Math Ch-1 Mock Test

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| By Harsh Sharma
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Harsh Sharma
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Quizzes Created: 1 | Total Attempts: 208
| Attempts: 208
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  • 1/10 Questions
    1. The decimal expansion of number has: - ProProfs

    1. The decimal expansion of number has:

    • A terminating decimal
    • Non-terminating but repeating
    • Non-terminating non repeating
    • Terminating after two places of decimal
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About This Quiz

This mock test for Math Chapter 1 covers basic arithmetic, algebra, and number theory, including decimal expansions, integer division, and calculations of HCF, LCM, and geometric dimensions.

Math Ch-1 Mock Test - Quiz

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  • 2. 
    The decimal expansion of the rational number will terminate after - ProProfs

    The decimal expansion of the rational number will terminate after

    • 2

    • 1

    • 3

    • 4

    Correct Answer
    A. 2
    Explanation
    The decimal expansion of a rational number will terminate after a certain number of decimal places if and only if the denominator of the rational number can be expressed as a power of 10. In this case, the denominator is 2, which can be expressed as 10^1. Therefore, the decimal expansion of the rational number will terminate after 1 decimal place, which is the correct answer.

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  • 3. 

    For any positive integer a and 3, there exist unique integers q and r such that a = 3q + r, where r must satisfy :

    • 0 ≤ r < 3

    • 1 < r < 3

    • 0 < r < 3

    • Terminating after two places of decimal

    Correct Answer
    A. 0 ≤ r < 3
    Explanation
    The statement "0 ≤ r < 3" is the correct answer because it satisfies the given conditions that r must be an integer and it must be between 0 and 3. This means that r can be either 0, 1, or 2, which are the only possible remainders when a is divided by 3.

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  • 4. 
    The values of x and y in the given figure are: - ProProfs

    The values of x and y in the given figure are:

    • X = 10; y = 14

    • X = 21; y = 84

    • X = 21; y = 25

    • Terminating after two places of decimal

    Correct Answer
    A. X = 10; y = 14
  • 5. 

    If two positive integers a and b are written as a = x3y2 and b = xy3; x, y are prime numbers, then HCF (a, b) is

    • XY

    • Xy2

    • X3y3

    • X2y2

    Correct Answer
    A. XY
    Explanation
    In this question, we are given that a = x^3y^2 and b = xy^3, where x and y are prime numbers. The highest common factor (HCF) of two numbers is the largest number that divides both of them. In this case, we can see that both a and b have factors of x and y. However, a has an additional factor of y^2, which is not present in b. Therefore, the largest number that divides both a and b is xy. Hence, the correct answer is XY.

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  • 6. 

    The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is completely divided by 2 the quotient is 33. The other number is:

    • 66

    • 130

    • 132

    • 196

    Correct Answer
    A. 66
    Explanation
    The highest common factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. The least common multiple (LCM) of two numbers is the smallest multiple that is divisible by both numbers. In this case, the HCF is 33 and the LCM is 264. When the first number is divided by 2, the quotient is 33. This means that the first number is 66 (33 multiplied by 2). Since the LCM is 264, the other number must be 264 divided by the first number, which is 66. Therefore, the other number is 66.

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  • 7. 

    What will be the least possible number of the planks, if three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length?

    • 5

    • 6

    • 7

    • Terminating after two places of decimal

    Correct Answer
    A. 5
    Explanation
    To divide the three pieces of timber into planks of the same length, we need to find the greatest common divisor (GCD) of the lengths of the timber. The GCD of 42, 49, and 63 is 7. Therefore, the planks will have a length of 7 meters. To find the least possible number of planks, we divide the total length of the timber (154 meters) by the length of each plank (7 meters), which gives us 22 planks. However, since we want the least possible number of planks, we need to round up to the next whole number, which is 23. Therefore, the least possible number of planks is 23 divided by 3 (since we have 3 pieces of timber), which equals 7.

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  • 8. 

    If A = 2n + 13, B = n + 7, where n is a natural number then HCF of A and B is:

    • 2

    • 1

    • 3

    • 4

    Correct Answer
    A. 2
    Explanation
    The HCF (Highest Common Factor) is the largest number that divides both A and B without leaving a remainder. In this case, A = 2n + 13 and B = n + 7. To find the HCF, we need to find the common factors of A and B. By simplifying the equations, we can see that A = 2(n + 6) + 1 and B = n + 6 + 1. It is clear that both A and B have a common factor of 2. Therefore, the HCF of A and B is 2.

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  • 9. 

    The product of rational and irrational no is

    • Rational

    • Irrational

    • Both of above

    • None of above

    Correct Answer
    A. Rational
    Explanation
    The product of a rational number and an irrational number is always rational. This is because when we multiply a rational number (which can be expressed as a fraction) with an irrational number, the result can still be expressed as a fraction. Therefore, the product is rational.

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  • 10. 

    L.C.M. of 23 × 32 and 22 × 33 is :

    • 23

    • 33

    • 23 x 33

    • 22 x 32

    Correct Answer
    A. 23
    Explanation
    The L.C.M. (Least Common Multiple) is the smallest multiple that two or more numbers have in common. In this case, we need to find the L.C.M. of (23 × 32) and (22 × 33). To find the L.C.M., we need to consider the highest power of each prime factor that appears in the given numbers. Both numbers have 2 as a common factor, and the highest power of 2 is 2^2. However, 23 is a prime number and does not have any common prime factors with the other number. Therefore, the L.C.M. is 23.

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  • Current Version
  • Mar 18, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • May 09, 2020
    Quiz Created by
    Harsh Sharma
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