A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :
- 125
- 150
- 180
- 160
The Correct Option is B
Solution and Explanation
\[ 17m = m + (m - 4) + (m - 4 \times 2) + \dots + (m - 4 \times 24) \]
\[ 17m = 25m - 4(1 + 2 + \dots + 24) \]
\[ 8m = 4 \times \frac{24 \times 25}{2} = 150 \]
Top Questions on Arithmetic Progression
- The sum of the first 10 terms of an arithmetic progression is 150. If the first term is 10, what is the common difference?
- VITEEE - 2025
- Mathematics
- Arithmetic Progression
- Consider two sets $ A $ and $ B $, each containing three numbers in A.P. Let the sum and the product of the elements of $ A $ be 36 and $ p $, respectively, and the sum and the product of the elements of $ B $ be 36 and $ q $, respectively. Let $ d $ and $ D $ be the common differences of A.P's in $ A $ and $ B $, respectively, such that $ D = d + 3 $, $ d>0 $. If $ \frac{p+q}{p-q} = \frac{19}{5} $, then $ p - q $ is equal to:
- JEE Main - 2025
- Mathematics
- Arithmetic Progression
- Given a series \( 5, 8, 11, 14, \dots \), if the \( n \)-th term of the given series is 320, then find \( n \) (where \( n \geq 1 \)):
- GATE XH-C1 - 2025
- Mathematics
- Arithmetic Progression
- For a set of \( n \) integers in arithmetic progression, the difference between twice the median of the set and the range of the set is equal to twice the first term.
- NPAT - 2025
- Quantitative Aptitude
- Arithmetic Progression
The remainder when \( 64^{64} \) is divided by 7 is equal to:
- JEE Main - 2025
- Mathematics
- Arithmetic Progression
Questions Asked in JEE Main exam
- If $ \alpha $ is a root of the equation $ x^2 + x + 1 = 0 $ and $$ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20$$, then n is equal to _______
- JEE Main - 2025
- Sequence and series
x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)
- JEE Main - 2025
- Equilibrium
- The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
- A metal complex with a formula MC$\ell_4$3NH$_3$ is involved in sp$^3$d$^2$ hybridisation. It upon reaction with excess of AgNO$_3$ solution gives ‘x’ moles of AgCl. Consider ‘x’ is equal to the number of lone pairs of electron present in central atom of BrF$_5$. Then the number of geometrical isomers exhibited by the complex is ________
- JEE Main - 2025
- Coordination chemistry
The molar conductance of an infinitely dilute solution of ammonium chloride was found to be 185 S cm$^{-1}$ mol$^{-1}$ and the ionic conductance of hydroxyl and chloride ions are 170 and 70 S cm$^{-1}$ mol$^{-1}$, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is 85.5 S cm$^{-1}$ mol$^{-1}$, its degree of dissociation is given by x $\times$ 10$^{-1}$. The value of x is ______. (Nearest integer)
- JEE Main - 2025
- Electrochemistry