Test: Differential Calculus - Civil Engineering (CE) MCQ

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Match the List–I with List–II.

If an error of 1% is made in measuring the major and minor axes of an ellipse, then the percentage error in the area is approximately equal to

Consider the Assertion (A) and Reason (R) given below:

Reason (R): Given function u is homogeneous of degree 2 in x and y.
Of these statements

If u = x log xy, where x³ + y³ + 3xy = 1, then du/dx is equal to

f(x) = x²e^-x is increasing in the interval

The minimum distance from the point (4, 2) to the parabola y² =​ 8x is

The co-ordinates of the point on the parabola y = x² + 7x + 2 which is closest to the straight line y = 3x - 3, are

The shortest distance of the point (0, c), where 0 ≤ c ≤ 5, from the parabola y = x² is 

The set of equations

has infinite solutions, if a=

The maximum value of ( 1/x)^x is 

The minimum value of 3x+5y such that:

is ___________.

The condition for which the eigenvalues of the matrix

are positive, is

The maximum value of f ( x) = (1 + cos x) sin x is

The solution to the system of equations

The greatest value of

on the interval [0, π/2] is 

For what value of a, if any, will the following system of equations in x, y and z have a solution
2x + 3y = 4
x + y + z = 4
x + 2y - z = a