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Mathematical Ability Test-3

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Mathematical Ability Test-3
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  • Question 1
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    Solution

     

  • Question 2
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    In a class of 135 students, the numbers of boys is twice that of girls. One-sixth of the boys and one-third of the girls failed in the final examination. Find the percentage of students who passed the examination.

    Solution

    Let the number of girls be x.

    ∴ Number of boys = 2x

    Total number of students = x + 2x = 3x 

    ⇒ 135 = 3x

     

  • Question 3
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    Solution

     

  • Question 4
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    The angles of elevations of the top of the tower from two points in the same straight line and at a distance of 9 m and 16 m from the base of the tower are complementary. The height of the tower is:

    Solution

     

  • Question 5
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    If ABCD is a square and A, B, C and D are centers of circles and all circles have a radius 2 cm. then find the area of the circle whose center is O.

    Solution

     

  • Question 6
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    The angle of depression of a car, standing on the ground, from the top of a 75m tower, is 30. The distance of the car from the base of the tower (in metres) is:

    Solution

    Let AB be a tower.

    Given, The length of tower (AB) = 75m

    From A, the angle of depression of a car C on the ground is 30°.

     

  • Question 7
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    If the focus of a parabola is (−8,−2) and the directrix is y = 2x − 9, then the equation of the parabola is:

    Solution

    If S = (x1,y1) is the focus of parabola and P(x,y) is any point on parabola and directrix is given as ax + by + c = 0 then equation of parabola is:

    SP = Distance of "p" from directrix.

    For P(x,y) and line ax + by + c = 0 the distance is:

     

  • Question 8
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    Pipe A can fill the tank in 15 min and B can fill the tank in 45 min then in how many minutes both can fill 50% of the tank.

    Solution

    Given:

    Pipe A can fill tank =15 min

    Pipe B can fill tank =45 min

     

  • Question 9
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    Solution

     

  • Question 10
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    What is the value of cos 46° cos 47° cos 48° cos 49° cos 50° …. cos 135°

    Solution

    Given: cos 46° cos 47° cos 48° cos 49° cos 50° …. cos 135°

    As we know that, cos 90° = 0.

    ⇒ cos 46° cos 47° cos 48° cos 49° cos 50° …. cos 135°= cos 46° cos 47° cos 48° cos 49° cos 50° … cos 90°… cos 135° = 0.

     

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