Please wait...

NDA I 2025 Mathematics Test - 2
Result
NDA I 2025 Mathematics Test - 2
  • /

    Score
  • -

    Rank
Time Taken: -
  • Question 1/10
    2.5 / -0.83

    The distance between the foci of a hyperbola is 16 and its eccentricity is √2. Its equation is

    Solutions

    The distance between the foci of a hyperbola is 16 and its eccentricity e = √2.

    We know that The distance between the foci of a hyperbola = 2ae 

    ⇒ 2ae = 16

  • Question 2/10
    2.5 / -0.83

    Solutions

    ⇒ α ∈  (–3, 0)

    Hence option (2) is correct.

  • Question 3/10
    2.5 / -0.83

    Solutions

    Calculation:

    Enclosed Area

  • Question 4/10
    2.5 / -0.83

    Solutions

    Concept:

    If the function f(x) has an extremum at x = a then f'(a) = 0

    Calculations:

  • Question 5/10
    2.5 / -0.83

    Solutions

    xp + y (y(yp + z) + z(xp + y)) - (yp + z) (x(yp + z) - y(xp + y)) + 0(xz - y2) = 0

    xp + y (y2p + yz - xzp - yz) - (yp + z) (xyp + xz - xyp - y2) = 0

    (xp + y) (y2 p - xzp) - (yp + z) (xz - y2) = 0

    (xp + y) p(y2 - xz) + (yp + z) (y2 - xz) = 0

    (y2 - xz) ((xp + y)p + (yp + z)) = 0

    (y2 - xz) (xp2 + yp + yp + z) = 0

    (y2 = xz) (xp2 + 2yp + z) = 0

    The determinant will be 0 if (y2 - xz) will be 0 which is geometric mean.

    Hence x, y and z are in G.P.

  • Question 6/10
    2.5 / -0.83

    Solutions

    CONCEPT:

    • Fundamental Theorem of Calculus (Newton-Leibniz formula)

  • Question 7/10
    2.5 / -0.83

    The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y increasing at the rate of 4 cm/minute. If given that x = 0.06 meter and y = 0.02 meter than find the rate of change of area of the Rectangle?

    Solutions

    Concept:

    • Area of rectangle A = x × y where, x = length of side in meter and y = width of rectangle in meter.
    • Rate of change always defines as a differentiation of Quantity with respect to time.
    • Decreasing rate always represent by negative sign and increasing rate by positive sign.

    Calculation:

    Given that,

  • Question 8/10
    2.5 / -0.83

    Let f(x + y) = f(x) f(y) and f(2) = 4 for all x, y ϵ R, where f(x) is continuous function. What is f' (2) equal to?

    Solutions

  • Question 9/10
    2.5 / -0.83

    An unbiased coin is tossed 3 times, if the third toss gets head what is the probability of getting at least one more head?

    Solutions

  • Question 10/10
    2.5 / -0.83

    Consider the following in respect of the function f(x) = |x - 3|:

    1. f(x) is continuous at x = 3

    2. f(x) is differentiable at x = 0.

    Which of the above statements is / are correct?

    Solutions

    LHD = RHD, so f(x) is differentiable at x = 0.

    Hence, option (3) is correct.

User Profile
-

Correct (-)

Wrong (-)

Skipped (-)


  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
Get latest Exam Updates
& Study Material Alerts!
No, Thanks
Click on Allow to receive notifications
×
Open Now