List of practice Questions

Evaluate the following expression: $ \frac{\cos 75^\circ - \cos 15^\circ}{\cos 75^\circ + \cos 15^\circ} $
In a linear programming problem (L.P.P.), the corner points of the feasible region are $ (5, 0), (10, 0) $ and } $ (4, 1) $. Find the maximum value of $ Z = 2x + 3y $.
Evaluate the integral: $ \int \frac{1}{x(x^4 + 1)} \, dx $
Evaluate the following expression: $ \frac{\cos 75^\circ - \cos 15^\circ}{\cos 75^\circ + \cos 15^\circ} $
The breaking strain of a yarn is 1.5. If the stress (\( \sigma \)) and the strain (\( \epsilon \)) of the yarn are related as, \( \sigma = 1.5 \epsilon^2 \), then the work factor of the yarn (rounded off to 2 decimal places) is:
In a projectile weaving machine, the projectile travels through the shed at an average speed of 24 m/s taking \( \frac{2}{3} \) of the loom cycle. If the efficiency of the weaving machine is 90%, the weft insertion rate (m/min) is:
A needlepunching machine has two needle boards which operate sequentially at the same frequency to produce nonwoven with 200 punches/cm\(^2\). Each needle board has 40000 needles per meter width. If the delivery speed of the machine is 80 m/min, then the frequency (strokes/min) of each needle board is:
A spun yarn made of circular polyester fibres of 10 µm diameter is cut normal to the yarn axis. If the helix angle of a fibre is \( 40^\circ \), then the area (µm\(^2\)) of that fibre projected on the cut-section of the yarn (rounded off to 1 decimal place) is:
A chute feed system feeds a fibre batt of linear density 300 g/m to a card. The waste extracted by the card is 5% and the total mechanical draft is 100. The linear density (ktex) of card sliver (correct up to 2 decimal places) is:
Evaluate the integral: $ \int_0^\pi \frac{\tan x}{\cos x} \, dx = \int_0^\pi \frac{\sin x}{\cos^2 x} \, dx $
A polymer melt being extruded through a spinneret hole of circular cross-section exhibits a die-swell ratio of 2.2. The extrusion velocity and volumetric flow rate during this extrusion process are 20 m/min and \(2.6 \times 10^{-8}\) m\(^3\)/s, respectively. The maximum diameter (mm) of the extruded melt after exit from the spinneret hole (rounded off to 2 decimal places) is:
A circular hollow polyester fibre with a tenacity of 0.02 N/tex breaks at 0.2 N. If the density of polyester is 1.38 g/cm\(^3\) and the inner diameter of the fibre is 40 µm, the outer diameter (µm) of the fibre (rounded off to 1 decimal place) is:
Let \( X \) be a Poisson distributed random variable with parameter \( \lambda (> 0) \) such that it satisfies the equation \[ P(X = 1) = 3P(X = 3) - P(X = 2) {. Then, the value of } \lambda { is:} \]
If \( u(x, y, z) = x^2y + y^2z + z^2x \), the value of \[ \frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} { at the point } (1,1,1) { is:} \]
A cotton fabric is printed using resist style with a reactive dye for ground colour and a chemical resist agent. Amongst the following, the correct statement(s) is/are:
Consider a cationic and an anionic softener both having linear alkyl chains. Upon application on cotton fabric, the orientation of the softener molecules on fabric can be described by the following statement(s):
Amongst the following, the correct reason(s) for high pilling tendency in a woven fabric is/are:
Amongst the following, the parameter(s) relevant to fibre fineness measurement using vibration method, is/are:
Amongst the following, the instrument(s) used for measurement of neps in cotton fibre tuft is/are:
Amongst the following, producing a dense fabric in a weaving machine require(s):
Amongst the following, the machine(s) that remove(s) neps is/are:
Amongst the following, the correct statement(s) for regenerated cellulosic fibres is/are:

Group I indicates chemical agents and Group II indicates their functions. Match the agent with its function.


 

If melting, pyrolysis, and combustion temperatures of polyester fibre are denoted by \(T_m\), \(T_p\), and \(T_c\) respectively, then the correct order of temperatures is:

Group I lists the components of the weaving machine and Group II lists their functions. Match the component with its function.