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CDS II 2021 Mathematics Test - 16
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CDS II 2021 Mathematics Test - 16
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  • Question 1/10
    1 / -0.33

    A heavy metallic cylindrical roller of length 3 m is being used in road construction. It takes eight complete rounds to roll a distance of 20 m. What area of the road it covers in one round?

    Solutions

     

  • Question 2/10
    1 / -0.33

    Solutions

     

  • Question 3/10
    1 / -0.33

    A hemispherical cup of radius 4 cm is filled to the brim with coffee. The coffee is then poured into a vertical cone of radius 8 cm and height 16 cm. the percentage of the volume of the cone that remains empty is :

    Solutions

     

  • Question 4/10
    1 / -0.33

    In how much time a sum of money will become four times at 12 % per annum simple interest?

    Solutions

    Shortcut

    Let principal= 1

    Amount=4

    So interest= amount-principal= 4-1 = 3

     

  • Question 5/10
    1 / -0.33

    The average weight of 70 students in a class is 38 .5 kg. If 15 students having average weight 55 kg leave the class and 20 students have average weight 60.4 kg join the class, then what is the average weight (in kg) of the students in the class (correct to two decimal places)?

    Solutions

    Average weight of 70 students in a class is 38.5 kg

    Sum of weight of 70 students = 70 × 38.5 = 2695 kg

    Now, 15 students having average weight 55 kg leave the class

    Hence, Total number of students = 70 – 15 = 55

    Sum of weight of 55 students = 2695 kg - (15 × 55)kg = 2695 – 825 =1870 kg

    After that, 20 students have average weight 60.4 kg join the class.

    Hence, Total number of students = 55+20 = 75

     

  • Question 6/10
    1 / -0.33

    AOB is a quadrant sector of radius r cut from a circle of center O. A semicircle of center P is drawn outside of quadrant taking AB as diameter. What is the difference between area of whole geometry and that of quadrant?

    Solutions

    The shaded region will represent the difference between the areas of whole geometry and that of sector AOBD.
    AOB is quadrant circle its mean triangle is a right angle triangle

     

  • Question 7/10
    1 / -0.33

    In a quadrilateral, the length of one of its diagonal is 50 cm and the perpendiculars drawn on this diagonal from the other two vertices measure 30 cm and 22 cm respectively. Find the area of the quadrilateral.

    Solutions

     

  • Question 8/10
    1 / -0.33

    Which of the following is a perfect square?

    Solutions

    Consider option A.

    We know that number ending with 2,3,7and 8 can never be perfect square.

    So, 336332 is not a perfect square.

    Consider option B.

    As there are exact pairs of similar prime factor.

    Hence, it is a perfect square.

    Consider option C.

    225250

    When a number ends with odd number of zeros , then it is not a perfect square.

    Consider option D

    Here, we can not form exact pairs of similar prime factors.

    ⇒ 4032 is not a perfect square.

     

  • Question 9/10
    1 / -0.33

    Find the remainder when 55552222 is divided by 7 ?

    Solutions

    Using Fermat’s little theorem,

    When ap-1 is divided by p where a is any natural number and p is any prime number and a and p must be coprime then remainder will be 1.

     

  • Question 10/10
    1 / -0.33

    The sides of a triangular field are 41 m, 40 m and 9 m. The number of rose beds that can be prepared in the field if each rose bed, on an average, needs 900 square cm space, is

    Solutions

     

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