WBJEE · Maths · Permutation Combination
A letter lock consists of three rings with 15 different letters. If \(\mathrm{N}\) denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then
- A 482 divides \(\mathrm{N}\)
- B N is the product of two distinct prime numbers.
- C \(\mathrm{N}\) is the product of three distinct prime numbers.
- D 16 divides \(\mathrm{N}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{N}\) is the product of three distinct prime numbers.
Step-by-step Solution
Detailed explanation
Hint : Number of unsuccessful attempts \(=15^3-1=3374=2 \times 1687=2 \times 7 \times 241\) Divisible by 482 \(\mathrm{N}\) is the product of three distinct prime number
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
- The value of \(\int_{-2}^2(x \cos x+\sin x+1) d x\) isWBJEE 2011 Easy
- If the matrix \(M_r\) is given by \(M_r=\left(\begin{array}{cc}r & r-1 \\ r-1 & r\end{array}\right)\) for \(r=1,2,3, \ldots\) then \(\operatorname{det}\left(\mathrm{M}_1\right)+\operatorname{det}\left(\mathrm{M}_2\right)+\ldots . .+\operatorname{det}\left(\mathrm{M}_{2008}\right)=\)WBJEE 2023 Medium
- For all real values of \(a_{0}, a_{1}, a_{2}, a_{3}\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{z}}{3}+\frac{a_{3}}{4}=0,\) the equation \(a_{0}+a_{1} x+a_{2} x^{2}+a_{3} x^{3}=0\) has a real root in the intervalWBJEE 2015 Hard
- The value of \(\frac{\sin 55^0-\cos 55^{\circ}}{\sin 10^0}\) isWBJEE 2010 Easy
- If \(C\) is a point on the line segment joining \(A(-3,4)\) and \(B(2,1)\) such that \(A C=2 B C\), then the coordinate of \(C\) isWBJEE 2009 Easy
- A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss isWBJEE 2011 Easy
More PYQs from WBJEE
- Let \(f:[a, b] \rightarrow \mathbb{R}\) be continuous in \([a, b]\), differentiable in \((a, b)\) and \(f(a)=0=f(b)\). ThenWBJEE 2022 Medium
- \(\mathrm{Na}_2 \mathrm{CO}_3\) is prepared by Solvay process but \(\mathrm{K}_2 \mathrm{CO}_3\) cannot be prepared by the same becauseWBJEE 2023 Easy
- If \(0 \leq A \leq \frac{\pi}{4},\) then \(\tan ^{-1}\left(\frac{1}{2} \tan 2 A\right)+\tan ^{-1}(\cot A)+\tan ^{-1}\left(\cot ^{3} A)\right.\)
is equal toWBJEE 2018 Medium - If the point \((2 \cos \theta, 2 \sin \theta)\) for \(0 \in(0,2 \pi)\) lies in the region between the lines \(x+y=2\) and \(x-y=2\) containing the origin, then \(\theta\) lies inWBJEE 2015 Hard
- If \(\frac{\cos A}{3}=\frac{\cos B}{4}=\frac{1}{5},-\frac{\pi}{2} < A < 0,-\frac{\pi}{2} < B < 0\) then value of \(2 \sin A+4 \sin B\) isWBJEE 2010 Medium
- Let \(f(x)=2 x^{2}+5 x+1\). If we write \(f(x)\) as \(f(x)=a(x+1)(x-2)+b(x-2)(x-1)+c(x-1)(x+1)\)
for real numbers \(a, b, c,\) thenWBJEE 2014 Hard