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JEE Advanced Mathematics Test 2
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JEE Advanced Mathematics Test 2

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  • Question 1/10
    4 / -1

    If a, b, c are in G.P. then-

    Solutions

     

  • Question 2/10
    4 / -1

    The coefficient of xk (0 ≤ k ≤ n) in the expansion of E = 1+ (1 + x) + (1 + x)2 +......... + (1+x)n is-

    Solutions

  • Question 3/10
    4 / -1

    Sixteen men compete with one another in running, swimming and riding. How many prize lists could be made if there were altogether 6 prizes of different values, one for running, 2 for swimming and 3 for riding ?

    Solutions

    Since any person may get one or more prizes in different categories 

    No. of ways of getting one prize for running = 16 

    No. of ways of getting 2 prizes for swimming

    = 16 × 15 (Since one person cannot get similar kind of prizes at a time) 

    No. of ways of getting 3 prizes for riding 

    = 16 × 15 × 14 

    ∴ Total no. of ways (using multiplication rule) 

    = 16 × 16 × 15 × 16 × 15 × 14 

    = (16)3 × (15)2 × 14 = 12902400 Ans.

     

  • Question 4/10
    4 / -1

    The sum of n terms of an A.P. is an (n – 1). The sum of the squares of these terms is-

    Solutions

     

  • Question 5/10
    4 / -1

    The equations of tangents to the ellipse 9x2 + 16y2 = 144 which pass through the point (2, 3) is -

    Solutions

     

  • Question 6/10
    4 / -1

    The equation to the circle which passes through the points (1, – 2) and (4, –3) and which has its centre on the straight line 3x + 4y = 7 is –

    Solutions

     

  • Question 7/10
    4 / -1

    The value of the expression

    1. (2 –ω) . (2 – ω2) + 2 . (3 – ω) (3 – ω2) + ....... + (n – 1) (n – ω) (n – ω2), where ωis an imaginary cube root of unity is-

    Solutions

     

  • Question 8/10
    4 / -1

    Let f’(sin x) < 0 & f ‘‘ (sin x) > 0, ∀x ∈ (0, π/2) and g(x) = f(sin x) + f(cos x), then g(x) is decreasing in-

    Solutions

    x∈(0, π/2)

    g'(x) = f ' (sin x) cos x – f ' (cos x) sin x 

    ∴f ' (sin x) < 0 

    ∴f ' (cos x) < 0 

    f’’ (sin x) > 0 

    ∴f’’(cos x) > 0 

    g”= f”(sin x) cos2x – f ' (sin x) sin x – f ' (cos x) cos x + f”(cos x) sin2x 

    g”(x) >0

    For critical point of g(x) 

    g'(x) = 0 

    ⇒x = π/4 

    So, x = π/4 is point of minima 

    g(x) decreases in (0, π/4 )

    So, it decreases in (- π/2 , π/2 )

     

  • Question 9/10
    4 / -1

    Solutions

     

  • Question 10/10
    4 / -1

    If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is -

    Solutions

     

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