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MATHS Assertion (A) & Reason (B) MCQ

Permutation and Combinations · Rajasthan Board (RBSE) STD 11 Science (Rajasthan - English Medium). 5 questions.

Questions

Assertion (A) & Reason (B) MCQ

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5 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: If n is a positive integer, then n(n2 - 1) (n +2) is divisible by 24.
Reason: Product of r consecutive whole numbers is divisible by $\angle\text{r}.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.

Solution:

n(n2 - 1) (n + 2) = (n - 1) n(n + 1) (n + 2) is the product of four consecutive whole numbers and hence it is divisible by $\angle4=24.$

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Question 21 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Number of rectangles on a chess board is 8C2 × 8C2.
Reason: To form a rectangle, we have to select any two of the horizontal line and any two of the vertical line.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is wrong statement but Reason is correct statement.

Solution:

In a chess board, there are 9 horizontal and 9 vertical lines.

Number of rectangles of any size are 9C2 × 9C2.

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Question 31 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Number of lines formed by joining n points on a circle $(\text{n}\geq2)$ is $\frac{\text{n}(\text{n}-1)}{2}.$
Reason: $\text{C}(\text{n},2)=\frac{\text{n}(\text{n}-1)}{2}.$
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion is correct statement but Reason is wrong statement.

Solution:

Number of lines is ${^\text{n}}\text{C}_{2}=\frac{\text{n}(\text{n}-1)}{2}$

$\text{C}(\text{n},3)=\frac{\text{n}!}{3!(\text{n}-3)!}$

$=\frac{\text{n}(\text{n}-1)(\text{n}-2)}{6}.$

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Question 41 Mark
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is 9C3.
Reason: The number of ways of choosing any 3 places, from 9 different places is 9C3.
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement.
Answer
  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.

Solution:

Let the number of ways of distributing n identical objects among r persons such that each person gets atleast one object is same as the number of ways of selecting (r - 1) places out of (n - 1) different places, ie, n-1Cr-1.

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Question 51 Mark
 Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:

Assertion: Product of five consecutive natural numbers is divisible by 4!.

Reason: Product of n consecutive natural numbers is divisible by (n + 1)!.

  1. Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  2. Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  3. Assertion is correct statement but Reason is wrong statement.
  4. Assertion is wrong statement but Reason is correct statement. 
Answer
  1. Assertion is correct statement but Reason is wrong statement.

Solution:

Product of n consecutive natural numbers

$=(\text{m}+1)(\text{m}+2)(\text{m}+3)...(\text{m}+\text{n}),\text{m}\in\text{W}$

$=\frac{(\text{m}+\text{n})!}{\text{m}!}=\text{n}!\times\frac{(\text{m}+\text{n})!}{\text{m}!\text{n}!}=\text{n}!\times{^{\text{m}+\text{n}}}\text{C}_{\text{m}}.$

⇒ Product is divisible by n! and so it is always divisible by (n - 1)! but not by (n + 1)!.

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Assertion (A) & Reason (B) MCQ - MATHS STD 11 Science Questions - Vidyadip