Assertion-Reason MCQs for Sub-Topics of Topic 1: Numbers & Numeriacal Applications

Question 1.

Assertion (A): Every natural number is a whole number.

Reason (R): The set of whole numbers includes all natural numbers and zero.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The number $\pi$ is an irrational number.

Reason (R): An irrational number has a non-terminating and non-recurring decimal expansion.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): Every integer can be written in the form $\frac{p}{q}$, where $p, q$ are integers and $q \neq 0$.

Reason (R): The set of integers is a subset of the set of rational numbers.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The number 1 is a prime number.

Reason (R): A prime number has exactly two factors: 1 and itself.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The sum of a rational number and an irrational number is always irrational.

Reason (R): Real numbers are the union of rational and irrational numbers.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): In the Indian System, the number 56,789 is read as fifty-six thousand seven hundred eighty-nine.

Reason (R): In the Indian System, commas are placed after the tens place, then after every two digits.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The place value of the digit 3 in the number 43,567 is 3000.

Reason (R): The place value of a digit is determined by its position in the number and the base of the number system.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): The Roman numeral for 49 is XLIX.

Reason (R): In Roman numerals, a smaller value symbol placed before a larger value symbol is subtracted from the larger value.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): One crore is equal to ten million.

Reason (R): The Indian and International systems of numeration group place values differently after the thousands place.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The general form of a 2-digit number with digits $a$ and $b$ (where $a$ is the tens digit) is $10a + b$.

Reason (R): The value of a digit in a number is its face value multiplied by its place value.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): The number $\frac{5}{4}$ is located between 1 and 2 on the number line.

Reason (R): $\frac{5}{4}$ can be written as $1 \frac{1}{4}$, which is greater than 1 and less than 2.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): To represent $\sqrt{3}$ on the number line, we can use a right-angled triangle with sides 1 and $\sqrt{2}$.

Reason (R): By the Pythagorean theorem, $1^2 + (\sqrt{2})^2 = 1 + 2 = 3$, so the hypotenuse is $\sqrt{3}$.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): Successive magnification helps to visualize the position of irrational numbers on the number line.

Reason (R): Irrational numbers have non-terminating, non-recurring decimal expansions, requiring closer examination of segments.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The number line is a visual representation of the set of real numbers.

Reason (R): Every point on the number line corresponds to a unique real number, and every real number can be represented by a unique point on the number line.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): Between any two integers on the number line, there is always another integer.

Reason (R): The set of integers is discrete, with a finite gap between consecutive integers.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): $-10 < -5$.

Reason (R): On the number line, the number to the right is always greater than the number to the left.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The absolute value of any integer is always positive.

Reason (R): The absolute value of a number is its distance from zero on the number line.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): There are infinitely many rational numbers between any two distinct rational numbers.

Reason (R): The average of two distinct rational numbers is always a rational number between them.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): $0.5 > 0.4$.

Reason (R): To compare decimals, we compare digits from left to right; the first place where they differ determines which number is larger.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The absolute value of 0 is 0.

Reason (R): Zero is the origin point on the number line.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): $5 \times (-3) = -15$.

Reason (R): The product of a positive integer and a negative integer is always a negative integer.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): $\frac{1}{2} + \frac{1}{3} = \frac{5}{6}$.

Reason (R): To add fractions with different denominators, find a common denominator and add the equivalent fractions.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): $10 - [5 - (3 - 1)] = 8$.

Reason (R): According to BODMAS, operations inside brackets are performed first, starting from the innermost bracket.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): $\sqrt{2} + \sqrt{3}$ is an irrational number.

Reason (R): The sum of two irrational numbers is always an irrational number.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): Dividing 1 by 0 is undefined.

Reason (R): Division by zero is not allowed in arithmetic operations on real numbers.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): For any two real numbers $a$ and $b$, $a+b = b+a$.

Reason (R): Addition of real numbers is commutative.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The number 144 is divisible by 9.

Reason (R): A number is divisible by 9 if the sum of its digits is divisible by 9.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): The product of any two odd numbers is an odd number.

Reason (R): The units digit of the product is the units digit of the product of the units digits of the original numbers.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): For any real number $a$, $a \times \frac{1}{a} = 1$, provided $a \neq 0$.

Reason (R): $\frac{1}{a}$ is the additive inverse of $a$.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The sum of the first 5 odd natural numbers is 25.

Reason (R): The sum of the first $n$ odd natural numbers is $n^2$.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): The fraction $\frac{15}{20}$ can be reduced to $\frac{3}{4}$.

Reason (R): To reduce a fraction to its simplest form, divide the numerator and denominator by their HCF.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The decimal equivalent of $\frac{1}{8}$ is 0.125.

Reason (R): To convert a fraction to a decimal, divide the numerator by the denominator.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): 0.75 and $\frac{3}{4}$ are equivalent.

Reason (R): Terminating decimals can be converted to fractions with denominators that are powers of 10.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): $1 \frac{2}{5}$ is an improper fraction.

Reason (R): A mixed number consists of a whole number part and a proper fraction part.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): 1.5, 2.34 are like decimals.

Reason (R): Like decimals have the same number of digits after the decimal point.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): The decimal expansion of $\frac{1}{3}$ is $0.333...$

Reason (R): The decimal expansion of a rational number is either terminating or non-terminating recurring.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The number $0.123456789101112...$ is irrational.

Reason (R): The decimal expansion is non-terminating and the pattern does not repeat in a fixed block of digits.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): $0.\overline{4}$ can be expressed as $\frac{4}{9}$ in $\frac{p}{q}$ form.

Reason (R): Let $x = 0.\overline{4}$. Then $10x = 4.\overline{4}$. Subtracting $x$ from $10x$ gives $9x = 4$, so $x = \frac{4}{9}$.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The denominator of $\frac{1}{\sqrt{5}}$ is rationalized by multiplying the numerator and denominator by $\sqrt{5}$.

Reason (R): Rationalizing the denominator means converting the denominator to a rational number.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The decimal expansion of $\frac{3}{25}$ is terminating.

Reason (R): The denominator of $\frac{3}{25}$ in simplest form is 25, whose prime factors are only 5.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): 12 is a factor of 36.

Reason (R): A factor divides the number completely, leaving no remainder.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): 45 is a multiple of 9.

Reason (R): A multiple is obtained by multiplying the number by an integer.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): 17 is a prime number.

Reason (R): A prime number has exactly two distinct factors: 1 and itself.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The number 36 is divisible by 4.

Reason (R): A number is divisible by 4 if the sum of its digits is divisible by 4.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The prime factorization of 75 is $3 \times 5^2$.

Reason (R): Prime factorization expresses a number as a product of its prime factors.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): The HCF of 12 and 18 is 6.

Reason (R): The HCF is the product of the lowest powers of common prime factors.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The LCM of 10 and 15 is 30.

Reason (R): The LCM is the smallest common multiple of the given numbers.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): If the HCF of two numbers is 1, they are called co-prime.

Reason (R): Co-prime numbers have no common factors other than 1.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): For any two positive integers $a$ and $b$, $HCF(a, b) \times LCM(a, b) = a \times b$.

Reason (R): This relation holds true only for prime numbers.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): To find the smallest number divisible by 12, 18, and 24, we should find their LCM.

Reason (R): The LCM of a set of numbers is the smallest number that is a multiple of all the numbers in the set.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): When 17 is divided by 5, the quotient is 3 and the remainder is 2.

Reason (R): According to Euclid's Division Lemma, $a = bq + r$, where $0 \leq r < b$. For $a=17, b=5$, we have $17 = 5 \times 3 + 2$, and $0 \leq 2 < 5$.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): Euclid's Division Algorithm is used to find the LCM of two numbers.

Reason (R): Euclid's Division Algorithm provides a step-by-step procedure to compute the HCF of two positive integers.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): The prime factorization of 90 is $2 \times 3^2 \times 5$.

Reason (R): The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of primes, ignoring the order.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): In Euclid's Algorithm for HCF(a,b), the process stops when the remainder becomes 1.

Reason (R): The HCF is the divisor at the step where the remainder is 0.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The Fundamental Theorem of Arithmetic can be used to prove that $\sqrt{2}$ is irrational.

Reason (R): The theorem implies that in the prime factorization of any perfect square, the exponents of all prime factors are even.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): $2^3 \times 2^4 = 2^{12}$.

Reason (R): When multiplying exponents with the same base, add the powers.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): $(3^2)^3 = 3^6$.

Reason (R): When raising a power to another power, multiply the exponents.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): $10^0 = 1$.

Reason (R): Any non-zero number raised to the power of zero is 1.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): $5^{-2} = \frac{1}{25}$.

Reason (R): A number raised to a negative exponent is equal to the reciprocal of the base raised to the positive exponent.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The standard form of 0.000078 is $7.8 \times 10^{-5}$.

Reason (R): In standard form ($a \times 10^n$), $a$ must be a number such that $1 \leq |a| < 10$.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): 49 is a perfect square.

Reason (R): A perfect square is a number obtained by squaring an integer.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The square root of 64 is 8.

Reason (R): The square root of a number $x$ is the number $y$ such that $y^2 = x$.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): (3, 4, 5) is a Pythagorean triplet.

Reason (R): In a Pythagorean triplet $(a, b, c)$, $a^2 + b^2 = c^2$. For (3, 4, 5), $3^2 + 4^2 = 9 + 16 = 25 = 5^2$.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The number of zeros at the end of a perfect square is always odd.

Reason (R): The prime factorization of a perfect square has all prime factors raised to an even power.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): The square root of 0.49 is 0.7.

Reason (R): $(\text{square root of numerator}) / (\text{square root of denominator})$ gives the square root of a fraction.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): 125 is a perfect cube.

Reason (R): A perfect cube is a number obtained by cubing an integer.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The cube root of -64 is -4.

Reason (R): The cube of a negative number is negative, and the cube root of a negative number is negative.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): The units digit of the cube of a number ending in 3 is 7.

Reason (R): The units digit of $3^3$ is 7.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The cube root of $\frac{8}{125}$ is $\frac{2}{5}$.

Reason (R): The cube root of a fraction is the cube root of the numerator divided by the cube root of the denominator.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): To make 24 a perfect cube, it should be multiplied by 9.

Reason (R): The prime factorization of 24 is $2^3 \times 3$. To make it a perfect cube, the exponent of 3 must be a multiple of 3. The smallest such multiple is 3. So we need $3^2=9$.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): Rounding 467 to the nearest hundred gives 500.

Reason (R): When rounding to the nearest hundred, if the digit in the tens place is 5 or greater, round up the hundreds digit.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): Rounding 12.34 to the nearest tenth gives 12.3.

Reason (R): When rounding to the nearest tenth, if the digit in the hundredths place is less than 5, keep the tenths digit the same.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): Estimating the product of 18 and 32 by rounding to the nearest ten gives $20 \times 30 = 600$.

Reason (R): Estimation provides an exact value for the calculation.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): Rounding $\textsf{₹} 299.50$ to the nearest Rupee gives $\textsf{₹} 300$.

Reason (R): If the fractional part is 0.50 or greater, round up to the next whole number.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): Rounding 1,23,456 to the nearest lakh (Indian System) gives 1,00,000.

Reason (R): The digit in the ten thousands place is 2, which is less than 5, so the lakh digit remains the same and subsequent digits are zeroed.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): $\log_{10} 1000 = 3$.

Reason (R): The logarithm of a number to a given base is the power to which the base must be raised to get the number.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): $\log (A \times B) = \log A + \log B$.

Reason (R): This is the quotient rule of logarithms.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): Antilog$_{10}(2.3010)$ is approximately 200.

Reason (R): The antilogarithm is the inverse of the logarithm operation, meaning if $\log_b A = C$, then Antilog$_b(C) = A$.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The characteristic of $\log_{10} 0.045$ is -2.

Reason (R): For a number $N < 1$, the characteristic of $\log_{10} N$ is negative and one more than the number of zeros immediately after the decimal point.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): $\log_{10} 5 = \log_{10} 10 - \log_{10} 2$.

Reason (R): $\log_b (M/N) = \log_b M - \log_b N$ is a property of logarithms.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): $20 \pmod 6 = 2$.

Reason (R): The result of the modulo operation $a \pmod m$ is the remainder when $a$ is divided by $m$, where $0 \leq r < m$.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): $15 \equiv 3 \pmod{12}$.

Reason (R): $15 - 3 = 12$, and 12 is divisible by 12.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): If $a \equiv b \pmod m$ and $c \equiv d \pmod m$, then $a+c \equiv b+d \pmod m$.

Reason (R): Congruence is preserved under addition.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): The last digit of a number is the number modulo 10.

Reason (R): Modulo 10 operation gives the remainder when a number is divided by 10, which is the units digit.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): If $a \equiv b \pmod m$, then $a$ and $b$ belong to the same congruence class modulo $m$.

Reason (R): A congruence class modulo $m$ is the set of all integers that have the same remainder when divided by $m$.

(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.

(E) Both A and R are false.

Question 1.

Assertion (A): If a shopkeeper sold 150 kg of sugar on Monday and 175 kg on Tuesday, the total sale is 325 kg.

Reason (R): Total quantity is found by adding the quantities sold on individual days.

(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.

(E) Both A and R are false.

Question 2.

Assertion (A): The cost of 5 meters of cloth at $\textsf{₹} 120.50$ per meter is $\textsf{₹} 602.50$.

Reason (R): Total cost is found by multiplying the quantity by the price per unit.

(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.

(E) Both A and R are false.

Question 3.

Assertion (A): Converting 2.5 kilograms to grams gives 250 grams.

Reason (R): 1 kilogram is equal to 1000 grams, so multiply the number of kilograms by 1000 to convert to grams.

(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.

(E) Both A and R are false.

Question 4.

Assertion (A): If the sum of the digits of a two-digit number is 7, the number could be 16 or 61.

Reason (R): The number can be represented as $10t + u$, where $t$ is the tens digit and $u$ is the units digit, and $t+u=7$.

(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.

(E) Both A and R are false.

Question 5.

Assertion (A): A rectangular plot of land has length 50 m and width 30 m. Its area is 1500 sq m.

Reason (R): The area of a rectangle is given by Length $\times$ Width.

(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.

(E) Both A and R are false.