JEE Mains · Maths · STD 11 - 6. permutation and combination
The number of ordered pairs ( \(\mathrm{r}, \mathrm{k}\) ) for which \(6 \cdot ^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right)\cdot{^{36} \mathrm{C}_{\mathrm{r}+1}}\). where \(\mathrm{k}\) is an integer, is
- A \(3\)
- B \(2\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\(6 \times^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right)^{36} \mathrm{C}_{\mathrm{r}+1}\) \(k^{2}-3>0 \Rightarrow k^{2}>3\) \(\mathrm{k}^{2}-3=\frac{6 \mathrm{\times}^{35} \mathrm{C}_{\mathrm{r}}}{^{36} \mathrm{C}_{\mathrm{r}+1}}=\frac{\mathrm{r}+1}{6}\) Possible…
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 PQ and MN be two straight lines touching the circle \( x^{2}+y^{2}-4x-6y-3=0 \) at the points A and B respectively. Let O be the centre of the circle and \( \angle AOB=\pi/3. \) Then the locus of the point of intersection of the lines PQ and MN is:JEE Mains 2026 Hard
- If the sum of the first \(10\) terms of the series \(\dfrac{1}{1 + 1^4 \times 4} + \dfrac{2}{1 + 2^4 \times 4} + \dfrac{3}{1 + 3^4 \times 4} + \dfrac{4}{1 + 4^4 \times 4} + \ldots\) is \(\dfrac{m}{n}\), \(\gcd(m, n) = 1\), then \(m + n\) is equal to :JEE Mains 2026 Medium
- The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is \(......\).JEE Mains 2023 Hard
- Let \(A=\{z\in\mathbb{C}:|z-2|\le4\}\) and
\(B=\{z\in\mathbb{C}:|z-2|+|z+2|=5\}\).
Then the max \(\left\{\left| z _1- z _2\right|: z _1 \in A\right.\) and \(\left.z _2 \in B\right\}\) isJEE Mains 2026 Medium - If \(\int {{x^5}\,{e^{ - {x^2}}}\,dx\, = \,g\,(x)\,{e^{ - {x^2}}} + \,c,} \) where \(c\) is a constant of integration, then \(g(-1)\) is equal toJEE Mains 2019 Hard
- If \(\left({ }^{30} C_1\right)^2+2\left({ }^{30} C_2\right)^2+3\left({ }^{30} C_3\right)^2 \ldots \ldots \ldots . .30\left({ }^{30} C_{30}\right)^2=\frac{\alpha 60!}{(30!)^2}\), then \(\alpha\) is equal toJEE Mains 2023 Medium
More PYQs from JEE Mains
- Let \(z_1\) and \(z_2\) be two complex number such that \(z_1\) \(+z_2=5\) and \(z_1^3+z_2^3=20+15 i\). Then \(\left|z_1^4+z_2^4\right|\) equals-JEE Mains 2024 Hard
- Let \(\alpha\) and \(\beta\) be the roots of the equation \(\mathrm{x}^{2}-\mathrm{x}-1=0 .\) If \(\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1,\) then which one of the following statements is not true?JEE Mains 2020 Hard
- A coin is tossed three times. Let \(X\) denote the number of times a tail follows a head. If \(\mu\) and \(\sigma^2\) denote the mean and variance of \(X\), then the value of \(64\left(\mu+\sigma^2\right)\) is :JEE Mains 2025 Medium
- Let \(a-2 b+c=1\) If \(f(x)=\left|\begin{array}{lll}{x+a} & {x+2} & {x+1} \\ {x+b} & {x+3} & {x+2} \\ {x+c} & {x+4} & {x+3}\end{array}\right|,\) thenJEE Mains 2020 Hard
- Among the statements: \((S1):\) \(2023^{2022}-1999^{2022}\) is divisible by \(8.\) \((S2)\) : \(13(13)^{ n }-11 n -13\) is divisible by \(144\) for infinitely many \(n \in N\).JEE Mains 2023 Hard
- If the length of the perpendicular from the point \((\beta , 0, \beta )\, (\beta \neq 0)\) to the line \(\frac{x}{1} = \frac{{y - 1}}{0} = \frac{{z + 1}}{{ - 1}}\) is \(\sqrt {\frac{3}{2}} \), then \(\beta \) is equal toJEE Mains 2019 Medium