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CBSE Class 12 Pre Board 2020 : Mathematics - Prelim 2 (Delhi Public School (DPS), Jammu)

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DELHI PUBLIC SCHOOL, JAMMU ASSIGNMENT FOR PRE-BOARD -II Sub: Mathematics Class: XII Q1. Check whether the relation R in R of real numbers defined by R = {(a , b) : a b3} is reflexive, symmetric or transitive. Q2. . Show that the relation R in the set Z of integers given by R = {(a, b) : 2 divides an equivalence relation. Also find its all possible equivalence classes. Q3. F : R R, g : R given by f(x) = [x], g(x) = | |, then find (fog) ( 3 ) and (gof)( 3 ). 2 a b} is 2 +1 Q4. Show that the function f : N N defined by f(x) { 2 2 Q5. , , is not bijective. Consider f: R+ [-5, ) given by f(x) = 9x2 + 6x 5. Show that f is invertible with f-1(y) = +6 1 3 1 1 Q6. Prove that tan-13 + 1 7 = 4 . Q7. Prove that cos-113 + 1 5 = 1 65 . Q8. If A and B are symmetric matrices, determine whether AB BA is symmetric or skew symmetric matrix. 12 3 56 Q9. 1 Express [ 6 4 Q10. 0 1 Obtain the inverse of the matrix A = [1 2 3 1 Q11. 3 5 8 3] as a sum of symmetric and skew-symmetric matrices. 6 5 2 3] using elementary operations. 1 There are three families A, B and C. The number of men, women and children in these families are as under: Men Women Children Family A 2 3 1 Family B 2 1 3 Family C 4 2 6 Daily expenses of men, women and children are Rs.200, Rs.150 and Rs.200 respectively. Only men and women earn and children do not. Using matrix multiplication, calculate the daily expenses of each family

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