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31
TIFR CSE 2024 | Part A | Question: 1
If $\text{O}$ is the center of the circle, what is the area of the shaded portion in square cm? $4 \pi-4 \sqrt{2}$ $\frac{7}{2} \pi-4 \sqrt{2}$ $\frac{7}{2} \pi-4 \sqrt{3}$ $\frac{8}{3} \pi-4 \sqrt{3}$ $\frac{8}{3} \pi-4 \sqrt{2}$
If $\text{O}$ is the center of the circle, what is the area of the shaded portion in square cm?$4 \pi-4 \sqrt{2}$$\frac{7}{2} \pi-4 \sqrt{2}$$\frac{7}{2} \pi-4 \sqrt{3}$$...
admin
263
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admin
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Jan 12
Others
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32
TIFR CSE 2024 | Part A | Question: 2
Let $\sigma$ be a uniform random permutation of $\{1, \ldots, 100\}$. What is the probability that $\sigma(1)<\sigma(2)<\sigma(3)$ ... $\frac{3}{100 !}$ $\frac{3 !}{100 !}$ $\frac{6}{100}$ $\frac{1}{6}$ $\frac{1}{3}$
Let $\sigma$ be a uniform random permutation of $\{1, \ldots, 100\}$. What is the probability that $\sigma(1)<\sigma(2)<\sigma(3)$ (i.e., what is the probability that the...
admin
137
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admin
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Jan 12
Others
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33
TIFR CSE 2024 | Part A | Question: 3
There is a $100 \mathrm{~cm}$ long ruler that has 11 ants on positions $0 \mathrm{~cm}, 10 \mathrm{~cm}, 20 \mathrm{~cm}, 30 \mathrm{~cm}$, ..., $100 \mathrm{~cm}$. The ant at the $0 \mathrm{~cm}$ mark ... without knowing the directions of all ants. $100$ seconds. More than $100$ seconds, but cannot be determined without knowing the directions of all ants.
There is a $100 \mathrm{~cm}$ long ruler that has 11 ants on positions $0 \mathrm{~cm}, 10 \mathrm{~cm}, 20 \mathrm{~cm}, 30 \mathrm{~cm}$, ..., $100 \mathrm{~cm}$. The a...
admin
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admin
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Jan 12
Others
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34
TIFR CSE 2024 | Part A | Question: 4
Let $z_{1}, z_{2}, z_{3}, \ldots, z_{2023}$ be a permutation of the numbers $1,2,3, \ldots, 2023$. Which of the following is true about the product $\prod_{i=1}^{2023}\left(z_{i}-i\right)$ ? Note: The parity of an ... such that swapping their values does not change the parity of the above product. None of the above statements is true.
Let $z_{1}, z_{2}, z_{3}, \ldots, z_{2023}$ be a permutation of the numbers $1,2,3, \ldots, 2023$. Which of the following is true about the product $\prod_{i=1}^{2023}\le...
admin
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admin
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Jan 12
Others
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35
TIFR CSE 2024 | Part A | Question: 5
Let $p(x)$ be a polynomial with real coefficients which satisfies $p(r)=p(-r)$ for every real number $r$. Let $n \geq 5$ be a positive integer. Suppose that $p(i)=i$ for all $1 \leq i \leq n$. What is the maximum possible value of the absolute value of the coefficient of ${x^{5}}$ in $p(x)$ ? $0$ $5$ $10$ $n$ $n+1$
Let $p(x)$ be a polynomial with real coefficients which satisfies $p(r)=p(-r)$ for every real number $r$. Let $n \geq 5$ be a positive integer. Suppose that $p(i)=i$ for ...
admin
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admin
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Jan 12
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TIFR CSE 2024 | Part A | Question: 6
For each month in the year (i.e., January, February, March,...), let us assume the probability that a person's birthday falls in that particular month is exactly $1 / 12$, and let us assume that this is independent for different persons. What is the smallest value of ... is a pair of them born in the same month is at least $1 / 2$? $3$ $4$ $5$ $6$ $7$
For each month in the year (i.e., January, February, March,...), let us assume the probability that a person's birthday falls in that particular month is exactly $1 / 12$...
admin
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admin
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Jan 12
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TIFR CSE 2024 | Part A | Question: 7
Let $S:=\{(a, b) \mid 0 \leq a \leq 1,0 \leq b \leq 1\}$, a unit square, in $\mathbb{R}^{2}$. Let $B:=$ $\left\{(x, y) \mid x^{2}+y^{2} \leq 1\right\}$, a unit disk, in $\mathbb{R}^{2}$. Define the set $S+B$ as follows: \[ S+B:=\{(u, v) \ ... \text { such that } u=a+x, v=b+y\} . \] What is the area of $S+B$ ? $\pi+4$ $\pi+5$ $\pi+3$ $\pi+2$ None of the above.
Let $S:=\{(a, b) \mid 0 \leq a \leq 1,0 \leq b \leq 1\}$, a unit square, in $\mathbb{R}^{2}$. Let $B:=$ $\left\{(x, y) \mid x^{2}+y^{2} \leq 1\right\}$, a unit disk, in $...
admin
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admin
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Jan 12
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38
TIFR CSE 2024 | Part A | Question: 8
A palindrome is a string that reads the same in reverse (e.g. ABBA or KAYAK or MALAYALAM). How many strings of length 5 using the letters from $\{A, B, C, D, E\}$ have no palindromic substring of length at least 2? $243$ $405$ $540$ $675$ $1280$
A palindrome is a string that reads the same in reverse (e.g. ABBA or KAYAK or MALAYALAM).How many strings of length 5 using the letters from $\{A, B, C, D, E\}$ have no ...
admin
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admin
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Jan 12
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tifr2024
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TIFR CSE 2024 | Part A | Question: 9
Compute $\int_{16}^{\infty} \frac{1}{x} \cdot \frac{1}{\sqrt{\sqrt{x}-1}} d x$. $0$ $\frac{\pi}{3}$ $\frac{\pi}{2}$ $\frac{2 \pi}{3}$ $2 \pi$
Compute $\int_{16}^{\infty} \frac{1}{x} \cdot \frac{1}{\sqrt{\sqrt{x}-1}} d x$.$0$$\frac{\pi}{3}$$\frac{\pi}{2}$$\frac{2 \pi}{3}$$2 \pi$
admin
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admin
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Jan 12
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40
TIFR CSE 2024 | Part A | Question: 10
Let $\text{M}$ be a $3 \times 3$ matrix over the real numbers such that $\text{M}^{\text{T}} \text{M}=\mathbf{I}$. Consider the following statements. There exists a non-zero vector $x \in \mathbb{R}^{3}$ such that $M x=\mathbf{0}$. There ... /are true? Only $\text{(i)}$ Only $\text{(ii)}$. Only $\text{(iii)}$. All three statements. None of the three statements.
Let $\text{M}$ be a $3 \times 3$ matrix over the real numbers such that $\text{M}^{\text{T}} \text{M}=\mathbf{I}$. Consider the following statements.There exists a non-ze...
admin
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admin
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Jan 12
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41
TIFR CSE 2024 | Part A | Question: 11
Consider the following sequence of polynomials with real coefficients. \[ \begin{aligned} P_{0}(x) & =1 \\ P_{1}(x) & =2 x \\ P_{n+1}(x) & =2 x P_{n}(x)-P_{n-1}(x), \text { for all natural numbers } n \geq 1 . \end{aligned} \] ... }(x), P_{4}(x)\right\} \] in the vector space of polynomials in variable $x$ with real coefficients? $1$ $2$ $3$ $4$ $5$
Consider the following sequence of polynomials with real coefficients.\[\begin{aligned}P_{0}(x) & =1 \\P_{1}(x) & =2 x \\P_{n+1}(x) & =2 x P_{n}(x)-P_{n-1}(x), \text { fo...
admin
79
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admin
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Jan 12
Others
tifr2024
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42
TIFR CSE 2024 | Part A | Question: 12
A subset $\text{S}$ of the rational numbers is said to be "nice" if for every infinite sequence of $x_1, x_2, \ldots$ of elements from $\text{S}$, there is always two indices $i<j$ such that $x_i \leq x_j$. Consider the following ... $\text{(i)}$ and $\text{(iii)}$. All three statements are true. None of the three statements is true.
A subset $\text{S}$ of the rational numbers is said to be "nice" if for every infinite sequence of $x_1, x_2, \ldots$ of elements from $\text{S}$, there is always two ind...
admin
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Jan 12
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43
TIFR CSE 2024 | Part A | Question: 13
Let $n \geq 100$ be a positive integer. Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables, each taking values in the set $\{0,1\}$ such that $\operatorname{Pr}\left[X_{i}=1\right]=\frac{2}{3}$ for each $1 \leq i \leq n$ ... with respect to $x$. $0$ $n$ $\frac{2 n}{3}$ $\frac{4 n^{2}+2 n}{9}$ $\frac{4 n^{2}-4 n}{9}$
Let $n \geq 100$ be a positive integer. Let $X_{1}, X_{2}, \ldots, X_{n}$ be independent random variables, each taking values in the set $\{0,1\}$ such that $\operatornam...
admin
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Jan 12
Others
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44
TIFR CSE 2024 | Part A | Question: 14
Let $\text{A}$ and $\text{B}$ be two $n \times n$ invertible matrices with real entries such that every row in $\text{A}$ sums to $1$ and every row in $\text{B}$ sums to $2$ ... $\text{(iii)}$. Statements $\text{(i)}$ and $\text{(iii)}$ are true but not necessarily statement $\text{(ii)}$.
Let $\text{A}$ and $\text{B}$ be two $n \times n$ invertible matrices with real entries such that every row in $\text{A}$ sums to $1$ and every row in $\text{B}$ sums to ...
admin
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Jan 12
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TIFR CSE 2024 | Part A | Question: 15
Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only their own number and that it is different from the other one. The following conversation ensues ... was given $3$, Badri was given $4$. Asna was given $4$, Badri was given $3$. None of the above.
Suppose Michelle gives Asna and Badri two different numbers from $\mathbb{N}=\{1,2,3, \ldots\}$. It is commonly known to both Asna and Badri that they each know only thei...
admin
129
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Jan 12
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46
Made Easy Mock Test
Rohit Chakraborty
200
views
Rohit Chakraborty
asked
Jan 7
GATE
made-easy-test-series
programming-in-c
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47
Made Easy Test Series Mock Test
How to calculate the third option?
How to calculate the third option?
Rohit Chakraborty
198
views
Rohit Chakraborty
asked
Jan 7
GATE
made-easy-test-series
digital-logic
adder
multiple-selects
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1
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1
answer
48
made-easy
Rohit Chakraborty
143
views
Rohit Chakraborty
asked
Jan 7
GATE
made-easy-test-series
time-complexity
functions
multiple-selects
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49
can we write the same exam more than one time
Lokesh Budela
83
views
Lokesh Budela
asked
Jan 1
1
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0
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50
From where to practice questions for Data Science and AI paper of GATE 2024?
Which resources to follow to practice questions for DS and AI paper of GATE 2024? Which resources to follow? where to find them Questions for Mathematics and questions for AI? A bit of help on that would be much appreciated
Which resources to follow to practice questions for DS and AI paper of GATE 2024?Which resources to follow?where to find themQuestions for Mathematics and questions for A...
rajveer43
190
views
rajveer43
asked
Dec 10, 2023
GATE
gate-preparation
virtual-gate-test-series
cmi2022-datascience
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