left(x_{1}, y_{1}\right) \) of a tangent to the graph o... 2022-10-27 For \( n \in N \), let \( x_{n} \) be defined as \( \left(1+\frac{1}{n}\right)^{\left(n+x_{n}\ri... 2022-10-27 Match the statements of Column I with values of Column II.
\begin{tabular}{lll}
\hline & Column ... 2022-10-27 We say an equation \( f(x)=g(x) \) is consistent, if the curves \( y=f(x) \) and \( y=g(x) \) to... 2022-10-27 If \( C \) satisfies the equation \( \lim _{x \rightarrow \infty}\left(\frac{x+c}{x-c}\right)^{x... 2022-10-27 If the arithmetic mean of the product of all distinct pairs of positive integers whose sum is \(... 2022-10-27 Let \( K_{1}= \) Total number of ways of selecting of ball from a bag which contains \( n \) bal... 2022-10-27 A right angled triangle has legs 1 and \( x \). The hypotenuse is \( y \) and the angle opposite... 2022-10-27 Let \( f(x)=a x^{2}+b x+c ; a, b, c \in R \)
It is given \( |f(x)| \leq 1, \forall|x| \leq 1 \).... 2022-10-27 Let \( f: N \rightarrow R \) and \( g: N \rightarrow R \) be two functions and \( f(1)=0.8, g(1)... 2022-10-27 Let \( f: N \rightarrow R \) and \( g: N \rightarrow R \) be two functions and \( f(1)=0.8, g(1)... 2022-10-27 \( f(x), g(x), h(x) \) all are continuous and differentiable functions in \( [a, b] \) also \( a... 2022-10-27 The derivative of \( f(x)=\cos ^{-1}\left(\frac{1}{\sqrt{3}}(2 \cos x-3 \sin x)\right) \)
\[
+\l... 2022-10-27 This section is based on Statement I and Statement II. Select the correct answer from the codes ... 2022-10-27 If \( f(x), g(x) \) and \( h(x) \) are three polynomials of degree 2, then prove that \( \phi(x)... 2022-10-27 Differential coefficient of
\( \left(x^{\frac{l+m}{m-n}}\right)^{\frac{1}{n-l}} \cdot\left(x^{\f... 2022-10-27 If \( x^{2}+y^{2}=t-\frac{1}{t} \) and \( x^{4}+y^{4}=t^{2}+\frac{1}{t^{2}} \), then \( \left(\f...