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Mathematics Test - 7
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Mathematics Test - 7
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  • Question 1/15
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  • Question 2/15
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  • Question 3/15
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  • Question 4/15
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  • Question 5/15
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  • Question 6/15
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    If the lengths of the sides of a triangle are 3, 4, 5 units, then R (the circum-radius) is equal to

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  • Question 7/15
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    In a ΔABC, a = 13 cm, b = 12 cm and c = 5 cm. The distance of A from BC is

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  • Question 8/15
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    In ΔABC, if tan A/2 tan C/2 = 1/2, then a, b, c are in

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  • Question 9/15
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    Area of an equilateral triangle is √3 cm2. The length of each side of the triangle is

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  • Question 10/15
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    In a triangle, the lengths of the two larger sides are 10 cm and 9 cm respectively. If the angles of the triangle are in A.P, then the length of the third side (in cm) can be

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  • Question 11/15
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    The lengths of sides of a triangle are in the ratio 5 : 12 : 13 and its area is 270 cm2. The respective lengths of sides of the triangle (in cm) are

    Solutions

    Let the lengths of sides of the triangle be 5x, 12x, 13x; Obviously, the triangle is right-angled.

    Hence, area of the Δ = ½ (12x) (5x) ⇒ 30x2 = 270 ⇒ x = 3

    Hence, the lengths of sides (in cm) are 15, 36 and 39.

  • Question 12/15
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    Square the differential equation to remove the fraction,

    We get, order = degree = 2

  • Question 13/15
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    The number of arbitrary constants in the solution of a differential equation of degree 2 and order 3 is

    Solutions

    Note: The number of arbitrary constants in a solution of a differential equation of order n is equal to its order.

    Order of differential equation = Number of arbitrary constants = 3

  • Question 14/15
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    The order of a differential equation whose solution is y = a cos x + b sin x, where a and b are arbitrary constants, is

    Solutions

    The order of differential equation = number of arbitrary constants = 2

  • Question 15/15
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