ME : Gate 2019 Questions Papers & Answer key

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Ques. The candidates had to find the shape factor F12 for sphere within a sphere.

Ques. There was a question in which xyz= 192 and z = 4 and p is the average of x and y. The candidates had to find the minimum possible value of p.

Ques. If P fills a tank in 6 hours, Q in 9 hours and R can empty the tank in 12 hours. First P and R are opened for 4 hours and then P is closed and Q is opened after 6 hours after R. Calculate the time required to fill the tank?

Ques. Two immiscible incompressible fluids having the same densities but different viscosities are contained between two infinite parallel plates 2m apart.

Ans. 1 m/sec

Ques. A worker noticed that hour hand on the factory clock had moved 225° during her stay in work. How long does she stay in the factory?

(A) 3.75 hours
(B) 4 hours and 15 minutes
(C) 7.5 hours
(D) 8.5 hours

Ans. The correct option is (C)

Ques. A cube of side 100mm is placed at the bottom of a container. The density of cube material is800bg/m^3. A liquid of density 1000bg/m^3 is poured into the container. The minimum height to which the liquid should be poured into the container to just lift the block from the bottom?

Ans. 80 mm

Ques. The position vector (OD) ⃗ of P(20, 10) is rotated anticlockwise in XY plane by an angle of 30° such that the point P occurs position Q as shown. The coordinates of Q are

(A) (22.32, 8.26)
(B) (12.32, 18.66)
(C) (13.4, 22.32)
(D) (18.66, 12.32)

Ans. The correct option is (B)

Ques. A Parabolic x=y^2 with 0≤x≤1 as shown in figure. The volume obtained by solid of rotating the shaded area of 360° around the x – axis

(A) π
(B) π/4
(C) π/2
(D) 2π

Ans. The correct option is (D)

Ques. If the sum of two numbers is 26 and product is 165. The difference between the number is

(A) 4
(B) 6
(C) 3
(D) 5

Ans. The correct option is (A)

Ques. If dy/dx+7x^2 y=0 & y(0)=3/7, then find y(1)?

(A) 3/7 e^(-3/7)
(B) 7/3 e^(-7/3)
(C) 7/3 e^(-3/7)
(D) 3/7 e^(-7/3)

Ans. The correct option is (D)

Ques.  Evaluation of ∫_2^4 [x^3 dx] using a 2 –equal segment trapezoidal rule gives __________

Ans. 63

Ques. For the matrix 110 011 000. How many distinct Eigen values are there?

(A) 0
(B) 3
(C) 1
(D) 2

Ans. The correct option is (C)

Ques. The length of large stocks of Titanium rods follow normal distribution with μ=440 mm and standard deviation of 1 mm. What is the percentage of rods whose length lie between 438 mm and 441 mm?

(A) 81.85%
(B) 68.4%
(C) 86.64%
(D) 99.75%

Ans. The correct option is (A)

Ques. For the set of equations x+y+z=1 ax-ay+3z=5 5x-3y+az=6 has infinite solution if a=_________

(A) 4
(B) 3
(C) -3
(D) -4

Ans. The correct option is (A)

Ques. A harmonic function is analytic if it satisfies Laplace equation. If u(x,y)=2x^2-2y^2+4xy is a harmonic function, then its conjugate harmonic function v(x, y) is

(A) 4y^2-4xy+C
(B) 4xy-2x^2+2y^2+C
(C)-4xy+2y^2-2x^2+C
(D) 2x^2-2y^2+xy+Cr

Ans. The correct option is (B)