CBSE 11th Standard Maths Subject Sets HOT Questions 4 Mark Questions With Solution 2021
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CBSE 11th Standard Maths Subject Sets HOT Questions 4 Mark Questions With Solution 2021
11th Standard CBSE
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Reg.No. :
Mathematics
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In a survey of 400 movie viewers, 150 were listed as liking 'Veer Zaara', 100 were listed as liking 'Aitraaz' and 75 were listed both liking 'Aitraaz' as well as 'Veer zaara'.Find how many people liking neither 'Aitraaz' nor 'Veer Zaara'?
(a) -
Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in English and Mathematics but not in Science?
(a) -
Out of 100 students, 15 passed in English, 12 passed in Mathematics, 8 in Science, 4 in English and Science, 4 in all the three.Find how many students passed in Mathematics and Science but not in English?
(a) -
Prove that \(A-(B\cap C)=(A-B)\cup (A-C).\)
(a)
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CBSE 11th Standard Maths Subject Sets HOT Questions 4 Mark Questions With Solution 2021 Answer Keys
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The number of people who were liking neither (A) 'Aitraaz' nor 'Veer Zaara' (V) is given by
\(n({ V }^{ ' }\cap { A }^{ , }) ={ n(V\cup A) }^{ ' }\)
=\(n(\cup )-n(V\cup A)\)
=\(n(\cup )-n(V)-n(A)+n(V\cap A)\) -
n(E)=15,n(M)=12,n(s)=8,\(n(E\cap M)=6\)
\(n(M\cap S)=7,n(E\cap S)=4,n(E\cap M\cap S)=4\)
(i)\(n(E\cap M\cap \overline { S } )=n(E\cap M)-n(E\cap M\cap S)\)
=6-4=2 -
\(n(E\cap S\cap \overline { E } )=n(E\cap S)-n(E\cap M\cap S)\)
=74=3 -
To prove, that \(A-(B\cap C)=(A-B)\cup (A-C).\)
Let \(x\in A-(B\cap C)\)
\(\Rightarrow\quad x\in A\quad and\quad x\notin (B\cap C)\)
\(\Rightarrow \quad x\in A\quad and\quad (x\notin B\quad or\quad x \notin C)\)
\(\Rightarrow \quad (x\in A\quad and\quad x\notin B)\quad or\quad (x\in A\quad and\quad (x\notin C)\)
\(\Rightarrow \quad x\in (A-B)\quad or\quad x\in (A-c)\)
\(\Rightarrow \quad x\in (A-B)\cup (A-C)\)
\(\because \quad A-(B\cap C)\subseteq (A-B)\cup (A-C)\quad \quad \quad .....(i)\)
Again, let y \(\in\) \((A-B)\cup (A-C)\)
\(\Rightarrow \quad y\in (A-B)\quad or\quad y\in (A-c)\)
\(\Rightarrow \quad (y\in A\quad and\quad y\notin B)\quad or(y\in A\quad and\quad y\notin C)\)
\(\Rightarrow \quad y\in A\quad and\quad (y\notin B\quad or\quad y\notin C)\)
\(\Rightarrow\quad y\in A\quad and\quad y\notin (B\cap C)\Rightarrow y\epsilon A-(B\cap C)\Rightarrow y\epsilon A-(B\cap C)\)
\(\Rightarrow \quad (A-B)\cup (A-C)\subseteq A-(B\cap C) \quad \quad ........(ii)\)
From Eqs. (i) and (ii), we get
\(A-(B\cap C)=(A-B)\cup (A-C).\)
