COMEDK · Maths · 5. Sequences and Series
The last digit of \(\sum_{\substack{1 < p < 100 \\ p \rightarrow \text { prime }}} p !-\sum_{n=1}^{50}(2 n) !\) is
- A 2
- B 4
- C 6
- D 8
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\(\underset{\substack{1 < p < 100 \\ p \rightarrow p r i m e}}{ } P !-\sum_{n=1}^{50}(2 n !)=(2 !+3 !+5 !+7 !+\ldots)\) \(-(2 !+4 !+6 !+\ldots)\) After 5 ! the number will have 0 at the one's place. So, they will no effect the last digit of the total sum. Now last digit of…
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
- \(\text { If } \sin y=x(\cos (a+y)) \text {, then find } \dfrac{d y}{d x} \text { when } x=0\)COMEDK 2024 Medium
- Oil from a conical funnel is dripping at the rate of \(5 \mathrm{~cm}^3 / \mathrm{s}\). If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top isCOMEDK 2025 Medium
- If 3 cm/s is the rate at which the side of an equilateral triangle increases, then the rate of change of area, when the side is 12 cm is:COMEDK 2026 Easy
- Five persons \(A, B, C, D\) and \(E\) are in queue of a shop. The Probability that \(A\) and \(B\) are always together isCOMEDK 2022 Easy
- The circles \(a x^{2}+a y^{2}+2 g_{1} x+2 f_{1} y+c_{1}=0\) and \(b x^{2}+b y^{2}+2 g_{2} x+2 f_{2} y+c_{2}=0\) \((a \neq 0\) and \(b \neq 0)\) cut orthogonally ifCOMEDK 2016 Medium
- \(x=a(\theta+\sin \theta)\) and \(y=a(1-\cos \theta)\) represents the equation of a curve. If \(\theta\) changes at a constant rate \(k\) then the rate of change of the slope of the tangent to the curve at \(\theta=\dfrac{\pi}{3}\) isCOMEDK 2025 Medium
More PYQs from COMEDK
- 100 g of ice at \(0^{\circ} \mathrm{C}\) is mixed with 100 g of water at \(80^{\circ} \mathrm{C}\). The final temperature of the mixture is (Given, latent heat of fusion of ice, \(L_f=80 \mathrm{cal} / \mathrm{g}\) and specific heat capacity of water, \(S_{\text {water }}=1 \mathrm{cal} / \mathrm{g}^{\circ} \mathrm{C}\) )COMEDK 2024 Easy
- Column - I lists the waves of the electromagnetic spectrum. Column - II gives approximate frequency range of these waves. Match Column - I and Column - II and choose the correct match from the given choices.
No. Column I No. Column II A Radiowaves P \(10^{18}\) to \(10^{20}\) Hz B Microwaves Q \(10^{11}\) to \(5 \times 10^{14}\) Hz C Infrared R \(10^{4}\) to \(10^{8}\) Hz D X-rays S \(10^{9}\) to \(10^{12}\) Hz COMEDK 2024 Easy - A hollow prism is filled with water and placed in air. It will deviate the incident raysCOMEDK 2024 Medium
- The height at which the acceleration due to gravity becomes \(\dfrac{g}{16}\) (where, \(g=\) acceleration due to gravity on the surface of the earth) in terms of \(R\) is, if \(R\) is the radius of earth.COMEDK 2022 Easy
- 0.60 g of urea is dissolved in 360 g of water at room temperature. The vapour pressure of pure water is 35 mm of Hg , the lowering of vapour pressure at this temperature is:
[Molar mass of urea is \(60 \mathrm{~g} \mathrm{~mol}^{-1}\) ]COMEDK 2025 Medium - The solution of \(dy = \cos x (2 - y \ \text{cosec} \ x) dx\) where \(y = \sqrt{2}\) when \(x = \dfrac{\pi}{4}\) isCOMEDK 2026 Medium