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Maths Assertion (A) & Reason (B) MCQ

Real Numbers · CBSE STD 10 (CBSE - English Medium). 108 questions.

Questions · Page 3 of 3

Assertion (A) & Reason (B) MCQ

MCQ 1011 Mark
Statement A (Assertion) : $\sqrt{2}$ is an irrational number.
Statement $R$ (Reason) : If $p$ be a prime, then $\sqrt{p}$ is an irrational number.
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
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MCQ 1021 Mark
Statement A (Assertion) : $\sqrt{5}$ is an irrational number.
Statement $R$ (Reason) : If $m$ is a natural number which is not a perfect square, then $\sqrt{m}$ is irrational.
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : Clearly, 5 is not a perfect square.
$\therefore \sqrt{5}$ is irrational.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
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MCQ 1031 Mark
Statement A (Assertion): If $\operatorname{HCF}(209,737)$ $=11$ and $\operatorname{LCM}(209,737)=209 \times R$, then the value of $R$ is 68 .
Statement R (Reason) : For any two positive numbers $a$ and $b$, HCF $(a, b) \times \operatorname{LCM}(a, b)=a \times b$.
  • A
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • ✓
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: D.
Assertion (A) is false but reason $(R)$ is true.
(d) : Given, $\operatorname{HCF}(209,737)=11$ and
$\operatorname{LCM}(209,737)=209 \times R$
Clearly, $\operatorname{LCM}(209,737)=\frac{209 \times 737}{\operatorname{HCF}(209,737)}$
$\Rightarrow 209 \times R=\frac{209 \times 737}{11} \Rightarrow R=\frac{737}{11}=67$
$\therefore \quad$ Assertion is false but Reason is true.
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MCQ 1041 Mark
Statement A (Assertion): HCF of $(23,53)$ is 1 .
Statement $R$ (Reason) : If $p$ and $q$ are distinct primes, then $\operatorname{HCF}(p, q)=1$.
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
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MCQ 1051 Mark
Statement A (Assertion): If LCM of two numbers $=350$ and their product is $25 \times 70$, then their $HCF =5$.
Statement R (Reason) : LCM $\times$ Product of numbers $= HCF$.
  • A
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • ✓
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: C.
Assertion (A) is true but reason ( $R$ ) is false.
(c) : $LCM \times HCF$ of two numbers = Product of two numbers
$\Rightarrow 350 \times HCF =25 \times 70 \Rightarrow HCF =\frac{25 \times 70}{350}=5$
$\therefore \quad$ Assertion is true but reason is false.
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MCQ 1061 Mark
Statement A (Assertion) : For no value of $n$, where $n$ is a natural number, the number $8^n$ ends with the digit zero.
Statement R (Reason) : The prime factorisation of a natural number is unique, except for the order of its factors.
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : We have, $8^n=\left(2^3\right)^n=2^{3 n}$, so the only prime in the factorisation of $8^n$ is 2 . So from the uniqueness of the Fundamental Theorem of Arithmetic we can say that there are no other primes in the factorisation of $8^n$. So, there is no natural number $n$ for which $8^n$ ends with the digit zero.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
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MCQ 1071 Mark
Statement A (Assertion) : $11 \times 4 \times 3 \times 2+4$ is a composite number.
Statement R (Reason) : Every composite number can be expressed as product of primes.
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a): We have, $11 \times 4 \times 3 \times 2+4$
$=(11 \times 3 \times 2+1) 4=67 \times 4=67 \times 2^2$
The given number can be expressed as product of primes. So, it is a composite number.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
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MCQ 1081 Mark
Statement A (Assertion) : The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively is 127 .
Statement R (Reason) : HCF = Product of the smallest power of each common prime factor in the numbers.
  • ✓
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
  • B
    Both assertion $(A)$ and reason $(R)$ are true and reason $(R)$ is not the correct explanation of assertion (A).
  • C
    Assertion (A) is true but reason ( $R$ ) is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.
Answer
Correct option: A.
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion (A).
(a) : Required number
$=$ HCF of (1657 - 6) and (2037 - 5)
$= HCF$ of 1651 and 2032
Since, $1651=127 \times 13$ and $2032=127 \times 2^4$
So, HCF of 1651 and 2032 is 127.
$\therefore \quad$ Assertion and Reason both are true and Reason is the correct explanation of Assertion.
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Assertion (A) & Reason (B) MCQ - Page 3 - Maths STD 10 Questions - Vidyadip