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Straight Lines Test 2

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Straight Lines Test 2
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  • Question 1
    1 / -0
    Choose the correct option for the following.
    $$n!=n(n-1)(n-2).....3.2.1$$
    Solution
    Factorial : the product of an integer and all integer less than that 
    $$\therefore n!=n\times (n-1)\times (n-2)............3\times 2\times 1$$

    $$\therefore $$ The given statement 
    $$n!=n\times (n-1)\times (n-2)............3\times 2\times 1$$ is True
  • Question 2
    1 / -0
    The positions of the first and the fifth digits in the number 83256479 are interchanged. Similarly the positions of the second and the sixth digits are interchanged and so on. Which of the following will be the third to the right of the seventh digit from the right end after rearrangement?
    Solution
    In the given number 83256479, the first and the fifth digits are interchanged.The number becomes 63258479.
    Then second and the sixth digit are interchanged. The number becomes 64258379.
    The third and the seventh digit are interchanged. The number becomes 64758329.
    The fourth and the eighth digit are interchanged. The number becomes 64798325.
    The seventh digit from the right end after rearrangement is 4.The third digit to the right of 4 is 8.
    Answer is Option D

  • Question 3
    1 / -0
    The area of a triangle whose vertices are $$(a, c+a), (a, c) $$ and $$(-a, c-a) $$ are 
    Solution
    Area of a triangle with vertices $$({ x }_{ 1 },{ y }_{ 1 })$$ ; $$({ x }_{ 2 },{ y

    }_{ 2 })$$  and $$({ x }_{ 3 },{ y }_{ 3 })$$  is $$ \left| \frac { {

    x }_{ 1 }({ y }_{ 2 }-{ y }_{ 3 })+{ x }_{ 2 }({ y }_{ 3 }-{ y }_{ 1 })+{ x }_{

    3 }({ y }_{ 1 }-{ y }_{ 2 }) }{ 2 }  \right| $$
    Hence, area of the triangle with given vertices is $$ \left| \frac { { a }(c-c+a)+a(c-a-c-a)-a(c+a-c) }{ 2 }  \right|  = \left| \frac { { a }^{ 2 }-2{ a }^{ 2 }-{ a }^{ 2 } }{ 2 }  \right|  = { a }^{ 2 } $$


  • Question 4
    1 / -0
    The greatest number that can be formed by the digits $$7,0,9,8,6,3$$
    Solution
    The greatest number that can be formed by the digits $$7,0,9,8,6,3$$ is $$9 8 7 6 3 0$$
    To achieve this arrange the given numbers in descending order.
  • Question 5
    1 / -0
    In numbers from $$1 \ to\  100$$ the digit "$$0$$" appears ____________times.
    Solution
    $$10, 20, 30, 40, 50, 60, 70, 80, 90, 100$$
    Thus the digit $$0$$ appears $$11$$ times.
  • Question 6
    1 / -0
    In the series given below. count the number of 9s, each of which Is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 9s are there?
    1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8
    Solution
    There are 3 such 9s that are not immediately preceded by 5 and immediately followed by 2 or 3 in the given series. They are marked in bold.
    1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8
    Answer is Option B
  • Question 7
    1 / -0
    Answer the question based on the set of numbers given.
    738 429 156 273 894
    What will be the difference between the first digit of the highest number as well as of the lowest number after the positions of the first two digits in each number are reversed?
    Solution
    In the given series 738 429 156 273 894 when the first two digits are reversed for every number, the number becomes 378 249 516 723 984. The highest and the lowest number of this series are 984 and 249 respectively.
    The difference between the first digits of these two numbers are $$9-2=7$$
    Answer is Option $$D$$
  • Question 8
    1 / -0
    How many combinations of two-digit numbers having 8 can be made from the following numbers?
    8, 5, 2, 1, 7, 6
    Solution
    The possible two-digit number are
    88, 85, 82, 81, 87, 86, 58, 28, 18, 78, 68
    These are 11 in number
  • Question 9
    1 / -0
    CE, GI, KM, OQ, ....
    Solution
    The letters of each term are alternate Also the last letter of each term and the first letter of the next term are alternate
  • Question 10
    1 / -0
    Which letter will be the fifth from the right if the first and second, the third and fourth and so on are interchanged among each other in the word "COMPANIONATE"?
    Solution
    When we interchange the first and the second, third and the fourth, and so on letters in the word COMPANIONATE, the new word becomes OCPMNAOIANET.
    Therefore, 5th letter from right is I
    Answer is Option B
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