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Assertion (A) & Reason (B) MCQ

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MCQ 11 Mark
Assertion (A): Suresh plans to go from Lucknow to Kanpur by bus and return back to Lucknow by a different bus. If there are only 10 buses running between Lucknow and Kanpur, then total number of ways in which Suresh can plan his journey is 90.
Reason (R): If an event can occur in $m$ different ways and a second event can occur in $n$ different ways, then either of the two events can occur in $(m+n)$ ways.
  • Both $A$ and $R$ are true and $R$ is the correct explanation of A .
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    $A$ is true but $R$ is false.
  • D
    A is false but R is true.
Answer
Correct option: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of A .
(a) Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
Explanation: Number of ways of going from Lucknow to Kanpur by bus $=10$
Number of ways of returning back by different bus $=9$
$\therefore$ By fundamental principle of counting, total number of ways $=10 \times 9=90$
$\therefore$ A is true.
Also, R is true but R is not the correct explanation of A .
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MCQ 21 Mark
Assertion (A): If $A$ and $B$ are events associated with a random experiment such that $A \subset B$, then $P(B-A)=$ $P(B)-P(A)$.
Reason (R): If $A \subset B$, then $A \cap B=A$.
  • Both A and R are true and R is the correct explanation of A .
  • B
    Both $A$ and $R$ are true but $R$ is not the correct explanation of A.
  • C
    $A$ is true but $R$ is false.
  • D
    A is false but $R$ is true.
Answer
Correct option: A.
Both A and R are true and R is the correct explanation of A .
(a) Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
Explanation: We know that $\mathrm{P}(\mathrm{B}-\mathrm{A})=\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})$
$\because A \subset B \Rightarrow A \cap B=A$
$\therefore \mathrm{R}$ is true.
So, $P(B-A)=P(B)-P(A)$
$\therefore A$ is true and $R$ is the correct explanation of $A$.
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Assertion (A) & Reason (B) MCQ - Applied Maths STD 11 Science Questions - Vidyadip