JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is _______.
- A 1405
- B 1406
- C 1407
- D 1408
Answer & Solution
Correct Answer
(A) 1405
Step-by-step Solution
Detailed explanation
(i) Single letter is used, then no. of words \(=5\) (ii) Two distinct letters are used, then no. of words \({ }^5 \mathrm{C}_2 \times\left(\frac{6!}{2!4!} \times 2+\frac{6!}{3!3!}\right)=10(30+20)=500\) (iii) Three distinct letters are used, then no. of words…
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
- \(\begin{aligned}
& \text { If } \frac{1}{1^4}+\frac{1}{2^4}+\frac{1}{3^4}+\ldots . . \infty=\frac{\pi^4}{90}, \\
& \frac{1}{1^4}+\frac{1}{3^4}+\frac{1}{5^4}+\ldots . . \infty=\alpha, \\
& \frac{1}{2^4}+\frac{1}{4^4}+\frac{1}{6^4}+\ldots . \infty=\beta,
\end{aligned}\)
then \(\frac{\alpha}{\beta}\) is equal toJEE Mains 2025 Medium - \(\smallint \frac{{{{\sin }^2}x{{\cos }^2}x}}{{{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}dx\)JEE Mains 2018 Hard
- Let \(R= \{(3, 3) (5, 5), (9, 9), (12, 12), (5, 12), (3, 9), (3, 12), (3, 5)\}\) be a relation on the set \(A= \{3, 5, 9, 12\}.\) Then, \(R\) isJEE Mains 2013 Hard
- The sum of coefficients of integral power of \(x\) in the binomial expansion \({\left( {1 - 2\sqrt x } \right)^{50}}\) is :JEE Mains 2015 Hard
- Let the domain of the function
\(f(x)=\cos ^{-1}\left(\frac{4 x+5}{3 x-7}\right)\) be \([\alpha, \beta]\) and the domain of \(\mathrm{g}(\mathrm{x})=\log _2\left(2-6 \log _{27}(2 \mathrm{x}+5)\right)\) be \((\gamma, \delta)\).
Then \(|7(\alpha+\beta)+4(\gamma+\delta)|\) is equal to ________JEE Mains 2025 Medium - Let \(\alpha\) be a root of the equation \(1+x^{2}+x^{4}=0\). Then the value of \(\alpha^{1011}+\alpha^{\text {2022 }}-\alpha^{\text {3033}}\) is equal toJEE Mains 2022 Medium
More PYQs from JEE Mains
- Let \(y=y(x), x>1\), be the solution of the differential equation \((x-1) \frac{d y}{d x}+2 x y=\frac{1}{x-1}\), with \(y(2)=\frac{1+e^{4}}{2 e^{4}}\). If \(y(3)=\frac{e^{\alpha}+1}{\beta e^{\alpha}}\). then the value of \(\alpha+\beta\) is equal toJEE Mains 2022 Medium
- Let \(\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}\) be a function defined by \(f(x)=\|x+2|-2| x\|\). If \(m\) is the number of points of local minima and \(n\) is the number of points of local maxima of \(f\), then \(m+n\) isJEE Mains 2025 Easy
- Let \(A=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]\) and \(B=\left[\begin{array}{ccc}9^{2} & -10^{2} & 11^{2} \\ 12^{2} & 13^{2} & -14^{2} \\ -15^{2} & 16^{2} & 17^{2}\end{array}\right]\), then the value of \(A ^{\prime} BA\) is.JEE Mains 2022 Medium
- Let \(f:\left[ { - 2,3} \right] \to \left[ {0,\infty } \right)\) be a continuous function such that \(f(1-x) = f(x)\) for all \(x \in \left[ { - 2,3} \right]\) . If \(R_1\) is the numerical value of the area of the region bounded by \(y =f (x), x = -2, x = 3\) and the axis of \(x\) and \({R_2} = \int\limits_{ - 2}^3 {x\,f\left( x \right)} dx\) , thenJEE Mains 2013 Hard
- If \(\sum_{r=1}^{30} \frac{r^2\left({ }^{30} C_r\right)^2}{{ }^{30} C_{r-1}}=\alpha \times 2^{29}\), then \(\alpha\) is equal to ______JEE Mains 2025 Hard
- Let \(A\) be a \(3 \times 3\) matrix with \(\operatorname{det}( A )=4\). Let \(R _{ i }\) denote the \(i ^{\text {th }}\) row of \(A\). If a matrix \(B\) is obtained by performing the operation \(R _{2} \rightarrow 2 R _{2}+5 R _{3}\) on \(2 A ,\) then \(\operatorname{det}( B )\) is equal to ...... .JEE Mains 2021 Medium