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141
NTA PhD Entrance Examination CS 2023| PART 1 | Question: 40
For $f(x)=\mathrm{px}^{2}+\mathrm{qx}+\mathrm{r}, \mathrm{x}$ lies in the range $[\mathrm{a}, \mathrm{a}+\mathrm{h}]$. The value of $\theta$, irrespective of the values of $\mathrm{p}, \mathrm{q}, \mathrm{r}, \mathrm{a}, \mathrm{h}, \mathrm{in}$ Langarge's theorem, is always $1 / 2$ $2$ $1$ $3 / 2$
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 41
Which of the following correctly explains a latent variable? Useful in algebraic manipulations Observable variable that may influence the criterion variables Unobservable variable which may influence the criterion variables Discrete variable
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 42
Match $\text{List I}$ with $\text{List II}$ LIST I LIST II Rosenzweig test Related to sociology Thematic apperception test Psychological test Rorschach test Assess personality characteristics Doll-play test Describe ambiguous scenes Choose the correct answer from options given ... $\text{A-I, B-IV, C-III, D-II}$
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 43
A problem in Mathematics is given to 3 students whose chances of solving it are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$. Find the probability of solving it correctly by only one of them. $\frac{3}{4}$ $\frac{11}{24}$ $\frac{13}{24}$ $\frac{1}{4}$
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 44
Match List I with List II List I List II Casual analysis Prediction of the dependent variable based on its covariance with all concerned independent variables. Canonical analysis Functional relationships existing between two or more variables. Inferential analysis Estimate the ... $\text{A-I, B-IV, C-III, D-II}$
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 45
Let $\mathrm{f}: \mathrm{G}_{1} \rightarrow \mathrm{G}_{2}$ be a homomorphism of groups, and let $\mathrm{a}$ and $\mathrm{b}$ be elements of $\mathrm{G}_{1}$. Also, assume $\mathrm{K}$ to be the kernel of $\mathrm{f}$ ... $\text{A, B and C}$ only $\text{B, C and D}$ only $\text{A, C and D}$ only
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 46
For the function $f(x)=|x-3|$, where $x$ is a real number, which of the following statements are true? $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=3$. $f(x)$ is not differentiable at $x=3$. $\mathrm{f}(\mathrm{x})$ ... $\text{B, C and D}$ only $\text{A, C and D}$ only $\text{A, B and D}$ only
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148
NTA PhD Entrance Examination CS 2023| PART 1 | Question: 47
The value of $\int \frac{d x}{x\left(x^{3}+1\right)}$ is $\frac{1}{3} \log \left|\frac{x^{3}}{x^{3}+1}\right|+c$ $\frac{1}{4} \log \left|\frac{x^{3}}{x^{2}+1}\right|+c$ $\frac{1}{3} \log \left|\frac{x^{2}}{x^{2}+1}\right|+c$ $\frac{1}{3} \log \left|\frac{x^{2}}{x^{2}+x+1}\right|+c$
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NTA PhD Entrance Examination CS 2023| PART 1 | Question: 48
To determine validity, the types of criteria are Content validity Concurrent validity Criterion-related validity Construct validity Predictive validity Choose the most appropriate answer from options given below: $\text{A, B and C}$ $\text{A, B and D}$ $\text{A, C and E}$ $\text{A, C and D}$
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150
NTA PhD Entrance Examination CS 2023| PART 1 | Question: 49
The value of $\int_{0}^{\pi} \frac{x d x}{1+\sin x}$ is $2 \pi$ $\pi$ $\pi / 2$ $\pi^{2}$
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151
NTA PhD Entrance Examination CS 2023| PART 1 | Question: 50
If $x^{m} y^{n}=(x+y)^{m+n}$, then $d y / d x$ is equal to $\mathrm{y} / \mathrm{x}$ $\mathrm{x} / \mathrm{y}$ $xy$ $\mathrm{x}+\mathrm{y}$
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Can I get Into DRDO with degree in artificial intelligence and Data science through GATE CSE?
I'm asking this question because I have degree in Data Science and Artificial Intelligence and This year GATE IISC adds new subject Data science and Artificial intelligence(DA) before this ... 9. Information Science & Engg/Technology 10. Computer & Communication Engg 11. Computer Networking
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out of 130 students 60 are wearing hats to class 51 are wearing scarves and 30 are wearing both hats and scarves of the 54 students who are wearing sweater, 26 are wearing hats, 21 are wearing scarves and 12 are wearing both hats and scarves. everyone wearing neither a hat nor a scarves is wearing gloves. (a) how many students are wearing gloves? (b) how many students not wearing a sweater are wearing hats but not scarves?
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 2
Given $3$ literals $\text{A, B}$, and $\text{C}$, how many models are there for the sentence $\text{A $\vee$ $\neg$ B $\vee$ C}$ ?
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 3
Which of the following first-order logic sentence matches closest with the sentence "All students are not equal"? ...
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 4
The mean of the observations of the first $50$ observations of a process is $12$. If the $51$ $\text{st}$ observation is $18$, then, the mean of the first $51$ observations of the process is $12$ $12.12$ $12.36$ $18$
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 6
Which among the following may help to reduce overfitting demonstrated by a model Change the loss function. Reduce model complexity. Increase the training data. Increase the number of optimization routine steps. $\text{ii and i}$ $\text{ii and iii}$ $\text{i, ii, and iii}$ $\text{i, ii, iii, and iv}$
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 8
Given $\mathrm{n}$ indistinguishable particles and $m(>n)$ distinguishable boxes, we place at random each particle in one of the boxes. The probability that in $\mathrm{n}$ ... $\frac{1}{m^{n}}$ $\frac{1}{m}$
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 9
For two events $\text{A}$ and $\text{B}$, $\text{B}$ $\subset$ $\text{A}$ Which of the following statement is correct? $P(B \mid A) \geq P(B)$ $P(B \mid A) \leq P(B)$ $P(A \mid B)<1$ $P(A \mid B)=0$
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GATE Data Science and Artificial Intelligence 2024 | Sample Paper | Question: 10
$\mathrm{X}$ is a uniform distribution random variable with support in $[-2,2] \mathrm{U}[99.5$, $100.5]$. The mean of $\mathrm{X}$ is __________.
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