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Textile Engineering Gate 2024 Questions with Answer

Ques 14 GATE 2024

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person.

The typical energy density (kcal/g) of these macronutrients is given in the table.
The total fat (all three types), in grams, this person consumes is _______.

A

44.4

B

77.8

C

100

D

3,600


(b) is the correct answer.

Ques 15 GATE 2024

A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is _______.

A

18

B

24

C

20

D

21


(c) is the correct answer.

Ques 16 GATE 2024

The least number of squares to be added in the figure to make AB a line of symmetry is

A

6

B

4

C

5

D

7


(b) is the correct answer.

Ques 17 GATE 2024

The approximate value of the integral
∫23 dx / x
using Simpson's rule with h = 0.5 is _______.

A

0.12

B

0.19

C

0.41

D

0.58


(c) is the correct answer.

Ques 18 GATE 2024

The differential equation
dy/dx = M(x, y) / N(x, y)
is exact if _______.

A

∂M / ∂y = ∂N / ∂x

B

∂M / ∂x = ∂N / ∂y

C

∂M / ∂y + ∂N / ∂x = 0

D

(∂M / ∂y) × (∂N / ∂x) = 0


(a) is the correct answer.

Ques 19 GATE 2024

The value of the integral
∫0∞ dx / (ex + e-x)
is _______.

A

0

B

π / 4

C

π / 2

D

π


(b) is the correct answer.

Ques 20 GATE 2024

If g(x) is a continuous function such that ∫ab g(x)dx = β then the correct statement(s), amongst the following, is/are _______.

A

∫a+1b+1 g(x - 1)dx = β

B

∫(1-a)/2(1-b)/2 2 g(1 - 2x)dx = β

C

∫0b-a g(x + a)dx = β

D

∫0a-b g(a - x)dx = β


(a,b,c) is the correct answer.

Ques 21 GATE 2024

A continuous random variable X has the following probability density function

If mean of X is 0.64, then the value of k (rounded off to 2 decimal places) is _______.


(3.75) is the correct answer.

Ques 22 GATE 2024

The three eigenvalues of the matrix

are λ₁ = 5 and λ₂ = λ₃ = -3. The value of x is _______.

A

-2

B

0

C

2

D

4


(a) is the correct answer.

Ques 23 GATE 2024

A scientist wants to find the root of the equation 2x³ + x² - 1 = 0 lying in (0, 1). He applies Secant method only once by taking two initial guesses 0.5 and 0.7. The value of the root is approximately _______.

A

0.55

B

0.60

C

0.65

D

0.75


(c) is the correct answer.

Ques 24 GATE 2024

Consider the following function

If f(x) is continuous at x = 1, then the value of k (correct up to 2 decimal places) is _______.


(0.24) is the correct answer.

Ques 25 GATE 2024

A textile company decides to find the coefficient of correlation (r) between fibre quality (X) and yarn quality (Y). The company randomly selects 10 samples and observes the following: ΣX = 50, ΣY = 40, ΣX² = 260, ΣY² = 228, ΣXY = 222 and r(X, Y) = 0.84. If the correct pairs (X = 4, Y = 11) and (X = 6, Y = 9) are taken wrongly as (X = 6, Y = 15) and (X = 4, Y = 5), respectively, then the correct value of r(X, Y) (rounded off to 2 decimal places) is _______.


(0.97) is the correct answer.

Ques 26 GATE 2024

One kg bone-dry cotton fabric is padded with water to obtain 80% wet pick up. The temperature of the wet fabric after padding is 30oC. Assume the specific heat of water to be 1 cal/(g⋅oC); the latent heat of evaporation of water to be 540 cal/g and the specific heat of cotton to be 0.3 cal/(g⋅oC). The energy (kcal) required to dry the fabric completely (in integer) is _______.


(462) is the correct answer.

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