Basic Mathematics — Winter 2024

If A  1,2,3,4, B   3 , 4 , 9 , 1 1  and C   2 , 1 1 , 1 8 , 2 2  then find (i) ( A  B ) , (ii) ( B  C ) , (iii) ( A  C ) , (iii) ( A  B  C ) .05

Find edges, vertices, parallel edges, loops, degree of vertices from the following graph

Solve the equation 3 x 2  5 x  2 .

Find real and imaginary part of3  4 i i05 .

Let f:A → Bwhere A={1,2,3} ; B={1,2,3,4,5,6,7} f(x) = 2x then find domain, co-domain and range of f.

Let u = (2, 3, −4) and v = (1, −5, 8). Then find u + v, 5u ,−v ,2u − 3v, u ・ v

11 40 28 If | 3 12 8 | = 0 Then find a a 2

Consider the following relation on {1, 2, 3, 4, 5, 6} R    i , j  : i  j  2 05 . Is Rreflexive, symmetric or transitive ?

Find A Band B A 1 −1 1 1 2 3 , where A = [−3 2 −1] , B = [2 4 6] −2 1 0 1 2

Find standard deviation of the following data x 10 11 12 13 14 15 16 17 18 f05

Three unbiased coins are tossed. Find the probability of getting (i) exactly two heads (ii) atleast one tail

Find the quartile deviation from the following data: Class 5-10 10-15 15-20 20 -25 25-30 30-35 35-40 40-45 Frequency 5 6 15 10 5 4 2

If Aand Bare two events such that2 P  A   0 . 3 , PB0.4and P  A  B   0 . 2 , find (i) P  A  B      (ii) P A (iii) P B (iv) P  A  B 

P  A  B 05

State De Morgan’s Law and prove it using postulates

Check whether F2 is a minimization of F1 , where, F1  x  y  z  x  y  z  x  y and F2  x  y  x  z05 .

Use truth table to prove that  A  B   A  C   A   B C 05

Design a Boolean function of ABCDusing logic gates