| Post Name | ASSISTANT DIRECTOR (Industries and Commerce) |
|---|---|
| Question Paper Code | 150/2024 |
| Category Code | 630/2023 |
| Date of Test | 30 October 2024 |
| Medium of Question | ENGLISH |
| Exam Type | OMR Examination |
| Total Questions | 100 |
1
\begin{bmatrix} 0 & h & -g \\ -h & 0 & f \\ g & -f & 0 \end{bmatrix} is a __________________________________
Answer
B. Skew-Symmetric
2
If A is a \(5 \times 3\) matrix and B is a \(3 \times 2\) matrix, then what is the order of the product AB?
Answer
A. 5 \times 2
3
If A' denotes the transpose of A, then \((AB)' =\):
Answer
C. B'A'
4
The condition for a system of homogeneous linear equations in n variables to have \(n - r\) linearly independent solutions, where \(r\) is the rank of the coefficient matrix, is:
Answer
C. r < n
5
The sum of the eigen values of \(\begin{bmatrix} 5 & 4 & 1 \\ 1 & 2 & 2 \\ 3 & 2 & 0 \end{bmatrix}\) is :
Answer
B. 7
6
The number of independent eigen vectors for a matrix with \(n\) distinct eigen values is :
Answer
A. n
7
If every minor of order greater than or equal to \(r\) of a matrix \(A\) is zero, then rank of \(A\) is:
Answer
D. less than r \(\bf{3}\)
8
The product of the eigen values of \(\begin{bmatrix} 2 & 3 \\ 7 & 8 \end{bmatrix}\) is :
Answer
C. 5
9
Find \(\lim_{x\to 2^+} f(x)\) for the function graphed in the following figure: \(\overline{2}\) \(\mathbf{1}\) \(-1\) \(\overline{3}\)
Answer
D. \quad \infty
10
For what values of x, if any, is the function \(f(x) = \frac{x^2 - 4}{x^2 - 5x + 6}\) discontinuous?
Answer
C. x = 2 and x = 3
11
If the line \(3x - 2y = 7\) is tangent to the graph of \(y = f(x)\) at \(x = 1\), then what is the value of \(f'(1)\)?
Answer
D. \frac{3}{2}
12
Find the value of \(c \in (-4,6)\), appearing in the Mean Value Theorem if \(f(x) = 2x^2 - 3x\):
Answer
B. 1
13
The derivative of an increasing function is:
Answer
D. positive
14
At a point of inflexion of a function, its third derivative is :
Answer
Question Cancelled
15
Evaluate \int_{0}^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}}:
Answer
A. \frac{\pi}{4}
16
Evaluate the area of the tangent cut off from the parabola \(x^2 = 8y\) by the line \(x-2y+8=0\):
Answer
Question Cancelled
17
Evaluate \(\lim_{(x,y)\to(2,1)} [8x^2y^3-10]\):
Answer
A. 22
18
If \(D=2\sqrt{x^3+y^2}\) is the length of the diagonal of a rectangle whose sides are x and y, that are allowed to vary, what is the rate of change of \(D\) with respect of \(x\) at the point \((1, 2)\):
Answer
A. \frac{3}{\sqrt{5}}
19
Evaluate \int_{0}^{2y} (3x^2 - y) dx dy:
Answer
D. \frac{4}{3}
20
Evaluate \(\int_{1}^{2} \int_{0}^{1} 10xy^2 z^3 dz dy dx\):
Answer
A. 20
21
Solution of the differential equation \(ydx + x dy = 0\) is:
Answer
A. xy = k
22
Solution of the differential equation \(\frac{d^2y}{dx^2} + 4y = 0\) is :
Answer
A. y = c_1 \cos 2x + c_2 \sin 2x
23
Solution of the differential equation \(x^2y'' + xy' + y = 0\) is
Answer
C. y = c_1 \cos(\ln x) + c_2 \sin(\ln x)
24
\frac{dy}{dx} + y \tan x = \sec x has the solution:
Answer
C. y \sec x = \tan x + c
25
Find the mean of 20, 22, 28, 24:
Answer
C. 23.5
26
If a random variable follows Poisson distribution and \(P(1) = P(0)\), then mean of the distribution is:
Answer
A. 1
27
Variance of the Uniform distribution with probability density function \(f(x) = \frac{1}{3}\), \(3 < x < 6\) is:
Answer
A. \frac{3}{4}
28
If \(E(X) = 5\) then \(E(X + 2)\) is:
Answer
A. 7
29
If mean and variance of a binomial distribution are 4 and 2 respectively then probability of failure is:
Answer
A. \(\frac{1}{2}\)
30
Find the probability of getting 2 red balls from 4 red balls and 3 white balls :
Answer
A. \frac{2}{7}
31
If X follows normal distribution with mean 10 and variance 4, then \(P(X < 10)\) equals:
Answer
B. 0.5
32
Value of correlation co-efficient ranges between:
Answer
A. 1 and 1
33
The probability of getting a ticket, with number a multiple of 5 in a random draw from a bag containing tickets of even numbers from 1 to 100 is:
Answer
A. \frac{1}{5}
34
If the joint probability density function of a two dimensional random variable \((X, Y)\) is \(f(x, y) = 2\), \(0 < x < 1\), \(0 < y < x\) then the marginal density function of Y is:
Answer
B. 2(1-y), 0 < y < 1
35
If X_1, X_2, X_3, \ldots, X_n are independently and identically distributed random variables with variance \(\sigma^2\), then \(V\left(\frac{X_1 + X_2 + X_3 + \dots + X_n}{n}\right)\) equals :
Answer
B. \frac{\sigma^2}{n}
36
If A and B are two independent events then:
Answer
A. P(A/B) = P(A)
37
The first iterative solution of \(x^3 + x^2 - 3x - 3 = 0\) which lies between 1 and 2 given by Regula-Falsi method is:
Answer
A. 1.571
38
Newton-Raphson method gives first iterative solution of \(\sqrt[3]{2} \;\) as :
Answer
A. 1.33
39
First and second forward differences of 2 from the below table are: \(\overline{2}\) \(\overline{4}\) 31 \(\boldsymbol{\mathcal{X}}\) : 77 \(8\,\) \(\overline{5}\) \(y\):
Answer
A. 2,
40
Lagrange's interpolating polynomial which fits the data (1, 0), (2, 3), (3, 8) is:
Answer
B. x^2-1
41
The ratio between the Einstein's coefficients for spontaneous and stimulated emissions is :
Answer
B. \frac{8 \pi h v^3}{c^3}
42
A ruby laser pulse is contributed by \(3\times10^{20}Cr^{3+}\) ions. Calculate the energy of the pulse if the wavelength is \(6630 \, \text{A}^{\circ}\):
Answer
B. \(90\ J\)
43
What is the expression for the acceptance angle of an optical fibre whose cladding and core have refractive indices \(\mu_1\) and \(\mu_2\) respectively?
Answer
D. \sin^{-1}\sqrt{\mu_2^2-\mu_1^2}
44
The sensing medium in an intrinsic optical fibre sensor is :
Answer
A. Fibre
45
Which material is commonly used in the production of blue LEDs?
Answer
C. Gallium Nitride
46
The Fermi level in an \(n\)-type semiconductor lies :
Answer
C. Closer to the conduction band
47
For a silicon semiconductor at 300 K, the intrinsic carrier concentration is \(1.5 \times 10^{10} cm^{-3}\). If the donor concentration is \(1 \times 10^{15} cm^{-3}\). What is the hole concentration?
Answer
D. 2.25 \times 10^5 cm^{-3}
48
In BCS theory, Cooper pairs are composed of which of the following particles?
Answer
A. Two electrons with opposite spins and momentum
49
The London penetration depth of a superconductor is:
Answer
B. \lambda = \left(\frac{m}{n\mu_0 e^2}\right)^{1/2}
50
What is the critical field for lead at 3.59 K if the critical field at 0K is \(6.5 \times 10^4\) A/m. The critical temperature for lead is 7.18K?
Answer
D. 4.875 \times 10^4 A/m
51
In which of the following applications are infrasonic waves most commonly used?
Answer
B. Earthquake monitoring
52
What does an acoustic absorption coefficient \(\alpha\) value of 1.0 indicate?
Answer
B. The material absorbs all sound energy
53
A change in the intensity level of 1 dB alters the intensity of sound by:
Answer
C. 26%
54
The property of sound closely related to its pitch is:
Answer
A. Frequency
55
What is the primary purpose of using a coupling gel in medical ultrasound imaging?
Answer
C. To eliminate air between the transducer and the skin
56
The monomers of Kevlar are:
Answer
D. Paraphenylene diamine and Tererphthalic acid
57
What is the purpose of developing chamber in TLC?
Answer
B. To separate the components of the mixture
58
Which of the following is a p-type dopant for polyaniline (PANI)?
Answer
D. Iodine
59
The low thermal expansion of borosilicate glass is primarily due to the presence of:
Answer
B. Boron trioxide
60
Which of the following ingredient in Portland cement regulates the setting time of cement?
Answer
C. Gypsum
61
TGA can be used for :
Answer
D. Analysing the thermal stability of polymers
62
What of the following statements are correct for carbon dioxide molecule? I. All molecular vibrations of carbon dioxide are not IR active II. Four molecular vibrations are possible for carbon dioxide III. Only two absorption bands are observed in the IR spectrum of carbon dioxide
Answer
C. I, II and III
63
Which is the most common fissionable nuclei used in Pressurised Water Reactors?
Answer
A. Uranium
64
What is the purpose of the Scanning coil in Scanning Electron Microscope?
Answer
D. To deflect the electron beam
65
The absorbance of 0.002 M solution of a dye shows an absorbance of 0.1750 at 720 nm; while a test solution of the same dye shows absorbance of 0.2625 under the same conditions. Find the concentration of the test solution:
Answer
B. 0.003 M
66
International day for the preservation of the ozone layer is observed on :
Answer
C. September 16
67
Both top-down approaches and bottom-up approaches are used to synthesis nanomaterials. Which of the following is a top-down method to synthesise nanomaterials?
Answer
A. Laser ablation
68
Which of the following water treatment helps to remove dissolved gases?
Answer
C. Aeration
69
Which of the following polymer membrane is used in PEM fuel cells?
Answer
B. Nafion
70
Blue baby syndrome or methemoglobinemia is caused by excess concentration of in drinking water :
Answer
A. Nitrate ions
71
Which management concept suggests that low-importance decisions be handled by subordinates, so that managers can focus on high-importance decisions?
Answer
A. Management By Exception
72
A process in which a group of individuals generate and state ideas, but in which the rules prohibit questioning, evaluating, or rejecting any ideas, even if they seem ridiculous is called?
Answer
B. Brain storming
73
What kind of organizational structure combines a vertical chain of command with horizontal reporting requirements?
Answer
B. Matrix
74
In an organization if the manager once determines policy, program's and limitations for action and the entire process is entrusting to the subordinates for execution, then the leadership style is called?
Answer
Question Cancelled
75
Functional managers are responsible :
Answer
A. For A Single Area Of Activity
76
Find Breakeven point in units as per the following details: Sales @ Rs.30 per unit, Variable cost @ Rs.15 per unit and Fixed cost Rs.45,000. produced 2500 units.
Answer
C. 3000
77
That the authority rests solely with the management with no right to anyone to challenge it is the basis of the :
Answer
C. Unitary approach
78
During the selection process while the candidate is being evaluated, the candidate too tries to evaluate the company and its culture, apart from the job, and comes to a decision about suitability of the organization, this means that
Answer
C. The selection process also involves selling the organization to the candidate
79
Which component of performance management refers to communicating a firm's higher-level goals throughout the organization and then translating them into departmental and individual goals?
Answer
D. Direction sharing
80
A process theory of motivation is most likely to focus on :
Answer
B. Expectancies regarding work outcomes
81
Liquidity risk:
Answer
A. Increases whenever interest rates increase
82
The method that calculates the expected monetary gain or loss from a project by discounting all expected future cash inflows and outflows to the present point in time, using the required rate of return is:
Answer
A. Net present value
83
According to the capital-asset pricing model (CAPM), a security's expected (required) return is equal to the risk-free rate plus a premium :
Answer
Question Cancelled
84
The return on capital employed shows the combined effect of:
Answer
C. Net Profit Ratio and Capital Turnover Ratio
85
model states that the value of a company's shares is sustained by the expectation of future dividends:
Answer
A. The dividend valuation model
86
Debt Financing is a cheaper source of finance because of :
Answer
C. Tax-deductibility of Interest
87
Which of the following statements are correct? 1. Staff manager is authorized to direct the work of a subordinate and is responsible for accomplishing the organizations task \(\overline{2}\). Staff authority gives a manager right to advice other managers or employees 3. Controlling labor cost is one of the primary responsibilities of Line manager
Answer
D. 2 and 3 are correct
88
A machine operator is injured while working with heavy machinery, leading to a temporary disability that prevents them from working for five days. According to the Workmen's Compensation Act, 1923, which of the following most accurately outlines the employer's liability in this case?
Answer
A. The employer is liable to pay compensation as the operator miss more than three days of work due to injury.
89
Which of the following criticism is incorrect related to Forced distribution method? \(\mathbf{1}\). It damages moral of employees by placing them in lower rating categories, as they may feel demotivated and disengaged. 2. It does not produce relative rating for pay rise 3. Force ranking measure use subjective assessment to grade the employee, which makes it challenging to meaningfully differentiate employees.
Answer
C. Only 2 is incorrect
90
According to the Industrial Disputes Act, 1947, regarding the representation of parties in a dispute, which of the following accurately outlines the entitlements of a workman who is a party to an industrial dispute? \(\mathbf{1}\). A workman can be represented by any member of the executive or other office bearer of a registered trade union of which he is a member. 2. If the workman is not a member of any trade union, he can be represented by any workman employed in the same industry, authorized in the prescribed manner A workman can be represented by a member of the executive or other office bearer 3. of a federation of trade unions, regardless of whether his trade union is affiliated to it.
Answer
A. Only 1 and 2
91
Philip Kotler defines various demand states. Consider the following examples of product demand in India: \(\mathbf{1}\) Spotify users subscribe to the premium service to avoid listening to ads, which they find intrusive and disruptive during their music experience. 2. A state government offers highly subsidized green materials to build sustainable homes, but most consumers are unaware of the program or its benefits. 3. State transport buses are consistently overcrowded, with more passengers than available seats. \(\overline{4}\). Restaurants serving traditional foods experience a decline in demand as younger consumers shift their preferences toward Western cuisines. Which of the following options correctly identifies the demand state for each example?
Answer
C. 1: Negative Demand, 2: Non-existent Demand, 3: Overfull Demand, 4: Declining Demand
92
Which of the following statements are true related to market research? 1. Ethnographic research is one of the best methods for gathering all necessary insights in a short period of time. 2. Experimental Research is designed to eliminate competitive explanation of the findings. 3. Focus group research requires researcher to gather marketing insight by observing unobtrusively as customers shop or consume product.
Answer
A. Only 2 is true
93
According to Alan R. Andreasen to be labelled social marketing, a program: 1. Must not apply commercial marketing technology. 2. Have as its bottom line the influencing of voluntary behavior. 3. Primarily seek to benefit individuals/families or the broader society and not the marketing organization itself. Which of the above statement is incorrect?
Answer
A. Only 1 is incorrect
94
Which of the following examples best illustrates the representativeness heuristic in consumer decision-making? 1. A consumer buys a product solely because it was featured in a celebrity’s social media post, associating the celebrity’s popularity with the product’s value. 2. Consumers tend to view brands with similar packaging in the same product category as having similar quality and meeting the typical standards of that category. 3. Consumers viewing recent product failure to inflate the likelihood of future product failure and buys a product warranty. 4. A customer sees a pizza worth 1500/- on the menu and as a result, perceives a pizza worth 750/- as a good deal, even though it’s still relatively expensive.
Answer
B. 2
95
Which of the following statements about Cultural Branding are true? 1. The concept of Cultural Branding is primarily attributed to Douglas B. Holt. 2. Cultural Branding defines a brand as a performer of and container for an identity myth. 3. The most appropriate application of cultural branding is for new fashion and new technology.
Answer
D. Statement 1 and 2 are true
96
Which of the following strategic actions are most appropriate during the decline stage? 1. Reducing marketing expenditures and shifting resources toward R and D for new product innovations while gradually phasing out underperforming product lines. 2. Adopting a market penetration strategy by lowering prices to attract price-sensitive customers, thus extending the life of the product in saturated markets. 3. Utilizing rebranding and repositioning to revive consumer interest, targeting new demographics and exploring alternative uses for the existing product.
Answer
B. Only 1 and 3
97
Arrange the following steps for benchmarking in correct order: 1. Plan \(\overline{2}\). Decide what to benchmark 3. Study others \(\overline{4}\). Understand the current performance Use the findings 5. 6. Learn from data
Answer
D. 2, 4, 1, 3, 6, 5
98
In the DMAIC process, which of the following combinations of technique and stage is incorrectly matched? 1. Design of Experiments (DOE) - Improve \(\overline{2}\). Value Stream Map - Define 3. Pareto Chart - Control 4. Failure Mode and Effects Analysis (FMEA) - Analyze
Answer
B. Only 3
99
A production process has a fixed cost of Rs. 1,10,000 per year and a variable cost of Rs. 2 per unit. If the selling price of the product is Rs. 14 per unit, what is the annual break-even quantity for the process?
Answer
D. 9.167 units
100
A firm is trying to determine the setup cost for a manufacturing operation to accommodate an Economic Order Quantity (EOQ) of 20 units for a part. The following data is available : \(\bullet\) Annual demand \((D) = 20,000\) units \(\bullet\) Holding cost per unit per year \((H) = Rs. 15/\) \(\bullet\) Production rate \((P) = 80\) units per day Daily demand rate (d) = 20 units per day \(\bullet\) \(EOQ = 20\) units Setup cost \((S)\) = unknown What is the setup cost (S) for this process?
Answer
B. Rs. 0.15 per setup
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