AP EAMCET · Maths · Permutation Combination
If \(1 \times 1 !+2 \times 2 !+3 \times 3 !+\ldots+n \times n !=11 !-1\), then the maximum value of \({ }^n C_r\) is
- A 462
- B 252
- C 162
- D 512
Answer & Solution
Correct Answer
(B) 252
Step-by-step Solution
Detailed explanation
\begin{aligned} & 1 \times 1 !+2 \times 2 !+\ldots+n \times n ! \\ & =(2-1) \times 1 !+(3-1) \times 2 !+\ldots+[(n+1)-1] \times n ! \\ & =\{2 \times 1 !+3 \times 2 !+4 \times 3 !+\ldots(n+1) \times n !\} \\ & \quad-\{1 \times 1 !+1 \times 2 !+1 \times 3 !+\ldots+1 \times n !\}…
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
- If \(A=\left[\begin{array}{lll}2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2\end{array}\right]\) and \(\alpha, \beta, \gamma\) are the roots of the equation represented by \(|A-x I|=0\), then \(\alpha^2+\beta^2+\gamma^2=\)AP EAMCET 2025 Medium
- If \(A\) and \(B\) are mutually exclusive events with \(P(A)=\frac{1}{4}\) and \(P(B)=\frac{3}{7}\). Then, what is the value of \(P(A / A \cup B)=\) ?AP EAMCET 2021 Easy
- In a \(\triangle \mathrm{ABC}\) if \(a=13, b=14, c=15\) then \(r_1=\)AP EAMCET 2024 Easy
- The ratio in which \(y z\)-plane divides the line segment joining \((-3,4,-2)\) and \((2,1,3)\) isAP EAMCET 2007 Easy
- If the form of the solution of the differential equation \(\left(y^3+x\right) \frac{d y}{d x}=y\) when \(y(4)=2\) is \(y^3=a x+b\), then \(4 a+12 b^2=\)AP EAMCET 2017 Medium
- \(\sin \frac{\pi}{12} \sin \frac{2 \pi}{12} \sin \frac{3 \pi}{12} \sin \frac{4 \pi}{12} \sin \frac{5 \pi}{12} \sin \frac{6 \pi}{12}=\)AP EAMCET 2025 Medium
More PYQs from AP EAMCET
- \(\vec{c}\) is a vector along the bisector of the internal angle between the vectors \(\vec{a}=4 \hat{i}+7 \hat{j}-4 \hat{k}\) and \(\vec{b}=12 \hat{i}-3 \hat{j}+4 \hat{k}\). If the magnitude of \(\vec{c}\) is \(3 \sqrt{13}\) then \(\vec{c}=\)AP EAMCET 2024 Medium
- Assertion (A) At critical temperature, surface tension of liquids become zero.
Reason (R) At critical temperature, intermolecular forces for liquids and gases become equal.AP EAMCET 2021 Medium - For the curve \(y=5 x-2 x^3\), if \(x\) increases at the rate of 2 units/sec, the rate of change in the slope of the curve at \(x=3\) is ......../secAP EAMCET 2021 Easy
-
In the above reaction electrophile is substituted at meta position only, due to
I. Electron density is more at ortho \& para position
II. Electron density is relatively less at ortho \& para position
III. Electron density is less at meta position
IV. Electron density is relatively more at meta position Correct answer isAP EAMCET 2023 Medium - The value of \({ }^7 P_3-3\left({ }^6 P_2\right)\) is equal toAP EAMCET 2021 Medium
- Let \(\mathbf{A}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}\). If \(\mathbf{B}\) is a vector in \(X Y\) plane such that \((\mathbf{A}+\mathbf{B}) \cdot \mathbf{B}=15\) and \(\mathbf{A} \cdot \mathbf{B}=6\), then \(|\mathbf{B}|\) isAP EAMCET 2021 Easy