AP EAMCET · Maths · Permutation Combination

The number of integers greater than 3000 that can be formed by any number of digits from \(0,1,2,3,4,5\) without repetition in each number is

A \(1630\)
B \(1380\)
C \(1260\)
D \(1200\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(1380\)

Step-by-step Solution

Detailed explanation

Number of 4-digit integers: First digit \(\in \{3,4,5\}\) (3 options). Remaining 3 digits from 5: \(P(5,3)\). \(3 \times P(5,3) = 3 \times 5 \times 4 \times 3 = 180\) Number of 5-digit integers: First digit \(\in \{1,2,3,4,5\}\) (5 options). Remaining 4 digits from 5:…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

A question paper consists of two sections having 3 and 4 questions respectively. The following note is given on the paper. "It is not necessary to attempt all the questions. One question from each section is compulsory". In how many ways can a candidate select the questions?

AP EAMCET 2022 Medium

The probability distribution of a random variable X is as follows. Then the mean of X is

\(\mathrm{X} = \mathrm{x}_{\mathrm{i}}\)	\(-2\)	\(-1\)	\(0\)	\(1\)	\(2\)
\(\mathrm{P}\left(\mathrm{X} = \mathrm{x}_{\mathrm{i}}\right)\)	\(\mathrm{k}^2 / 3\)	\(\mathrm{k}^2\)	\(2 \mathrm{k}^2 / 3\)	\(k / 2\)	\(k / 2\)

AP EAMCET 2025 Medium

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