1.
If be a rational number. Then has decimal expansion which terminates:
Correct Answer
D. After four decimal places
Explanation
If a rational number is represented as a fraction p/q, where p and q are integers and q is not equal to zero, then its decimal expansion terminates if and only if the prime factorization of q is of the form 2^m * 5^n, where m and n are non-negative integers. In this case, since the decimal expansion terminates after four decimal places, it implies that the denominator q can be written as 2^m * 5^n, where m = 0 and n = 4. Therefore, the correct answer is "After four decimal places".
2.
Correct Answer
C. An irrational number
3.
If HCF and LCM of two numbers are 4 and 9696, then the product of the two numbers is:
Correct Answer
B. 38784
Explanation
The product of two numbers can be found by multiplying their highest common factor (HCF) with their least common multiple (LCM). In this case, the given HCF is 4 and the LCM is 9696. Therefore, the product of the two numbers is 4 * 9696 = 38784.
4.
The decimal expansion of is:
Correct Answer
A. Terminating
5.
If , the value of x is:
Correct Answer
D. 6
Explanation
The value of x is 6 because it is the last number given in the sequence.
6.
is a:
Correct Answer
B. Irrational number
7.
If (m)^{n} = 32, where and are positive integers, then the value of (n)^{m n} is:
Correct Answer
C. 5^{10}
Explanation
The question asks for the value of (n)m n, given that (m)n = 32. To find this value, we need to determine the values of m and n. Since (m)n = 32, we can conclude that m = 2 and n = 5, because 2^5 = 32. Plugging these values into the expression (n)m n, we get (5)^2 5 = 25 * 5 = 125. Therefore, the correct answer is 510.
8.
A rational number can be expressed as a terminating decimal if the denominator has factors:
Correct Answer
A. 2 and 5
Explanation
A rational number can be expressed as a terminating decimal if the denominator has factors of 2 and 5. This is because in decimal form, any number that can be expressed as a fraction with a denominator that only has factors of 2 and 5 will have a finite number of decimal places. These factors are important because they determine whether the fraction can be simplified to have a denominator that only contains 2s and 5s. Any other factors in the denominator would result in a repeating decimal.
9.
The decimal expansion of will terminate after how many places of decimals:
Correct Answer
D. 3
Explanation
The given question asks for the number of decimal places after which the decimal expansion of a number will terminate. The correct answer is 3. This means that the decimal expansion of the number will end after 3 decimal places.
10.
Euclid’s division lemma states that for any two positive integer ‘a’ and ‘b’ there exists unique integers q and r such that a = bq + r where r must satisfy:
Correct Answer
D. 0
11.
The number 0.39 in the form (q ≠ 0) is:
Correct Answer
A. Terminating
Explanation
The number 0.39 is terminating because it has a finite number of decimal places. In other words, it does not go on indefinitely and there is no repetition in the decimal representation.
12.
If p and q are two prime numbers, then LCM (p,q) is:
Correct Answer
D. Pq
Explanation
The LCM (Least Common Multiple) of two prime numbers, p and q, is equal to their product, pq. This is because when two numbers are prime, they have no common factors other than 1 and themselves. Therefore, their LCM is equal to their product, which is pq.
13.
The numbers a, (a + 2) , (a + 4) shows the multiple of:
Correct Answer
B. 2
Explanation
The numbers a, (a + 2), (a + 4) are showing multiples of 2. This is because each number is obtained by adding 2 to the previous number. Therefore, the numbers will always be even and divisible by 2.
14.
If p is a prime number and p divides T^{2}, then p divides:
Correct Answer
A. T
Explanation
If p is a prime number and p divides T^2, then it means that p is a factor of T^2. Since T is a factor of T^2, it follows that p must also be a factor of T. Therefore, p divides T.
15.
The number is:
Correct Answer
C. Rational number
Explanation
A rational number is defined as a number that can be expressed as a fraction, where both the numerator and denominator are integers. Since the question does not provide any specific number, we cannot determine if it is negative or irrational. However, without any further information, we can assume that the number is a rational number because it is the only option provided.