| Post Name | INDUSTRIES EXTENSION OFFICER (Industries and Commerce) |
|---|---|
| Question Paper Code | 021/2025 |
| Category Code | 030/2024 |
| Date of Test | 18 February 2025 |
| Medium of Question | ENGLISH |
| Exam Type | OMR Examination |
| Total Questions | 100 |
1
In a given electrical network, the equations for the currents i1, i2, i3 are 3i1 + 3i2 + 2i3 = 1 \(i_1 + 2i_2 = 4\), \(10i_2 + 3i_3 = -2\), the values of \(i_1\) and \(i_3\) are
Answer
A. 2, β 4
2
One solution of the system of equations x + y + z = 1, x + 2y + 3z = \mu, x + 5y + 9z = \( \mu^2 \) is
Answer
B. (1, -2, 2)
3
The rank of the matrix given by the system of equations 3x + y + z = 8, 2x - 3y - 2z = -5, \(7x + 2y - 5z = 0\) is
Answer
B. 3
4
If A is matrix of order 5 and det A = 0 then rank of A will be
Answer
B. Less than 5
5
Let A be a 2 Γ 2 real matrix with trace A = -7 and det A = 6. What is the value of trace A2?
Answer
C. 37
6
The largest eigen value and the corresponding eigen vector of \begin{bmatrix} 1 & -2 \\ -5 & 4 \end{bmatrix} are
Answer
D. 6; (2, -5)
7
If 6 is an eigen value of A = \begin{bmatrix} 3 & -1 & 1 \ -1 & 5 & -1 \ 1 & -1 & 3 \end{bmatrix}, find the eigen values of A - 5I.
Answer
C. 1, -2, -3
8
The eigen vectors of a 3 Γ 3 matrix A corresponding to the eigen values 1, 1, 3 are 0, 1, 1 respectively. Find A.
Answer
A. \begin{bmatrix} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 0 & 0 & 1 \end{bmatrix}
9
Value of \lim_{t\to\infty} \frac{e^t + t^2}{e^t - t}
Answer
D. 1
10
Let f(t) = \begin{cases} t-2, & t2 \end{cases} i. lim f(t) ii. lim f(t) iii. \(\lim_{t \to 2} f(t)\) are
Answer
Question Cancelled
11
The interval in which G(1) lies when G'(t) = \frac{1}{3-t^2} and G(0) = 1 is
Answer
A. \[ \left( \frac{4}{3}, \frac{3}{2} \right) \]
12
\int_c^{c_2} f(x) dx is numerically equal to the
Answer
C. area bounded by y = f(x), the x - axis and the ordinates at c1 and c2
13
The rate of change of z = x2 cos xy with respect to x at the point (0.5, \pi) is
Answer
B. \frac{-\pi}{4}
14
The celsius temperature in a region in space is given by T(x, y, z) = 2x2 - xyz. A particle is moving in this region and its position at time t is given by x = 2t2, y = 3t, z = -t2 where time is measured in seconds and distance in meters. How fast is the temperature experienced by the particle changing in degrees celsius per second when particle is at the point P(8, 6, -4)?
Answer
C. 736
15
The local linear approximation at the point (x0, y0, z0) of f (x, y, z) = x2 - xy + 3 sin z is given by L(x, y, z) = 3x - 2y + 3z - 2. Determine (x0, y0, z0).
Answer
B. (2, 1, 0)
16
The value of βu/βx at (x, y, z) = (Ο/4, 1/2, β1/2) for u = e^(qr) sinβ»ΒΉ p, p = sin x, q = zΒ² ln y, r = 1/z
Answer
Question Cancelled
17
Change in value of f = \frac{x + y}{xy} from P(-1, -2) to Q = (-1.02, -2.04) is
Answer
C. 0.03
18
The value of the integral \int_0^1 \int_{4x}^4 e^{-y^2} dydx is
Answer
C. \frac{1-e^{-16}}{8}
19
\int_{1}^{2} \int_{z}^{2} \int_{0}^{y\sqrt{3}} \frac{y}{x^{2} + v^{2}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
Answer
B. \frac{\pi}{6}
20
Area of the region enclosed between the parabola x2 = 2y and the line y = 2x is
Answer
A. \frac{16}{2}
21
The degree of the differential equation x \frac{dx}{dv} + \frac{dy}{dx} = y is
Answer
B. 2
22
The solution of the differential equation x \frac{dy}{dx} - y = 0, y(1) = 4 represents
Answer
A. Straight line
23
A solution of the linear differential equation \frac{d^2y}{dx^2} + 3\frac{dy}{dx} + 2y = 0, y(0) = 3, y(1) = \frac{1}{e^2} + \frac{2}{e} is
Answer
A. v(x) = e^{-2x} + 2e^{-x}
24
Which of the following is a solution to the Cauchy Euler differential equation \(x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - 9y = 0, x > 0\)?
Answer
D. \frac{1}{v^3}
25
The mean of a set of numbers is 54. If 5 is added to each of the members in the set, the mean of the new set is
Answer
A. 59
26
The two lines of regressions are 3x + 5y = 11 and 15x + y = 10. The correlation coefficient is
Answer
C. -1/5
27
The probability density function of a continuous random variable X is f(x) = \begin{cases} e^{-x}, & x \ge 0 \\ 0, & x < 0 \end{cases} The cumulative probability function F(1) is
Answer
A. 1 β e -1
28
Let X be a random variable where E(X) is the expectation of X and V(X) is the variance of X. If A and B are arbitrary constants, which of the following statement is/are correct? i. E(AX + B) = AE(X) + B ii. V(AX + B) = AV(X) + B iii. E(AX + B) = AE(X) iv. V(AX + B) = A2 V(X)
Answer
C. Only i and iv
29
The probability density function of a random variable X is given by \(f(x) = \begin{cases} 0.5, & 0 \le x \le 2 \\ 0, & \text{otherwise} \end{cases}.\) Which of the following probabilities are correct? i. \(P(X < 1) = 0.5\) ii. \(P(X > 1) = 1\) iii. P(X < 0.5) = 0.25 iv. P(X > 0.5) = 0.5
Answer
C. Only i and iii
30
Let X be a random variable follows binomial distribution b(x; n, p) with mean 8 and variance 2. The probability of success p is
Answer
B. 3/4
31
A continuous random variable X follows exponential distribution f(x) = \lambda e^{-\lambda x} , 0 β€ x 0. Which of the following condition is true?
Answer
B. The mean of the distribution is \frac{1}{\lambda}
32
If X and Y are two random variables follows normal distribution with P(X β€ -2) = P(Y β₯ 2). The means of X and Y are -1 and 1 respectively. If the standard deviation of X is 1, then the standard deviation of Y is
Answer
B. 1
33
The probability mass function P(X) of the Poisson distribution satisfies P(X = 0) = P(X = 1). The variance is
Answer
B. 1
34
The standard deviation of uniformly distributed random variable defined in the interval [1, 2] is
Answer
A. \frac{1}{\sqrt{12}}
35
A random variable X is uniformly distributed over [0, 2] and another random variable Y is uniformly distributed over [0, 3]. If X and Y are independent, then P(max (X, Y)> 1) is
Answer
C. 5/6
36
Let X be a normal random variable with mean 1 and variance 4. The probability P(X < 0) is
Answer
B. greater than 0 but less than 0.5
37
Newton-Raphson iteration formula for finding \sqrt{N}, where N > 0 is
Answer
D. x_{n+1} = \frac{x_n^2 + N}{2x_n}
38
The value of the function f(x) for different values of x are f(1) = -1, f(2) = -1, f(3) = 1 and f(4) = 5. Then f(x) attains
Answer
Question Cancelled
39
Consider the following statements. i. Lagranges interpolation formula is applicable only when arguments are equispaced. ii. Newton's forward interpolation formula is applicable only when arguments are equispaced. Which of the above is/are correct?
Answer
B. ii only
40
Consider the integral I = \int_0^6 x^2 dx and J is the value of the integral computed using Simpson's one third rule by dividing the interval into 6 equal subintervals, then |I β J| is
Answer
A. 0
41
The ratio of Einstein's coefficients at spontaneous emission of radiation and stimulated emission of radiation varies with the frequency 'v' of the incident radiation as
Answer
D. v3
42
The energy of laser pulse in a ruby laser of wavelength 662 nm is (Given, Planck's constant = 6.62Γ10-34 J.s, velocity of light = 3 Γ 108 m/s)
Answer
B. 3 \times 10^{-19} \, J
43
The wavelength of He-Ne laser is
Answer
C. 632.8 nm
44
A Nd: YAG laser emits light of wavelength 1054 nm. The duration of pulses is 10 ns. The coherence length is
Answer
B. 3 m
45
Polymer optical fibre of diameter 1 mm with high purity polymethyl methacrylate (PMMA) core of refractive index 1.54 and fluorinated polymer cladding of refractive index 1.456 are commercially available with a numerical aperture (NA) of 0.50. The acceptance angle of the fibre is
Answer
B. 30Β°
46
When the launch end of a multimode step index fibre of 200 ΞΌm/ 230 ΞΌm (core-cladding) diameter is immersed in water,
Answer
D. none of the above
47
The V-number of a multimode step-index fibre is 60. The number of modes guided through the fibre will be
Answer
B. 1800
48
In optical fibre technology, an optical fibre whose core has a refractive index that decreases with increasing radial distance from the fibre axis is known as
Answer
C. graded-index fibre
49
A light emitting diode is made of GaAsP having a band gap of 1.91 eV. The wavelength of radiation emitted is
Answer
A. 649.2 nm
50
From the I-V characteristic curve of a silicon solar cell current at maximum power point Im = 3.50 A; voltage at maximum power point Vm = 0.50 V. The short circuit current is 3.50 A and the open circuit voltage is 0.60 V. The fill factor of the solar cell is
Answer
D. 83.3%
51
Which of the following best describes avalanche breakdown in a PN junction?
Answer
C. Caused by high electric field ionizing atoms in the depletion region
52
Pure silicon at 550 K has an intrinsic electron and hole concentration of 1 Γ 1016 m-3. When doped with indium, the hole concentration increases to 4 Γ 1022 m-3. What type of semiconductor is the doped material?
Answer
C. p-type semiconductor with electron concentration 2.5 Γ 109 m-3
53
Which material is commonly used for manufacturing Zener diodes?
Answer
A. Silicon
54
The Meissner effect refers to
Answer
B. The expulsion of magnetic fields from a superconductor below the critical temperature
55
Which statement is not correct about the Cooper pair?
Answer
B. The two electrons in a Cooper pair have opposite spins and same momenta
56
When Germanium is doped with Aluminum, what type of semiconductor is formed?
Answer
C. P-Type Semiconductor
57
Potential difference must be applied across a Josephson junction to emit electromagnetic radiation at a frequency of 1209 terahertz (THz) is approximately
Answer
D. 2.5 V
58
The critical temperature of a superconductor in the absence of a magnetic field is Tc. At what temperature will the critical magnetic field reach three-fourths of its value at 0 K?
Answer
C. T=1/2Tc
59
Why are germanium diodes preferred as temperature sensors at low temperatures compared to silicon diodes? Which statement is not correct?
Answer
Question Cancelled
60
How does the Fermi level behave in a PN junction when forward bias is applied?
Answer
C. The Fermi level bends downwards on the P-side and upwards on the N-side
61
What type of wave is typically used in industrial non-destructive testing?
Answer
B. Ultrasonic waves
62
Which of the following applications is associated with infrasonic waves?
Answer
C. Seismic activity monitoring
63
The intensity of the sound wave is increased to 100 times, calculate the change in its decibel level.
Answer
C. 20 dB
64
A SONAR system uses ultrasonic waves with a frequency of 20 kHz. If the speed of sound in water is 1500 m/s, calculate the wavelength of the wave.
Answer
B. 0.075 m
65
Calculate the reverberation time for a concert hall of volume 5000 m3 with a sound absorption of 500 sabins.
Answer
A. 1.61 sec
66
Reverberation time refers to the duration it takes for the sound intensity to decrease _____ after the sound source has stopped emitting. by _
Answer
D. 60 dB
67
Ultrasonics is used in pulsed Doppler imaging to measure
Answer
B. Blood flow velocity
68
What is the unit of sound absorption?
Answer
B. Sabin
69
In which of the following mediums do acoustic waves (sound waves) travel the fastest?
Answer
C. Steel
70
The time taken for an ultrasonic wave to return to the SONAR after reflection from the ocean floor is 6 seconds. If the speed of sound in water is 1500 m/s, the depth of the ocean is
Answer
B. 4500 m
71
Which one of the following has two of its dimensions outside the nanometric range and one is within the nano range? i. Nano films ii. Nano wires iii. Nano fibers iv. Nano tubes
Answer
D. Only i
72
To which class of nanomaterials does the CNT, graphene and fullerene belong i. Organic based ii. Inorganic based iii. Carbon based iv. None of the above
Answer
A. iii
73
A green colored glass has i. cobalt oxide ii. chromic oxide iii. cadmium sulfide
Answer
C. ii
74
Which of the following glass is shatter proof? i. Borosilicate glass ii. Photochromic glass iii. Safety glass iv. Soda glass
Answer
B. iii
75
The proportion of which of the following constituent is regulated to avoid disintegration of cement? i. lime ii. iron oxide iii. alumina iv. sulfur trioxide
Answer
C. i
76
Which of the following is an argillaceous raw material for the manufacture of Portland cement? i. Limestone ii. Coal iii. Clay iv. Gypsum
Answer
D. iii
77
The strength of Kevlar is due to i. Hydrogen bonding between carbonyl group and NH center ii. Electrostatic forces iii. Aromatic stacking interaction between adjacent strands
Answer
B. i and iii
78
The base present in DNA but absent in RNA is i. Adenine ii. Guanine iii. Thymine iv. Cytosine
Answer
A. iii
79
In conducting polymers, doping can be done because they have i. low ionization potential ii. high electron affinity iii. high ionization potential iv. low electron affinity
Answer
D. i and ii
80
The hybridization of carbon in polyacetylene is i. sp ii. sp2 iii. sp3
Answer
C. ii
81
Among the given molecules which is IR active?
Answer
A. H2O
82
IR spectrum of CO2 exhibits two characteristic bands at 2349 and 667 cm-1 which corresponds to
Answer
B. Asymmetric stretching and bending vibrations respectively
83
The higher \lambda_{max} shown by 1, 3, 5-hexatriene compared to 1, 3-butadiene is due to the presence of
Answer
B. Three double bonds which are in conjugation
84
A dye solution of concentration 0.06M displayed an absorbance of 0.06 at 470 nm while the test solution of same dye recorded an absorbance of 0.02 under the same experimental conditions. Calculate the unknown concentration of the test solution.
Answer
B. 0.02 M
85
In a broad temperature range, the TG profile of compound 1 exhibited a significant weight loss, while compound 2 showed no changes. Which of the following statement is correct about the above TG profiles?
Answer
A. Compound 1 is undergoing dehydration and compound 2 is thermally stable
86
In scanning electron microscopy, information regarding composition of a material can be obtained by analysing
Answer
C. Back scattered electrons
87
In a TLC experiment of a sample, two spots are appeared at 2.1 cm (X) and 4 cm (Y) from the base line. Which of the following statement is correct regarding the nature of the compound?
Answer
A. X is more polar compared to Y
88
Which of the following applications cannot be effectively performed using Gas Chromatography (GC)?
Answer
D. Separation and quantification of non-volatile proteins, peptides etc.
89
The glass transition temperature of a polymer can be determined by
Answer
B. Differential thermal analysis
90
In HPLC, components in a mixture is separated by
Answer
A. Difference in adsorption coefficients
91
Which of the following gases has the highest Global Warming Potential (GWP)?
Answer
C. CFC
92
Which of the following statement is correct about photochemical smog?
Answer
B. It is oxidizing in nature
93
Which of the following pairs is an example for fissile nuclides?
Answer
A. U235 and Pu239
94
Identify the correct increasing order of coal ranks
Answer
D. Peat, lignite, bituminous coal and anthracite
95
Which of the following statement is/are correct? i. Waste water from electroplating industry is highly toxic due to the presence of metal cyanides. ii. Waste water from textile industry has low biological oxygen demand. iii. Waste water from petrochemical industry contains inorganic and organic sulphur compounds.
Answer
C. Only i and iii
96
Example for an electrolyte used in lithium-ion cell is
Answer
B. Lithium hexafluorophosphate
97
Which of the following statement about hydrogen-oxygen fuel cell is/are correct? i. Hydrogen gas is oxidized at the anode to produce H+ ions. ii. KOH or phosphoric acid can be used as the electrolyte. iii. It is a galvanic cell where the reactants are supplied from outside rather than forming an integral part of the cell.
Answer
D. All of the above (i, ii and iii)
98
Which among the following is an anerobic method involved in waste water treatment?
Answer
D. UASB process
99
'Wet' natural gas contains
Answer
A. Methane and higher hydrocarbons
100
Which of the following statement is not correct regarding ion exchange process?
Answer
C. Water is first passed through anion exchanger and then through cation exchanger
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