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Maths Assertion (A) & Reason (B) MCQ

Real Numbers · CBSE STD 10 (CBSE - English Medium). 18 questions.

Questions

Assertion (A) & Reason (B) MCQ

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18 questions · timed · auto-graded

MCQ 11 Mark
Statement-1 (A): $ 2+\sqrt{2}$ is an irrational number.
Statement-2 (R): The sum of a non-zero rational number and an irrational number is always an irrational number.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 21 Mark
Statement-1 $(A)$ : The number $5^n$ cannot end with the digit 0 , where $n$ is a natural number.
Statement-2 $(R)$: Prime factorisation of 5 has only two factors 1 and 5.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-2 is true. Using statement-2, we find that only prime factors in the prime factorisation of 5 are 1 and 5 , not 2 . Hence, $5^n$ cannot end with the digit 0 . So, statement- 1 is also true and statement-2 is a correct explanation for statement-1. Hence, option (a) is correct.
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MCQ 31 Mark
Statement-1 (A): In the following figure, the perimeter of $\triangle A B C$ is a rational number.
Image
Statement-2 (R): The sum of the squares of two rational numbers is always rational.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: D.
Statement- 1 is false, Statement- 2 is true.
D
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MCQ 41 Mark
Statement-1 $(A)$ : The product of $(5+\sqrt{3})$ and $(2-\sqrt{3})$ is an irrational number.
Statement-2 $(R)$: The product of two irrational numbers is an irrational number.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: C.
Statement-1 is true, Statement-2 is false.
(C) Statement-1 is true, Statement-2 is false.
We find that $(5+\sqrt{3})(2-\sqrt{3})=7-3 \sqrt{3}$, which is an irrational number.
So, statement- 1 is true.
We observe that $\sqrt{5}$ and $3 \sqrt{5}$ are irrational numbers. But, their product $\sqrt{5} \times 3 \sqrt{5}=15$ is a rational number. So, statement-2 is false.
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MCQ 51 Mark
Statement-1 $(A)$: If 11 divides 627264, then 11 divides 792.
Statement-2 $(R)$ : Let $p$ be a prime number and a be a positive integer, if $p$ divides $a^2$, then pdivides $a$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Using Theorem 2 (page 1.3 of main book), we find that the statement- 2 is true. We observe that 11 is prime and it divides 627264 . Therefore, by using statement-2, 11 divides $\sqrt{627264}=792$. So, statement-1 is also true. Also, statement-2 is a correct explanation for statement-1.
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MCQ 61 Mark
Statement-1 $(A)$ : The square of an odd natural number leaves remainder 1 when divided by 4.
Statement-2 $(R)$ : The square of an odd natural number is of the form $4 k+1$ for some nonnegative integer number $k$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Let $n$ be an odd natural number. Then,
$
\begin{aligned}
& n=2 m-1 \text { for some natural number } m \\
\Rightarrow \quad & n^2=(2 m-1)^2=4 m^2-4 m+1=4 m(m-1)+1=4 k+1, \text { where } k=m(m-1)
\end{aligned}
$
So, statement-2 is true.
Now, $n^2=4 k+1 \Rightarrow n^2-4 k=1$
This means that when $n^2$ is divided by 4 , the remainder is 1 . So, statement 1 is also true and statement-2 is correct explanation for statement-1. Hence, option (a) is correct.
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MCQ 71 Mark
Statement-1 $(A)$: $ n^2+n$ is divisible by 2 for every natural number $n$.
Statement-2 $(R)$ : The product of two consecutive natural numbers is an even natural number.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Let $n$ and $n+1$ be two consecutive natural numbers. Then one of the two is even and the other is odd. Consequently, their product is always an even natural number. So, statement-2 is true. We find that $n^2+n=n(n+1)$ is the product of two consecutive natural numbers. So, by statement-2, it is even and hence divisible by 2 . Therefore, statement- 1 is also true and statement- 2 is a correct explanation for statement-1.
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MCQ 81 Mark
Statement-1 $(A)$: If product of two numbers is 5780 and theire HCF is 17, then teir LCM is 340.
Statement-2 $(R)$ : HCF is always a factor of $L C M$.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(B) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
We know that $\operatorname{HCF}(a, b) \times \operatorname{LCM}(a, b)=a b\qquad\ldots(i)$
Clearly, $17 \times 340=5780$. So, statement- 1 is true.
It is evident from (i) that HCF is always a factor of LCM. So, statement- 2 is also true. But, statement-2 is not the correct explanation for statement-1. Hence, option (b) is correct.
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MCQ 91 Mark
Statement-1 $(A):  \operatorname{If} L C M(60,72)=360$, then $\operatorname{HCF}(60,72)=12$.
Statement-2 $(R): \operatorname{HCF}(a, b) \times \operatorname{LCM}(a, b)=a+b$.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: C.
Statement-1 is true, Statement-2 is false.
(C) Statement-1 is true, Statement-2 is false.
We have, $60=2^2 \times 3 \times 5$ and $72=2^3 \times 3^2$
$
\therefore \quad \operatorname{LCM}(60,72)=2^3 \times 3^2 \times 5=360 \text { and } \operatorname{HCF}(60,72)=2^2 \times 3=12
$
So, statement- 1 is true.
We know that $\operatorname{HCF}(a, b) \times \operatorname{LCM}(a, b)=a \times b$. So, statement- 2 is false. Hence, option (c) is correct.
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MCQ 101 Mark
Statement-1 $(A)$ : If $H C F(90,144)=18$, then $\operatorname{LCM}(90,144)=720$.
Statement-2 $(R): \operatorname{HCF}(a, b) \times \operatorname{LCM}(a, b)=a \times b$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
We know that statement-2, being a standard result, is true. Using statement-2, we find that
$
\begin{aligned}
& \operatorname{HCF}(90,144) \times(\operatorname{LCM}(90,144)=90 \times 144 \\
\Rightarrow \quad & 18 \times \operatorname{LCM}(90,144)=90 \times 144 \Rightarrow \operatorname{LCM}(90,144)=720
\end{aligned}
$
So, statement- 1 is also true. Clearly, statement-2 is the correct explanation for statement-1. Hence, option (a) is correct.
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MCQ 111 Mark
Statement-1 (A): $\sqrt{2}+\sqrt{3}$ is an irrational number.
Statement-2 (R): If $p$ and $q$ are prime positive integers, then $\sqrt{p}+\sqrt{q}$ is an irrational number.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 121 Mark
Statement-1 (A): 997 is the largest three digit prime number.
Statement-2 (R): A positive integer $n$ is a prime number, if no positive integer less than or equal to $\sqrt{n}$ divides $n$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 131 Mark
Statement-1 (A): If HCF $(a, b)=4$ and $a b=96 \times 404$, then $\operatorname{LCM}(a, b)=9696$
Statement-2 (R): LCM of two numbers $a$ and $b=\operatorname{HCF}(a, b) \times a b$.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: C.
Statement-1 is true, Statement-2 is false.
C
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MCQ 141 Mark
Statement-1 (A): For any positive integer $n , n^3-n$ is divisible by 6 .
Statement-2 (R): Product of three consecutive natural numbers is always a multiple of 6 .
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 151 Mark
Statement-1 (A): HCF of two consecutive natural numbers is 1.
Statement-2 (R): HCF of two co-primes is 1
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 161 Mark
Statement-1 (A): $\sqrt{11}$ is an irrational number.
Statement-2 (R) : If p is a prime number, then $\sqrt{p}$ is an irrational number.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 171 Mark
Statement-1 (A): HCF (234,47) =1.
Statement-2 (R): HCF of two co-primes is always 1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
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MCQ 181 Mark
Statement-1 (A): HCF and LCM of two natural numbers are 25 and 815 respectively.
Statement-2 (R): LCM of two natural numbers is always divisible by their HCF.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • ✓
    Statement- 1 is false, Statement- 2 is true.
Answer
Correct option: D.
Statement- 1 is false, Statement- 2 is true.
D
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Assertion (A) & Reason (B) MCQ - Maths STD 10 Questions - Vidyadip