Question:
Five digit number is formed using the digits 0, 1, 2, 3, 4 and 5 without repetitions. Number of five digit numbers which are divisible by 10 is ________.
Five digit number is formed using the digits 0, 1, 2, 3, 4 and 5 without repetitions. Number of five digit numbers which are divisible by 10 is ________.
Show Hint
Fix the last digit as 0 first.
Updated On: Jun 26, 2026
- 360
- 240
- 120
- 480
- 520
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Concept
A number is divisible by 10 if its last digit is 0.
Step 2: Meaning
The 5th place (units) must be 0 (1 way).
Step 3: Analysis
Remaining 4 places must be filled by digits $\{1, 2, 3, 4, 5\}$ without repetition. Number of ways $= 5 \times 4 \times 3 \times 2 = 120$.
Step 4: Conclusion
Total numbers $= 120$. Final Answer: (C)
A number is divisible by 10 if its last digit is 0.
Step 2: Meaning
The 5th place (units) must be 0 (1 way).
Step 3: Analysis
Remaining 4 places must be filled by digits $\{1, 2, 3, 4, 5\}$ without repetition. Number of ways $= 5 \times 4 \times 3 \times 2 = 120$.
Step 4: Conclusion
Total numbers $= 120$. Final Answer: (C)
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Permutations Questions
- The number of ways in which $5$ ladies and $7$ gentlemen can be seated in a round table so that no two ladies sit together, is
- In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
- The value of \( {}^2P_1 + {}^3P_1 + \dots + {}^nP_1 \) is equal to:
- The value of \( {}^2P_1 + {}^3P_1 + \dots + {}^nP_1 \) is equal to:
- The value of \( {}^2P_1 + {}^3P_1 + \dots + {}^nP_1 \) is equal to:
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions