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Integers Test - 34

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Integers Test - 34
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  • Question 1
    1 / -0
    Choose the correct statement from following:
    Solution
    Clearly the first $$3-$$digits of each number are same.
    So, let us compare rest of the remaining $$5-$$digits of each number.
    For option $$\text{A}$$, we have
    $$68788,78688,88687$$
    Clearly, $$88687>78688>68788$$
    So, option $$\text{A}$$ is wrong.
    Now, check for option $$\text{D}$$
    We have, $$88687, 78688, 68788$$
    Clearly, $$88687>78688>68788$$$$
    So, option $$\text{D}$$ is correct.
  • Question 2
    1 / -0
    The identity elements with respect to addition in integers is 
    Solution
    Any  mathematical  object that ,when applied by an operation ,such as addition and multiplication ,to another mathematical object ,such as numbers , leaves the another object unchanged is called an identity object.
    The identity element with respect to addition in integers is '$$0$$'.
  • Question 3
    1 / -0
    Solve: $${(-12)\times (-3) \times 4\times (-6) =}$$ ?
    Solution
    $$(−12)×(−3)×4×(−6)=(36)\times 4\times (-6)\\ =144\times (-6)\\ =-864$$
  • Question 4
    1 / -0
    Suppose we represent the distance above the ground by a positive integer and that below the ground by a negative integer, then answer the following:
    An elevator descends into a mine shaft at the rate of $$5\text{ m/min}$$. What will be its position after one hour? 
    Solution
    Since, the elevator going down, so the distance covered by it will be represented by a negative integer.
    Change in position of elevator in one minute $$=$$ $$-5 \text{ m}$$

    Position of the elevator after $$60$$ minutes $$=$$ $$(-5)\times 60$$
                                                                         $$ =-300\ \text{ m}$$ 

    That means the position of the elevator will be $$ 300\text{ m}$$ below ground level.
  • Question 5
    1 / -0
    Sign of the product of 231 negative integer and 9 positive integer is
    Solution
    We know that the product of two integers with unlike signs (two integers, one with positive sign and one with negative sign) is always negative.

    The given two integers are $$-231$$ and $$+9$$ and the product of these integers is:

    $$(-231)\times (+9)=-(231\times 9)=-2079$$ which is a negative integer.

    Hence, sign of the product of the given integers is negative.
  • Question 6
    1 / -0
    Evaluate:
    $$\displaystyle (148)\div (-4)\quad $$
    Solution
    $$(148)\div(-4)=-148\div4=-37$$
  • Question 7
    1 / -0
    $$\displaystyle (-24)\times (-2)\times (-2)\times 0\times (-4) =$$
    Solution
    $$\displaystyle (-24)\times (-2)\times (-2)\times 0\times (-4)
    = +48\times 0\times -4
    =0\times -4
    =0 $$
  • Question 8
    1 / -0
    Product of two integers is - 48. lf one of the integers is - 6, then the other is ...........
    Solution

  • Question 9
    1 / -0
    $$\displaystyle (-8)\times (-2)\times (+3)\times (-4) = $$ 
    Solution
    $$ (-8)\times (-2)\times (+3)\times (-4)$$
    $$= +16\times  -12$$
    $$= -192 $$
  • Question 10
    1 / -0
    Check whether closure property is verified for integers for the given operation:$$(-50)-(-20)=-30$$
    Solution
    $$-50$$ is an integer and  $$-20$$ is also an integer.
    $$-50-(-20)=-30$$, which is an integer.
    Hence given Integers are closed under subtraction.
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