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GATE ME 2019: Topper's Mini Mock Quiz-1

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Question 1

A wire would enclose an area of

if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

Question 2

A book shelf has 27 books – 9 books each written by 3 eminent authors. If Raj selects any 2 books without looking at their author’s name, what is the probability that he picks up books written by different authors?

Question 3

The determinant of a 2x2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___.

Question 4

In an experiment with 15 observations on x, the following results we available

One observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is _____.

Question 5

The Laplace transform of te^t is

Question 6

For iron carbon diagram, the Gibbs phase rule is given by

Question 7

Two blocks are on the frictionless surface as shown in fig. having mass 1 kg and 2 kg. The 1 kg block moves with a speed 5 m/s towards other block kept at rest. The spring is attached to 2 kg block and has a spring constant 60 N/m. the maximum compression of spring (in m) is

Question 8

Oil of viscosity 0.085 Ns/m² is filled between two 120 cm long concentric cylinders having inner and outer radius as 5cm and 6cm. If the inner cylinder is fixed and outer cylinder I rotates at 900 rpm. If the inner cylinder is also rotates at 500 rpm in the same direction as that of outer cylinder. Then percentage reduction in shear stress is

Question 9

The net heat radiation from surface of two parallel plates (emissivity of 0.6) having temperature of T1 and T2 is to be reduced by 98%. Estimate the number of screens to be placed between the parallel plates to achieve the reduction in heat transfer assuming the emissivity of shield to be 0.03

Question 10

Match list – I and List – II and select the correct answer using the codes given below

Question 11

Right triangle PQR is to be constructed in the xy – plane so that the right angle is at P and line PR is parallel to the axis. The x and y coordinates of P, Q, and R are to be integers that satisfy the inequalities: –4 ≤ x ≤ 5 and 6 ≤ y ≤ 16. How many different triangles could be constructed with these properties?

Question 12

In the following question choose the word opposite in meaning to the given word.
EMACIATED

Question 13

the value of is

Question 14

The Laplace transform of the function sin² 2t is:

Question 15

From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if the first card is NOT replaced?

Question 16

A point mass is shot vertically up from ground level with a velocity of 4 m/s at time,

It loses 20% of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is

and that air resistance is negligible, the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of

Question 17

Consider two hydraulic turbines having identical specific speed and effective head at the inlet. If the speed ratio (N₁/N₂) of the two turbines is 2, then the respective power ratio (P₁/P₂) is ________

Question 18

Two fluids, A and B exchange heat in a counter flow heat exchanger. Fluid A enters at 420⁰C and has mass flow rate of 2 kg/s. fluid B enters at 20⁰C and also has mass flow rate of 2 kg/s, effectiveness of heat exchanger is 75%. The exit temperature (⁰C) of fluid B is (specific heat of fluid A is 1 kJ/kg-K and that of fluid B is 4 kJ/kg-K)

Question 19

The demand for an item is 900 units per month and the lead time is 10 days. In the past two month, the maximum demand observed is 50 units per day. For a re-ordering system based on inventory level, the re-order level (in units) is

Question 20

A rolling mill is operated by a gear mounted to motor having power 3 kW and running at a speed of 200 rad/s, if the diameter of the gear is 5 cm and the pressure angle of the gear is 20

. Find the normal force acted on the gear in N.

Question 21

A grinding operation require 5 kW of power to be carried by the motor. The material removal rate is given as 23.65 mm³/sec and the grinding ratio is given as 12. Find the wear rate (in mm³ /sec) of the grinding grains of the grinding wheel.

Question 22

The flexural rigidity (EI) of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load P and bending moment PL/2 are applied at the free end of the beam then the value of the slope at the free end is __________.

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Question 23

A toy car is made by a group of students for analyzing the effect of various forces in running a car. The car works with help of a slider crank mechanism fitted inside the toy car. The crank moves with a constant angular velocity of 10 rad/s and the crank radius is 60 mm. If the mass of the slider is 0.2 kg due to which wheel tends to leave the surface then find the hammer blow acting on the car.

Question 24

Moist air is treated as an ideal gas mixture of water vapor and dry air (molecular weight of air = 28.84 and molecular weight of water = 18). At a location, the total pressure is 100 kPa, the temperature is 30 °C and the relative humidity is 55%. Given that the saturation pressure of water at 30 °C is 4246 Pa, the mass of water vapor per kg of dry air is _____________ grams

Question 25

One kg of air (R = 287 J/kg-K) undergoes an irreversible process between equilibrium state 1 (20 °C , 0.9 m³) and equilibrium state 2 (20 °C, 0.6 m³) The change in entropy S₂ - S₁ (in J/kg-K) is_____?

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