COMEDK · Maths · 7. Binomial Theorem
If \({ }^n C_3=220\), then \(n=\) ?
- A 11
- B 12
- C 10
- D 9
Answer & Solution
Correct Answer
(B) 12
Step-by-step Solution
Detailed explanation
The formula for the combination is \(^{n}C_{r} = \dfrac{n!}{r!(n-r)!}\). Given \(^{n}C_{3} = 220\), we have \(\dfrac{n(n-1)(n-2)}{3 \times 2 \times 1} = 220\). \(n(n-1)(n-2) = 220 \times 6 = 1320\). We look for three consecutive integers whose product is \(1320\). Testing…
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 \(f(x) = \begin{cases} \dfrac{\sqrt{1+x} - \sqrt{1-x}}{\sin x}, & x \neq 0 \\ k, & x = 0 \end{cases}\) is continuous at \(x = 0\), then \(k =\)COMEDK 2026 Medium
- The digits of a three-digit number taken in an order are in geometric progression. If one is added to the middle digit, they form an arithmetic progression. If 594 is subtracted from the number, then a new number with the same digits in reverse order is formed. The original number is divisible byCOMEDK 2025 Medium
- Given, two vectors \(\hat{\hat{i}}-\hat{\mathfrak{j}}\) and \(\hat{\hat{i}}-2 \hat{\mathfrak{j}}\). The unit vector, coplanar with the two given vectors and perpendicular to \((\hat{\hat{\mathbf{i}}}-\hat{\hat{\mathfrak{j}}})\) isCOMEDK 2015 Easy
- If \(f(x)+2 f(1-x)=x^2+5 \forall\) real values of \(x\), then \(f(x)\) is given byCOMEDK 2022 Medium
- The domain of the function \(y=\dfrac{1}{\log _{10}(3-x)}+\sqrt{x+7}\) isCOMEDK 2024 Medium
- Ram obtained 60 and 85 in first two unit tests. The minimum marks he should get in the third test to have an average of atleast 55 marks isCOMEDK 2014 Easy
More PYQs from COMEDK
- When conc. \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is heated with \(\mathrm{P}_{2} \mathrm{O}_{5}\), the acid is converted intoCOMEDK 2020 Medium
- In the network shown in figure, the equivalent capacitance between points \(P\) and \(Q\) is
COMEDK 2022 Easy - At \(300 \mathrm{~K}\), the half-life period of a gaseous reaction at an initial pressure of \(40 \mathrm{~kPa}\) is 350 s. When pressure is \(20 \mathrm{~kPa}\), the half-life period is 175 s. What is the order of the reaction?COMEDK 2023 Medium
- \(A B C\) is a triangle, \(G\) is the centroid, \(D\) is the mid-point of \(B C\). If \(A=(2,3)\) and \(G=(7,5)\), then the point \(D\) isCOMEDK 2020 Medium
- In a deuterium-tritium fusion reaction given by \({ }_1^2 \mathrm{H}+{ }_1^3 \mathrm{H} \rightarrow{ }_2^4 \mathrm{He}+{ }_0^1 n\) the mass defect is given as 0.0188 u . The total energy released in the fusion reaction is:COMEDK 2025 Easy
- For a short magnet, the magnetic field on the axial line at a distance 10 cm from its centre is \(1.6 \mathrm{~m} \times 10^{-7} \mathrm{~T}\). What is the magnetic field on its equatorial line at the same distance 10 cm from its centre?COMEDK 2025 Easy