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# Calculus (Part - 1) - Civil Engineering Civil Engineering (CE) Notes | EduRev

## Topic wise GATE Past Year Papers for Civil Engineering

Created by: Gate Gurus

## Civil Engineering (CE) : Calculus (Part - 1) - Civil Engineering Civil Engineering (CE) Notes | EduRev

The document Calculus (Part - 1) - Civil Engineering Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)

Question 1: What is curl of the vector field 2x2yi + 5z2j - 4yzk?    [2019 : 1 Mark, Set-ll]
(a) -14zi-2x2k
(b) 6zi + 4x2j - 2x2k
(c) - 14zi + 6yj + 2x2k
(d) 6zi - 8xyj + 2x2yk
(a)
Solution: Question 2: Euclidean norm (length) of the vector [4 -2 -6]r is    [2019 : 1 Mark, Set-ll] Solution: Euclidean norm length Question 3: The following inequality is true for all x close to 0. What is tha value of [2019 : 1 Mark, Set-ll]
(a) 1
(b) 0
(c) 1/2
(d) 2
Solution:  Question 4: Consider the functions: x = y In φ and y = φ In y. which one of the following the correct expression for [2019 : 2 Mark, Set-l]    Solution:  ......(i) Question 5: Which one of the following is NOT a correct statement?    [2019 : 2 Marks, Set-I]
(a) The function has the global minima at x = e
(b) The function has the global maxima at x = a
(c) The function x3 has neither global minima nor global maxima
(d) The function |x| has the global minima at x = 0
Solution: Let y = x1/x
log y = logx/x y maximum (or) minimum when, is maximum (or) minimum  Question 6: For a small value of h, the Taylor series expansion for f(x +h) is [2019 : 1 Mark, Set-I] Solution: Taylor series of f (x + h) at x.
f(x + h) = f(x) + (x + h - x)  Question 7: Which of the following is correct?    [2019 : 1 Mark, Set-I] Solution: Question 8: The value (up to two decimal places) of a line along C which is a straight line joining (0, 0) to (1, 1) is _____.    [2018 : 2 Marks, Set-II]
Solution: (0, 0) to (1, 1) line is y = x Question 9: The value of the integral [2018 : 2 Marks, Set-I]   (d) ∏2
Solution:  Question 10: At the point x = 0, the function f(x) = x3 has    [2018 : 1 Marks, Set-I]
(a) local maximum
(b) local minimum
(c) both local maximum and minimum
(d) neither local maximum nor local minimum
Solution: Question 11: Consider the following definite integral: The value of the integral is    [2017 : 2 Marks, Set-II]    Solution:  Question 12: The tangent to the curve represented by y = x In x is required to have 45° inclination with the x-axis. The coordinates of the tangent point would be    [2017 : 2 Marks, Set-II]
(a) (1,0)
(b) (0,1)
(c) (1,1)
(d) Solution: tan 45° = In x + 1
1 = lnx + 1
⇒ Inx = 0
∴ x = 1

Putting x = 1 in the eq. of curve, we get y = 0.

Question 13:  The divergence of the vector field V = x2i + 2y3j + z4k at x = 1, y = 2, z = 3 is _________.    [2017 : 1 Mark, Set-II]
Solution: Question 14: Let w= f(x, y), where x and yare functions of t. Then, according to the chain rule dw/dt    [2017 : 1 Mark, Set-II]    Solution: W = f(x, y)
By Chain rule, Question 15: Let x be a continuous variable defined over the interval (-∞, ∞), and The integral is equal to    [2017 : 1 Mark, Set-I]    Solution: Let  e-x = t  Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

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