Mechanical Engineering Gate 2022 Set-2 Questions with Answer

Ques 40 GATE 2022 SET-2

Given If a and b are positive integers, the value of is ________.

Ques 41 GATE 2022 SET-2

A polynomial φ(s) = a_nsⁿ + a_n-1s^n-1 + ... + a₁s + a₀ of degree n > 3 with constant real coefficients a_n, a_n-1, ... a₀ has triple roots at s = -σ. Which one of the following conditions must be satisfied?

Ques 42 GATE 2022 SET-2

For the exact differential equation,

Ques 43 GATE 2022 SET-2

A square plate is supported in four different ways (configurations (P) to (S) as shown in the figure). A couple moment 𝐶 is applied on the plate. Assume all the members to be rigid and mass-less, and all joints to be frictionless. All support links of the plate are identical.

Ques 44 GATE 2022 SET-2

A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress σ_xx is ________.

Ques 45 GATE 2022 SET-2

A shaft AC rotating at a constant speed carries a thin pulley of radius 𝑟 = 0.4 m at the end C which drives a belt. A motor is coupled at the end A of the shaft such that it applies a torque 𝑀_H about the shaft axis without causing any bending moment. The shaft is mounted on narrow frictionless bearings at A and B where AB = BC = 𝐿 = 0.5 m. The taut and slack side tensions of the belt are 𝑇_H = 300 N and 𝑇_L = 100 N, respectively. The allowable shear stress for the shaft material is 80 MPa. The self-weights of the pulley and the shaft are negligible. Use the value of π available in the on-screen virtual calculator. Neglecting shock and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is _______ mm (round off to 2 decimal places).

Ques 46 GATE 2022 SET-2

The demand of a certain part is 1000 parts/year and its cost is ₹1000/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is ₹100/order and the lead time for receiving the orders is 5 days. If the holding cost is ₹20/part/year, the inventory level for placing the orders is _________ parts (round off to the nearest integer).

Ques 47 GATE 2022 SET-2

A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is ₹__________.

Ques 48 GATE 2022 SET-2

Which one of the following is an intensive property of a thermodynamic system?

Ques 49 GATE 2022 SET-2

Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume c_v is equal to 750 J∙kg^-1∙K^-1. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ___________ bar (in integer).

Ques 50 GATE 2022 SET-2

Wien’s law is stated as follows: λ_mT = C, where C is 2898 µm∙K and λ_m is the wavelength at which the emissive power of a black body is maximum for a given temperature T. The spectral hemispherical emissivity (𝜀 ) of a surface is shown in the figure below (1Å = 10^-10m). The temperature at which the total hemispherical emissivity will be highest is __________ K (round off to the nearest integer).

Ques 51 GATE 2022 SET-2

In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg. The exit of the compressor is superheated at condenser pressure with specific enthalpy equal to 300 kJ/kg. At the condenser exit, the refrigerant is throttled to the evaporator pressure. The coefficient of performance (COP) of the cycle is 3. If the specific enthalpy of the saturated liquid at evaporator pressure is 50 kJ/kg, then the dryness fraction of the refrigerant at entry to evaporator is _________.

Ques 52 GATE 2022 SET-2

Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train.
If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?