Previous Year Questions
1 paper · 65 questions — organised by subject with solutions and explanations.
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For a random variable, X, let be the sample average. The sample size is n. The mean and the standard deviation of X are μ and σ, respectively. The standard deviation of is
is equal to________.
At x = 0, the function (- ∞ 0) is
The function is singular at
The eigenvalues of the matrix are
The number of solutions of the simultaneous algebraic equations y = 3x + 3 and y = 3x + 5 is
The range of values of k for which the function f(x) = (k 2 - 4)x 2 + 6x 3 + 8x 4 has a local maxima at point x = 0 is
For the two functions f (x, y) = x 3 – 3xy 2 and g(x,y) = 3x 2 y – y 3 . Which one of the following options is correct?
A normal random variable X has the following probability density function , -∞ < x < ∞. Then
To solve the equation 2 sin x = x by Newton-Raphson method, the initial guess was chosen to be x = 2.0. Consider x in radian only. The value of x (in radian) obtained after one iteration will be close
A fair coin is tossed N times. The probability that head does not turn up in any of the tosses is
Two finance companies P and Q, declared fixed annual rates of interest on the amounts invested with them. The rates of interest offered by these companies may differ from year to year. Year-wise annua
Choose the most appropriate set of words from the options given below to complete the following sentence . _________ _______ is a will, _______ is a way.
(x % of y) + (y % of x) is equivalent to.
The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.
Today, we consider Ashoka as a great ruler because of the copious evidence he left behind in the form of stone carved edicts. Historians tend to correlate greatness of a king at his time with the avai
He turned a deaf ear to my request. What does the underlined phrasal verb mean?
Fact 1: Humans are mammals. Fact 2: Some humans are engineers. Fact 3: Engineers build houses. If the above statements are facts, which of the following can be logically inferred? I. All mammals build
A square pyramid has a base perimeter x, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?
If I were you, I __________ that laptop. It’s much too expensive.
Ananth takes 6 hours and Bharath takes 4 hours to read a book. Both started reading copies of the book at the same time. After how many hours is the number of pages remaining to be read by Ananth, twi
A 300 mm long copper wire of uniform cross-section is pulled in tension so that a maximum tensile stress of 270 MPa is developed within the wire. The entire deformation of the wire remains linearly el
Consider a circular cam with a flat face follower as shown in the figure below. The cam is rotated in the plane of the paper about point P lying 5 mm away from its centre. The radius of the cam is 20m
An ideal gas of mass m is contained in a rigid tank of volume V at a pressure p. During a reversible process its pressure reduces to . Following statements are made regarding the process. (P) Heat is
A 2 m × 2 m square opening in a vertical wall is covered with a metallic plate of the same dimensions as shown in the figure below. Consider the acceleration due to gravity to be 10.0 m/s 2 . Th
Which one of the following is a natural polymer?
A vertical cylindrical tank of 1 m diameter is filled with water up to a height of 5 m from its bottom. Top surface of water is exposed to atmosphere. A hole of 5 mm area forms at the bottom of the ta
The minimum thickness of the plate of the vessel of internal diameter 2 m is designed to withstand an internal pressure of 500 kPa (gauge). If the allowable normal stress at any point within the cylin
A helical gear with involute tooth profile has been machined with a disc-type form gear milling cutter. The helical gear has 30 teeth and a helix angle of 30°. The module of the gear milling cutte
A beam is subjected to an inclined concentrated load as shown in the figure below. Neglect the weight of the beam. The correct Free Body Diagram of the beam is
The elastic modulus of a rigid perfectly plastic solid is
An engine, connected with a flywheel, is designed to operate at an average angular speed of 800 rpm. During operation of the engine, the maximum change in kinetic energy in a cycle is found to be 6240
The figure below shows an air standard Diesel cycle in the p-V diagram. The cut-off ratio is given by:
A bar of rectangular cross-sectional area of 50 mm 2 is pulled from both sides by equal forces of 100 N as shown in the figure below. The shear stress (in MPa) along the plane making an angle 45°
A 1m × 10mm × 10mm cantilever beam is subjected to a uniformly distributed load per unit length of 100 N/m as shown in the figure below. The normal stress (in MPa) due to bending at point
A long slender metallic rod of length L is used as a fin. As shown in the figure below, the left end of the fin is kept at a constant temperature t b . The fin loses heat by convection to the atmosphe
In a fully developed turbulent flow through a circular pipe, a head loss of h 1 is observed. The diameter of the pipe is increased by 10% for the same flow rate and a head loss of h 2 is noted. Assume
Consider the following statements and choose the correct one: (P) Hardness is the resistance of a material to indentation. (Q) Elastic modulus is a measure of ductility. (R) Deflection depends on stif
ST and NT denote the standard time and the normal time, respectively, to complete a job. Allowance = LL × ST, where 0 < LL < 1. Which one of the following relationships is correct?
Five jobs need to be processed on a single machine. All the jobs are available for processing at time t = 0. Their respective processing times are given below. Jobs I II III IV V Processing times (in
For a process, the quality loss coefficient is 5. The target value on the dimension to be attained through the process is 50 mm. If the maximum loss permissible (in monetary terms) is INR 80, the maxi
The facility layout technique that uses relationship (REL) chart is
The throughput rate of a production system is 30 units per hour. The average flow time is 20 minutes & the cycle time is 3 minutes. The average inventory (in units) in system is_________?
Consider a network with nodes 1, 2, 3, 4, 5 and 6. The nodes are connected with directed arcs as shown in the table below. The respective costs (in INR) incurred while traversing the directed arcs are
Consider the following statements. (P) Computer aided process planning (CAPP) takes input from material requirement plan (MRP). (Q) Production flow analysis helps in work cell formation. (R) Group tec
Transportation costs (in INR/unit) from factories to respective markets are given in the table below. The market requirements and factory capacities are also given. Using the North-West Corner method,
A job consists of two work elements, P and Q. Completion time (in minutes) of each work element was measured. A pilot study involved collecting a sample of 40 observations. The results of this pilot s
Consider a system with 10 identical components connected in series. The time to failure of each component is exponentially distributed with a failure rate of 0.10 per 500 days. The reliability of the
In a given year, a restaurant earned INR 38,500 in revenues. In that year, total expenses incurred were INR 30,000 and the depreciation amount was INR 3,200. At 40% tax rate, the net cash flow (in INR
The ratio of press force required to punch a square hole of 30 mm side in a 1 mm thick aluminium sheet to that needed to punch a square hole of 60 mm side in a 2 mm thick aluminium sheet is________.
The roughness profile of a surface is depicted below. The surface roughness parameter Ra (in μm) is _______.
A quality control engineer has collected 5 samples, each of size 30. The numbers of defective items in the samples are given in the table below. Sample number I II III IV V Number of defective items 3
The limits of a shaft designated as 100h5 are 100.000 mm and 100.014 mm. Similarly, the limits of a shaft designated as 100h8 are 100.000 mm and 100.055 mm. If a shaft is designated as 100h6, the fund
In abrasive water jet machining, the velocity of water at the exit of the orifice, before mixing with abrasives, is 800 m/s. The mass flow rate of water is 3.4 kg/min. The abrasives are added to the w
Two flat steel sheets, each of 2.5 mm thickness, are being resistance spot welded using a current of 6000 A and weld time of 0.2 s. The contact resistance at the interface between the two sheets is 20
A single point right handed turning tool is used for straight turning. The feed is 0.25 mm/rev and the uncut chip thickness is found to be 0.25 mm. The inclination angle of the main cutting edge is 10
In a single-pass rolling operation, a 200 mm wide metallic strip is rolled from a thickness 10 mm to a thickness 6 mm. The roll radius is 100 mm and it rotates at 200 rpm. The roll-strip contact lengt
In linear gas tungsten arc welding of two plates of the same material, the peak temperature T (in K) is given as , where q is the heat input per unit length (in J/m) of weld, α is the thermal di
A single axis CNC table is driven by a DC servo motor that is directly coupled to a lead screw of 5 mm pitch. The circular encoder attached to the lead screw generates 1000 voltage pulses per revoluti
A cylindrical bar of 100 mm diameter is orthogonally straight turned with cutting velocity, feed and depth of cut of 120 m/min, 0.25 mm/rev and 4 mm, respectively. The specific cutting energy of the w
Consider the following statements. (P) Electrolyte is used in Electro-chemical machining. (Q) Electrolyte is used in Electrical discharge machining. (R) Abrasive-slurry is used in Ultrasonic machining
Two cast iron blocks P and Q, each of 500 mm length, have the same cross-sectional area. Block P has rectangular cross-section of 100 mm × 200 mm. Block Q is of square cross-section. Both P and
A 60 mm wide block of low carbon steel is face milled at a cutting speed of 120 m/min, feed of 0.1 mm/tooth and axial depth of cut of 4 mm. A schematic representation of the face milling process is sh
Two solid cylinders of equal diameter have different heights. They are compressed plastically by a pair of rigid dies to create some percentage of reduction in their respectively heights. Consider tha
In powder metallurgy, sintering of the component