JEE Mains · Maths · STD 11 - 6. permutation and combination
Number of ways of arranging \(8\) identical books into \(4\) identical shelves where any number of shelves may remain empty is equal to
- A \(18\)
- B \(16\)
- C \(12\)
- D \(15\)
Answer & Solution
Correct Answer
(D) \(15\)
Step-by-step Solution
Detailed explanation
\(3\) Shelf empty \(:(8,0,0,0) \rightarrow 1\) way \(2\) shelf empty : \(\left.\begin{array}{c}(7,1,0,0) \\ (6,2,0,0) \\ (5,3,0,0) \\ (4,4,0,0)\end{array}\right] \rightarrow 4\) ways \(1\) shelf empty:…
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 A be the focus of the parabola \(y^{2}=8x.\) Let the line \(y=mx+c\) intersect the parabola at two distinct points B and C. If the centroid of the triangle ABC is \((\frac{7}{3},\frac{4}{3})\) , then \((BC)^{2}\) is equal to:JEE Mains 2026 Medium
- If the system of linear equations \(x + y + z = 5\) ; \(x = 2y + 2z = 6\) ; \(x + 3y + \lambda z = u (\lambda \, \mu \in R)\), has infinitely many solutions then the value of \(\lambda + \mu \) isJEE Mains 2019 Hard
- Let A be the point \((3, 0)\) and circles with variable diameter AB touch the circle \(x^2 + y^2 = 36\) internally. Let the curve C be the locus of the point B. If the eccentricity of C is \(e\), then \(72e^2\) is equal to _______.JEE Mains 2026 Hard
- If the mean of the following probability distribution of a random variable \(X\);
is \(\frac{46}{9}\) , then the variance of the distribution is\(X\) \(0\) \(2\) \(4\) \(6\) \(8\) \(P(X)\) \(a\) \(2a\) \(a+b\) \(2b\) \(3b\) JEE Mains 2024 Hard - Let \(y=y(x)\) be the solution of the differential equation \(\sec ^2 x d x+\left(e^{2 y} \tan ^2 x+\tan x\right) d y=0 \) , \(0 < x < \frac{\pi}{2}, y\left(\frac{\pi}{4}\right)=0\). If \(y\left(\frac{\pi}{6}\right)=\alpha\), Then \(\mathrm{e}^{8 \alpha}\) is equal to ...........JEE Mains 2024 Hard
- Let \(H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1\) be the hyperbola, whose eccentricity is \(\sqrt{3}\) and the length of the latus rectum is \(4 \sqrt{3}\). Suppose the point \((\alpha, 6), \alpha>0\) lies on \(H\). If \(\beta\) is the product of the focal distances of the point \((\alpha, 6)\), then \(\alpha^2+\beta\) is equal to :JEE Mains 2024 Hard
More PYQs from JEE Mains
- Let \(X\) be a binomially distributed random variable with mean \(4\) and variance \(\frac{4}{3}\). Then \(54 P ( X \leq 2)\) is equal to.JEE Mains 2022 Medium
- If \(\operatorname{I}(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n\gt0\), then \(I(9,14)+I(10,13)\) isJEE Mains 2025 Easy
- If the variance of the terms in an increasing \(A.P.\), \(b _{1}, b _{2}, b _{3}, \ldots b _{11}\) is \(90,\) then the common difference of this \(A.P.\) isJEE Mains 2020 Medium
- If \(\lim _{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{m \sqrt{5}}{n(2 n)^{2 / 3}}\), where \(\operatorname{gcd}(m, n)=1\), then \(8 m+12 n\) is equal to ...........JEE Mains 2024 Hard
- Consider the function \(f(x)=\frac{\mathrm{P}(\mathrm{x})}{\sin (\mathrm{x}-2)}, \quad \mathrm{x} \neq 2\) \(\quad \quad \quad \quad 7, \quad\quad\quad \mathrm{x}=2\) where \(P(x)\) is a polynomial such that \(P^{\prime \prime}(x)\) is always a constant and \(P(3)=9\). If \(f(x)\) is continuous at \(x=2\), then \(P(5)\) is equal to \(.....\)JEE Mains 2021 Hard
- Let \(\alpha\) and \(\beta\) be the roots of \(x^{2}-3 x+p=0\) and \(\gamma\) and \(\delta\) be the roots of \(x^{2}-6 x+q=0 .\) If \(\alpha\) \(\beta, \gamma, \delta\) form a geometric progression. Then ratio \((2 q+p):(2 q-p)\) isJEE Mains 2020 Hard