In a group of 400 people, 250 can speak Hindi and 200 can speak

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsShort Answer Type

121. Show that :

space space space space space space space straight A union left parenthesis straight B minus straight A right parenthesis space equals space straight A union straight B

114 Views

122.

If U = {a, b, c, d, e, f, g, h, k}, A = {a, b, c, d), B  = {b, d, f, h}, C = {c, d, e, f} find 

(a) B'     (b)   C'        space space space space space space space space space space space space left parenthesis straight c right parenthesis space space space left parenthesis straight A union straight B right parenthesis apostrophe space space space space space space space space space space space space space left parenthesis straight d right parenthesis space open parentheses straight B union straight C close parentheses apostrophe space space space space space space space space  (e)   (B - C)'
124 Views

123.

Find the following to make them true statements :


space space space space space space space space space left parenthesis straight a right parenthesis space space left parenthesis straight ϕ apostrophe right parenthesis apostrophe intersection straight A space equals space...... space space left parenthesis straight b right parenthesis space left parenthesis straight U apostrophe right parenthesis apostrophe union straight A space equals space....... space space space space space left parenthesis straight c right parenthesis space left parenthesis straight A intersection straight B right parenthesis apostrophe space equals space.......

space space space space space space space space space space space left parenthesis straight d right parenthesis space open parentheses straight A intersection straight ϕ close parentheses apostrophe space equals space....... space space space space space space left parenthesis straight e right parenthesis space open parentheses straight A union straight A apostrophe close parentheses apostrophe equals space......... space space space space space left parenthesis straight f right parenthesis space open parentheses straight A intersection straight A apostrophe close parentheses apostrophe space equals space.......... space space space space space space space

127 Views

124. If A and B are two sets, then

space space space space space space left parenthesis straight i right parenthesis space straight n left parenthesis straight A minus straight B right parenthesis space equals space straight n left parenthesis straight a right parenthesis minus straight n left parenthesis straight A intersection straight B right parenthesis          
122 Views

Advertisement
125.

Prove that :  space space space space space straight n left parenthesis straight A increment straight B right parenthesis space equals straight n left parenthesis straight A right parenthesis space plus space straight n left parenthesis straight B right parenthesis minus 2 straight n space left parenthesis straight A intersection straight B right parenthesis

128 Views

126.

If A, B and C be three sets, then

space space space space space space space space space space space space space space space straight n left parenthesis straight A union straight B union straight V right parenthesis space equals space straight n left parenthesis straight A right parenthesis space plus straight n left parenthesis straight B right parenthesis space plus straight n left parenthesis straight C right parenthesis space minus straight n left parenthesis straight A intersection straight B right parenthesis minus straight n left parenthesis straight B intersection straight C right parenthesis minus straight n left parenthesis straight C intersection straight A right parenthesis plus straight n left parenthesis straight A intersection straight B intersection straight C right parenthesis

122 Views

Advertisement

127.

In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English?


Let  A = set of people who can speak Hindi.

Let B = set of people who can speak English.

Number of people = 400                                               space space space space space space rightwards double arrow space space space straight n left parenthesis straight A union straight B right parenthesis space equals space 400 space             ...(i)

Number of people who can speak hindi = 250      space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space straight n left parenthesis straight A right parenthesis space equals space 250                   ....(ii)

Number of people who can speak English = 200    space space space space space space space space space space space space space space space space space rightwards double arrow space space space space space space straight n left parenthesis straight B right parenthesis space equals space 200                  ...(iii)

Number of people who can speak both Hindi and englsih  = space space space space space space space straight n left parenthesis straight A intersection straight B right parenthesis

We  know that   

space space space space space space space space space space space space straight n left parenthesis straight A union straight B right parenthesis space equals space straight n left parenthesis straight A right parenthesis space plus space straight n left parenthesis straight B right parenthesis space minus space straight n left parenthesis straight A intersection straight B right parenthesis

∴    space space space space space space space space space space space space 400 space equals space 250 space plus space 200 space minus space straight n left parenthesis straight A intersection straight B right parenthesis

space space space space space space space space space space space space rightwards double arrow space space space space space space space space space space space space space straight n left parenthesis straight A intersection straight B right parenthesis space equals space 250 plus 200 minus 400 equals 50

Hence, the number of people, who can speak both languages.

space space space space space space space space space space space space space equals space straight n left parenthesis straight A union straight B right parenthesis equals 50

160 Views

Advertisement
128.  X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and (X ∩ Y) has 10 elements. How many elements does Y have?
123 Views

Advertisement
129.

In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?

125 Views

130. In a group of people, 50 speak both English and Hindi and 30 speak English but not Hindi. If all the people speak at least one of the two languages, how many speak English?
655 Views

Advertisement