PRACTICE QUESTIONS ON SETS AND RELATIONS FOR CA FOUNDATION

1)  If the universal set is X = {x : x∈  1≤x ≤ 12} and A = {1, 9, 10}, B = {3, 4, 6 ,11, 12} and C = {2, 5, 6} are subsets of X then set A U(BnC) is

(a) {3, 4, 6, 12}    (b) {1, 6, 9, 10}

(c)  {2, 5, ,6, 11}     (d) None

Solution

2)  Out of 2000 employees in an office 48% preferred coffee(c), 54% liked tea(T), 64% used to smoke (S). Out of the total 28% used C and T, 32% used T and S and 30% preferred C and S, only 6% did none of these. The number having all the three is/

(a) 360       (b) 380     (c)  300    (d) None

Solution

3)  If f(x) = x + 3 and g(x) = x² and (gof)(x) is 

(a) (x + 3)²     (b) x² + 3    (c)  x²(x + 3)    (d) None

Solution

4) If f(x) = 1/(1 - x), then f^-1(x) is

(a) 1-x     (b) (x-1)/x   (c)  x/(x - 1)    (d) None

Solution

5) If f(x) = x + 3, g(x) = x² then fog(x) is 

(a) x²+ 3     (b) x² + x + 3    (c)  (x + 3)²    (d) None

Solution

6) The number of subsets of the set {2, 3, 5}

(a) 3     (b) 8    (c)  6    (d) None

Solution

7) The null set is represented by 

(a)  Ø      (b) {0}    (c) {Ø}   (d) None

Solution

8) If P = {1, 2, 3, 5, 7} and Q = {1, 3, 6, 10, 15}, Universal set S = {1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15}

The cardinal number of PnQ is

(a)  3     (b) 2    (c) 0   (d) None

Solution

9) At a certain conference of 100 people there are 29 Indian women and 23 Indian men. Out of these Indian people 4 are doctors and 24 are either men or doctors. There are no foreign doctors. The number of women doctors attending the conference is.

(a)  2     (b) 4    (c) 1   (d) None

Solution

10) Out of 150 students 45 passed in Accounts 50 in Maths. 30 in both Accounts and Maths. 32 in both Maths and costing 35 in both Accounts and Costing. 25 students passes in all the three subjects. Find the number who passes at least in any one of the subjects.

(a)  63     (b) 53    (c) 73   (d) None

Solution

11)  f(x) = f(x - 1) + f(x - 2), if f(0) = 0, f(1) = 1, x = 2, 3, 4..... then what is f(7).

(a)  8     (b) 13    (c) 3   (d) 5

Solution

12)  f(x) = 2x³ + 1 then what is f-1(x) options

a)  1/2 (x - 1)^1/3     b) [(x - 1)/2]^1/3

c) [(x - 1)/2]^1/2        d) None

Solution

13)  6. If A = {1,2,3,4,5,6,7,8,9,} B = {1,3,4,5,7,8};C = {2,6,8,} then find (A – B)UC =

(a) {2, 6}       (b) {2, 6, 8}     (c) {2, 6, 8, 9}   (d) None of these

Solution

14)  If f (x) = x² and g(x) =√x then

(a) gof(3) = 3     (b) gof(–3) = 9

(c) gof(9) = 3     (d) gof(–9) = 3

Solution

15)  A= {1,2,3,4, ............... 10} a relation on A,

R = {(x, y)/x+ y =10, x ∈ A,y ∈ A,X ≥ Y} then Domain of R^–1 is

(a) {1, 2, 3, 4, 5}      (b) {0, 3, 5, 7, 9}

(c) {1, 2, 4, 5, 6, 7}    (d) None of these

Solution

16)  If A = {a, b, c, d}; B = {p, q, r ,s} which of the following relation is a function from A to B

(a) R₁= {(a, p), (b, q),(c, s)} (b) R₂ = {(p, a}, (b, r),(d, s)}

(c) R₃ = {(b, p),(c, s),(b, r)} (d) R₄ = {(a, p)(b, r)(c, q), (d, s)}

Solution