Download App

Maths Assertion (A) & Reason (B) MCQ

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

Questions

Assertion (A) & Reason (B) MCQ

Take a timed test

5 questions · auto-graded multiple-choice test.

MCQ 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 $n(n^2 - 1) (n +2)$ is divisible by $24.$
Reason: Product of $r$ consecutive whole numbers is divisible by $\angle\text{r}.$
  • ✓
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • B
    Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  • C
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: A.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
$n(n^2 - 1) (n + 2) = (n - 1) n(n + 1) (n + 2)$ is the product of four consecutive whole numbers and hence it is divisible by $\angle4=24.$
View full question & answer→
MCQ 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 $^8C_2 \times\ ^8C_2.$
Reason: To form a rectangle, we have to select any two of the horizontal line and any two of the vertical line.
  • A
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • B
    Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  • C
    Assertion is correct statement but Reason is wrong statement.
  • ✓
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: D.
Assertion is wrong statement but Reason is correct statement.
In a chess board, there are $9$ horizontal and $9$ vertical lines. Number of rectangles of any size are $^9C_2 \times\ ^9C_2.$
View full question & answer→
MCQ 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: $\text{C}(\text{n},2)=\frac{\text{n}(\text{n}-1)}{2}.$
  • A
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • B
    Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
Number of lines is ${^\text{n}}\text{C}_{2}=\frac{\text{n}(\text{n}-1)}{2}$
$\text{C}(\text{n},3)=\frac{\text{n}!}{3!(\text{n}-3)!}$
$=\frac{\text{n}(\text{n}-1)(\text{n}-2)}{6}.$
View full question & answer→
MCQ 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 $^9C_3.$
Reason: The number of ways of choosing any $3$ places, from $9$ different places is $^9C_3.$
  • ✓
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • B
    Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  • C
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: A.
Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
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, $^{n-1}C_{r-1}.$
View full question & answer→
MCQ 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 $(n + 1)!.$
  • A
    Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
  • B
    Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
  • ✓
    Assertion is correct statement but Reason is wrong statement.
  • D
    Assertion is wrong statement but Reason is correct statement.
Answer
Correct option: C.
Assertion is correct statement but Reason is wrong statement.
Product of $n$ consecutive natural numbers
$=(\text{m}+1)(\text{m}+2)(\text{m}+3)...(\text{m}+\text{n}),\text{m}\in\text{W}$
$=\frac{(\text{m}+\text{n})!}{\text{m}!}$
$=\text{n}!\times\frac{(\text{m}+\text{n})!}{\text{m}!\text{n}!}$
$=\text{n}!\times{^{\text{m}+\text{n}}}\text{C}_{\text{m}}.$
$\Rightarrow$ Product is divisible by $n!$ and so it is always divisible by $(n - 1)!$ but not by $(n + 1)!.$
View full question & answer→
Generate Paper FreeAll Permutation and Combinations topics