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Mathematics Test 30
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Mathematics Test 30

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  • Question 1/10
    4 / -1

    If the coefficients of rth, (r+ 1)th and (r + 2)th terms in the binomial expansion of (1 + y)m are in A.P., then m and r satisfy the equation

    Solutions

     

  • Question 2/10
    4 / -1

    Let P be the point (1, 0) and Q a point on the locus y2 = 8x. The locus of mid-point of PQ is

    Solutions

    P = (1, 0) 
    Q = (h, k) such that k2 = 8h 
    Let (α, β) be the midpoint of PQ

     

  • Question 3/10
    4 / -1

    The equation of the tangent to the curve   that is parallel to the x-axis is

    Solutions

    Since the tangent is parallel to x axis, the slope of the tangent is 0, or y' =0. Also, equation of the tangent will be of the form, y=k. Let's find the value of x first.

  • Question 4/10
    4 / -1

    If ω (≠ 1) is a cube root of unity, and (1 + ω)7 = A + Bω. Then (A, B) equals:

    Solutions

    (1 + ω)7 = A + Bω
    We know that 1 + w + w2 = 0 

    => (-ω2)7 = A + Bω 
    => -w14 = A + Bω 
    => - ω12 x ω2 = A + Bω 
    w12 = 1
    => -ω2 = A + Bω 
    1 + ω = A + Bω 
    ⇒ A = 1, B = 1. 
    Hence, option B is correct.

     

  • Question 5/10
    4 / -1

    Area of the greatest rectangle that can be inscribed in the ellipse 

    Solutions

    Area of rectangle ABCD = (2acosθ) (2bsinθ) = 2absin2θ 
    ⇒ Area of greatest rectangle is equal to 2ab, when sin2θ = 1. 

    Hence, option A is correct.

     

  • Question 6/10
    4 / -1

    Solutions

     

  • Question 7/10
    4 / -1

    Solutions

     

  • Question 8/10
    4 / -1

    The shortest distance between the line y – x = 1 and the curve x = y2 is

    Solutions

     

  • Question 9/10
    4 / -1

    A bird is sitting on the top of a vertical pole which is 20 m in height and its elevation from a point O on the ground is 45°. It flies off horizontally straight away from the point O. After one second, the elevation of the bird from point O is reduced to 30°. Calculate the speed (in m/s) of the bird.

    Solutions

     

  • Question 10/10
    4 / -1

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    Solutions

     

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