AP Inter 2nd Year Mathematics 2A Guess Paper 2025

1

For what values of x, the expression x ² - 5x - 14 is positive.

2

Find the number of ways of arranging the letter of the word ‘INTERMEDIATE’.

3

Find the mean deviation about the mean for the following data: 3, 6, 10, 4, 9, 10.

4

The probability for a contractor to get a road contract is 2/3 to get a building contract is 5/9. The probability to get at least one contract is 4/5. Find the probability that he gets both contracts.

5

If z = 2 – 3i then show that z ² – 4z + 13 = 0.

6

Find the numbers of terms in the expansion of (2x + 3y + z) ⁷ .

7

Find the number of ways of selecting a committee of 6 members out of 10 members always including a specified member.

8

If the letters of the word EAMCET are permuted in all possible ways and if the words they formed are arranged in the dictionary order, find the rank of the word EAMCET.

9

Find the probability of drawing an ace or a spade from a well shuffled pack of 52 playing cards.

10

Solve x ⁴ – 10x ³ + 26x ² – 10x + 1 = 0

11

State and prove Baye’s Theorem on probability.

12

If A, B, C are the angles of a triangle such that x = cisA, y = cisB, z = cisC, then find xyz.

13

If ²² C _r is the largest binomial coefficient in the expansion of (1 + x) ²² , then find the value of ¹³ C _r

14

If the mean, variance of a binomial variable of X are 2.4 and 1.44 respectively then find n, p.

15

Find the sum of all 4 digit numbers that can be formed using the digits 1, 3, 5, 7, 9.

16

Find the number of ways of selecting a cricket team of 11 players from 7 batsmen and 6 bowlers such that there will be at least 5 bowlers in the team.

17

Solve x ⁴ + 4x ³ - 2x ² - 12x + 9 = 0 given that it has two pairs of equal roots.

18

Find the cube root of 8.

19

Find the value of ¹⁰ C ₅ + 2 ¹⁰ C ₄ + ¹⁰ C ₃ .

20

Solve 8x ³ - 36x ² - 18x + 81 = 0 given that the roots are in AP.