JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(x\) and \(y\) be distinct integers where \(1 \leq x \leq 25\) and \(1 \leq y \leq 25\). Then, the number of ways of choosing \(x\) and \(y\), such that \(x + y\) is divisible by \(5\) , is \(.........\).
- A \(119\)
- B \(120\)
- C \(118\)
- D \(117\)
Answer & Solution
Correct Answer
(B) \(120\)
Step-by-step Solution
Detailed explanation
\(x+y=5 \lambda\) Cases: \(x\) \(y\) Number of ways \(5 \lambda\) \(5 \lambda\) \(20\) \(5 \lambda+1\) \(5 \lambda+4\) \(25\) \(5 \lambda+2\) \(5 \lambda+3\) \(25\) \(5 \lambda+3\) \(5 \lambda+2\) \(25\) \(5 \lambda+4\) \(5 \lambda+1\) \(25\) Total=120
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 \(f: R \rightarrow R\) be a function defined by \(f(x)=\left(2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right)^{\frac{1}{50}}\). If the function \(g(x)=f(f(f(x)))+f(f(x))\), the the greatest integer less than or equal to \(g (1)\) isJEE Mains 2022 Hard
- A value of \(x\) satisfying the equation \(\sin \left[ {{{\cot }^{ - 1}}\left( {1 + x} \right)} \right] = \cos \left[ {{{\tan }^{ - 1}}\,x} \right]\) , isJEE Mains 2017 Hard
- The area of the region bounded by the curve \(y=\max \{|x|, x|x-2|\}\), then \(x\)-axis and the lines \(x=-2\) and \(x=4\) is equal to _______ .JEE Mains 2025 Easy
- If \(\alpha\) satisfies the equation \(x^2+x+1=0\) and \((1+\alpha)^7=\mathrm{A}+\mathrm{B} \alpha+\mathrm{C}^2, \mathrm{~A}, \mathrm{~B}, \mathrm{C} \geq 0\), then \(5(3 A-2 B-C)\) is equal to ...........JEE Mains 2024 Hard
- Let \(f\) be a real valued function, defined on \(R -\{-1,1\}\) and given by \(f(x)=3 \log _{e}\left|\frac{x-1}{x+1}\right|-\frac{2}{x-1}\) Then in which of the following intervals, function \(f ( x )\) is increasing?JEE Mains 2021 Hard
- Let the line \(\ell: x =\frac{1- y }{-2}=\frac{ z -3}{\lambda}, \lambda \in R\) meet the plane \(P : x +2 y +3 z =4\) at the point \((\alpha, \beta, \gamma)\). If the angle between the line \(\ell\) and the plane \(P\) is \(\cos ^{-1}\left(\sqrt{\frac{5}{14}}\right)\), then \(\alpha+2 \beta+6 \gamma\) is equal toJEE Mains 2023 Hard
More PYQs from JEE Mains
- In a geometric progression, if the ratio of the sum of first \(5\) terms to the sum of their reciprocals is \(49\), and the sum of the first and the third term is \(35\) . Then the first term of this geometric progression isJEE Mains 2014 Hard
- Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line \(x+2\sqrt{2}y=4\). If the co-ordinates of the vertex A are (\(\alpha, \beta\)), then the greatest integer less than or equal to \(|\alpha+\sqrt{2}\beta|\) isJEE Mains 2026 Easy
- If \(1, \log _{10}\left(4^{x}-2\right)\) and \(\log _{10}\left(4^{x}+\frac{18}{5}\right)\) are in
arithmetic progression for a real number \(x\) then the value of the determinant \(\left|\begin{array}{ccc}2\left(x-\frac{1}{2}\right) & x-1 & x^{2} \\ 1 & 0 & x \\ x & 1 & 0\end{array}\right|\) is equal to ...... .JEE Mains 2021 Hard - Let \(a, b \in \mathbb{C}\). Let \(\alpha, \beta\) be the roots of the equation \(x^2 + ax + b = 0\). If \(\beta - \alpha = \sqrt{11}\) and \(\beta^2 - \alpha^2 = 3i\sqrt{11}\), then \((\beta^3 - \alpha^3)^2\) is equal to:JEE Mains 2026 Hard
- If the function \(f(x)=2 x^3-9 \mathrm{ax}^2+12 \mathrm{a}^2 \mathrm{x}+1\), where \(\mathrm{a} \gt 0\), attains its local maximum and local minimum values at \(p\) and \(q\), respectively, such that \(\mathrm{p}^2=\mathrm{q}\), then \(f(3)\) is equal to:JEE Mains 2025 Easy
- Let \(P\) be a point on the parabola, \(x^2 = 4y.\) If the distance of \(P\) from the centre of the circle, \(x^2 + y^2 + 6x + 8 = 0\) is minimum, then the equation of the tangent to the parabola at \(P,\) isJEE Mains 2018 Hard