Test: Differential Calculus

# Test: Differential Calculus

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## 20 Questions MCQ Test GATE Electrical Engineering (EE) 2023 Mock Test Series | Test: Differential Calculus

Test: Differential Calculus for Electronics and Communication Engineering (ECE) 2023 is part of GATE Electrical Engineering (EE) 2023 Mock Test Series preparation. The Test: Differential Calculus questions and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus.The Test: Differential Calculus MCQs are made for Electronics and Communication Engineering (ECE) 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Differential Calculus below.
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Test: Differential Calculus - Question 1

### If u = xm yn  then

Detailed Solution for Test: Differential Calculus - Question 1

Given that u = xyn

Taking logarithm of both sides, we get log u = m log x + n log y Differentiating with respect to x,we get Test: Differential Calculus - Question 2

### ​ ​ ​  to

Detailed Solution for Test: Differential Calculus - Question 2  Test: Differential Calculus - Question 3

### ​ ​ ​

Detailed Solution for Test: Differential Calculus - Question 3  Test: Differential Calculus - Question 4 Detailed Solution for Test: Differential Calculus - Question 4 f is a homogeneous function of degree one Test: Differential Calculus - Question 5 Detailed Solution for Test: Differential Calculus - Question 5 It is a homogeneous function of degree n Test: Differential Calculus - Question 6

Match the List–I with List–II.    Detailed Solution for Test: Differential Calculus - Question 6 It is a homogeneous function of
degree 2.  Test: Differential Calculus - Question 7

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

Detailed Solution for Test: Differential Calculus - Question 7

Let 2 a and 2 b be the major and minor axes of the ellipse Test: Differential Calculus - Question 8

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

Detailed Solution for Test: Differential Calculus - Question 8

Given that  u = xyf(y/x) Since it is a homogeneous function of degree 2. Test: Differential Calculus - Question 9

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

Detailed Solution for Test: Differential Calculus - Question 9

Given that u = x log xy ... (i)  Test: Differential Calculus - Question 10 Detailed Solution for Test: Differential Calculus - Question 10

The given function is homogeneous of degree 2. Test: Differential Calculus - Question 11

If a < 0, then f(x) = eax + e-ax is decreasing for

Detailed Solution for Test: Differential Calculus - Question 11  Test: Differential Calculus - Question 12

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

Detailed Solution for Test: Differential Calculus - Question 12  Test: Differential Calculus - Question 13

The least value of a for which f(x) = x2 + ax + 1 is increasing on ] 1, 2, [ is

Detailed Solution for Test: Differential Calculus - Question 13

f'(x) = (2x + a) Test: Differential Calculus - Question 14

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

Detailed Solution for Test: Differential Calculus - Question 14

Let the point closest to (4, 2) be (2t2,4) Test: Differential Calculus - Question 15

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

Detailed Solution for Test: Differential Calculus - Question 15

Let the required point be P(x, y). Then, perpendicular distance of P(x, y) from y -  3x - 3 = 0 is Test: Differential Calculus - Question 16

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

Detailed Solution for Test: Differential Calculus - Question 16

Let A (0,c) be the given point and P (x, y) be any point on y = x2 Test: Differential Calculus - Question 17

The maximum value of ( 1/x)x is

Detailed Solution for Test: Differential Calculus - Question 17

f (x) = (1 / x)x

f’ (x) = (1 / x)x (log (1 / x) – 1))

f’ (x) = 0

log (1 / x) – 1 = log e

1 / x = e

x = 1 / e

The maximum value of function is e1/e.

Test: Differential Calculus - Question 18 Detailed Solution for Test: Differential Calculus - Question 18  Test: Differential Calculus - Question 19

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

Detailed Solution for Test: Differential Calculus - Question 19  Test: Differential Calculus - Question 20

The greatest value of on the interval [0, π/2] is

Detailed Solution for Test: Differential Calculus - Question 20  ## GATE Electrical Engineering (EE) 2023 Mock Test Series

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