TS Inter 1st Year Mathematics 1A Guess Paper 2025

1

If A = {-2, -1, 0, 1, 2} and f: A → B is a surjection defined by f(x) = x2 + x + 1, then find B. (2 marks)

2

Find the vector equation of the line passing through the point 2i + 3j + k and parallel to the vector 4i – 2j + 3k.  (2 marks)

3

Define the Rank of a matrix.  (2 marks)

4

Find the angle between the vectors i¯+2j¯+3k¯¯¯ and 3i¯−2j¯+2k¯¯¯.  (2 marks)

5

Find the volume of the tetrahedron whose vertices are (1, 2, 1), (3, 2, 5), (2, -1, 0) and (-1, 0, 1). (4 marks)

6

If the position vectors of the points A, B, and C are -2i + j – k, -4i + 2j + 2k, and 6i – 3j – 13k respectively, and AB = λ AC, then find the value of λ. (4 marks)

7

Solve the equation √3 sin θ – cos θ = √2. (4 marks)

8

If θ is the angle between vectors i¯+j¯ and j¯+k¯¯¯, then find sin θ. (4 marks)

9

Solve the system of equations x – y + 3z = 5, 4x + 2y – z = 0, -x + 3y + z = 5 by using Cramer’s rule. (7 marks)

10

By using Cramer’s rule, solve the system of equations:

2x – y + 3z = 8, -x + 2y + z = 4, 3x + y – 4z = 0. (7 marks)

11

Find the volume of the tetrahedron whose vertices are (1, 2, 1), (3, 2, 5), (2, -1, 0) and (-1, 0, 1).  (7 marks)

12

x + y + z = 1, 2x + 2y + 3z = 6, x + 4y + 9z = 3. Solve the system of equations by using the matrix inversion method.  (7 marks)