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CDS II 2021 Mathematics Test - 14
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CDS II 2021 Mathematics Test - 14
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  • Question 1/10
    1 / -0.33

    The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rates of interest is

    Solutions

    Here, the principal and time are samebut rates are different .Hence, we get difference in simple interest due to difference in rates.

    Difference in 3 years = 13.50 Rs.

    Difference in 1 year = 13.50/3 = 4.50 Rs.

     

  • Question 2/10
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    Assuming that profit of a shopkeeper in a particular commodity is a linear expression of transportation charge(t) and the quantity of commodity (q). He earns a profit of Rs. 10,000 by selling 20 units at the transport charge of Rs. 400. He also earns a profit of Rs. 12,000 by selling 25 units at the transport charge of Rs. 600. What is the linear expression in t and q?

    Solutions

    Let the linear expression of transportation charge (t) and the quantity of commodity(q) is as follows-

    Earned profit=xt+yq

    Then as per the question

    10000=400t + 20q

    500=20t+q

    12000=600t+25q

    480=24t+q

    On solving the two equation we get t=-5 and q=600

    Required linear expression=600q-5t

     

  • Question 3/10
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    A and B together can complete a work in 16 days. A alone can complete the same work in 24 days. A and B started work and A left after 4 days. In how many days will the remaining work be completed by B?

    Solutions

    A and B together can complete a work in 16 days.

    A alone can complete the same work in 24 days.

    Let Total work = LCM (16,24) = 48 units

    Efficiency of A+B = 48/16 = 3 unit/day

    Efficiency of A = 48/24 = 2 unit/day

    Efficiency of B = 3 - 2 = 1 unit/day

    A and B started work and A left after 4 days.

    Work finished by A & B together in 4 days = 3 × 4 = 12 units

    Remaining work = 48 units - 12 units = 36 units

    Number of days required to complete the remaining work by B = 36/1 = 36 days

     

  • Question 4/10
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    If  then which one of the following is correct?

    Solutions

     

  • Question 5/10
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    Solutions

    I is correct

    From II: sec233-cot257=cosec237-tan253

    1/cos233 – cos257/sin257 = 1/sin237 – sin253/cos253

    1/cos233 - cos257/cos233 = 1/sin237 – sin253/sin237

    (1-cos257)/cos233 = (1-sin253)/sin237

    (1-sin233)/cos233 = (1-cos253)/sin237

    1=1 , Hence both the statements are correct

     

  • Question 6/10
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    A square is inscribed in a circle of diameter 2a and another square is circumscribing the circle. The difference between the areas of the outer and inner squares is

    Solutions

     

  • Question 7/10
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    Find the value x for which (8x+4), (6x-2) and (2x+7) are in AP.

    Solutions

    (8x+4), (6x-2) and (2x+7)are in AP.

    If the numbers a, b and c are in AP the 2b = a + c

    Then,

    2(6x – 2) = 8x + 4 + 2x + 7

    2x = 15

    X = 15/2

     

  • Question 8/10
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    Solutions

     

  • Question 9/10
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    If n is any natural number, then 52n - 1 is always divisible by how many natural numbers?

    Solutions

    we can observe that we get always factor of 24 and factors of 24 are 1,2,3,4,6,8,12,24.

    So, number of natural numbers that divides 52n - 1 are 8.

     

  • Question 10/10
    1 / -0.33

    Solutions

     

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