Mathematics-1 — Winter 2025

(a) Define the following terms

Set with example, Function, Cartesian product of sets. (ii) Coordinate Geometry, Scalar Matrix, Cardinality of Sets. (iii) De-Morgan's laws.

07 Define bijective function. If , show that f is bijective function.

If A={a,b,c,d}, B={b,c,d,g,h}, C={a,g,x,y,z} and D={b,d,x,z} then verify that

In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali? How many can speak both Hindi and Bengali?

Let A={1,2,3,5,6,7}, B={2,5,8,9} and C={1,4,6,10,11} then verify and represent a Venn diagram of

(i) is of 04 marks and (ii) is of 03 marks

Let and , then find (ii) If and , then find the value of x?

(i) is of 03 marks and (ii) is of 04 marks

If prove that (ii) Define followings

Even and odd functions with examples

One-one and onto functions with examples

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(i) is of 03 marks and (ii) is of 04 marks.

07 If and . then prove that

Find the inverse of the matrix

Use Cramer's rule to solve the equations

Define Rank of a matrix. Find the rank of the matrix using determinant method.

Prove that (-1,0), (0,3),(3,2) and (2,-1) are the vertices of square by using distance formula.

Find the angle between the lines and .

Find the coordinates of the point which divides the points A(8, -3) and (16,5) in the internal ratio 3:1 and externally in the ratio 4:3.

Find equation of the line passing from (7,-4) and (2,4). Find slope and intercepts. Page 2 of