Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Recent questions in Exam Queries
0
votes
0
answers
21
TIFR Mathematics 2024 | Part A | Question: 8
Consider the sequence $\left\{a_{n}\right\}$ for $n \geq 1$ ... $\lim _{n \rightarrow \infty} n^{2} a_{n}$ exists and equals 1
Consider the sequence $\left\{a_{n}\right\}$ for $n \geq 1$ defined by\[a_{n}=\lim _{N \rightarrow \infty} \sum_{k=n}^{N} \frac{1}{k^{2}} .\]Which of the following statem...
admin
85
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
22
TIFR Mathematics 2024 | Part A | Question: 9
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function that is a solution to the ordinary differential equation \[ f^{\prime}(t)=\sin ^{2}(f(t))(\forall t \in \mathbb{R}), \quad f(0)=1 . \] ... is neither bounded nor periodic $f$ is bounded and periodic $f$ is bounded, but not periodic None of the remaining three statements is correct
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function that is a solution to the ordinary differential equation\[f^{\prime}(t)=\sin ^{2}(f(t))(\forall t ...
admin
90
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
23
TIFR Mathematics 2024 | Part A | Question: 10
Let $B$ denote the set of invertible upper triangular $2 \times 2$ matrices with entries in $\mathbb{C}$, viewed as a group under matrix multiplication. Which of the following subgroups of $B$ is the normalizer of itself in $\text{B}$ ...
Let $B$ denote the set of invertible upper triangular $2 \times 2$ matrices with entries in $\mathbb{C}$, viewed as a group under matrix multiplication. Which of the foll...
admin
111
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
24
TIFR Mathematics 2024 | Part A | Question: 11
What is the least positive integer $n>1$ such that $x^{n}$ and $x$ are conjugate, for every $x \in S_{11}$? Here, $S_{11}$ denotes the symmetric group on $11$ letters. $10$ $11$ $12$ $13$
What is the least positive integer $n>1$ such that $x^{n}$ and $x$ are conjugate, for every $x \in S_{11}$? Here, $S_{11}$ denotes the symmetric group on $11$ letters.$10...
admin
93
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
25
TIFR Mathematics 2024 | Part A | Question: 12
Consider the following statements: $\text{(A)}$ Let $G$ be a group and let $H \subset G$ be a subgroup of index 2 . Then $[G, G] \subseteq H$. $\text{(B)}$ Let $G$ be a group and let $H \subset G$ be a subgroup that contains the commutator subgroup ... false $\text{(A)}$ is true and $\text{(B)}$ is false $\text{(A)}$ is false and $\text{(B)}$ is true
Consider the following statements:$\text{(A)}$ Let $G$ be a group and let $H \subset G$ be a subgroup of index 2 . Then $[G, G] \subseteq H$.$\text{(B)}$ Let $G$ be a gro...
admin
112
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
26
TIFR Mathematics 2024 | Part A | Question: 13
For any symmetric real matrix $A$, let $\lambda(A)$ denote the largest eigenvalue of $A$. Let $S$ be the set of positive definite symmetric $3 \times 3$ real matrices. Which of the following assertions is correct? There exist $A, B \in S$ ... $\lambda(A+B)=\max (\lambda(A), \lambda(B))$ None of the remaining three assertions is correct
For any symmetric real matrix $A$, let $\lambda(A)$ denote the largest eigenvalue of $A$. Let $S$ be the set of positive definite symmetric $3 \times 3$ real matrices. Wh...
admin
93
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
27
TIFR Mathematics 2024 | Part A | Question: 14
Let $\theta \in(0, \pi / 2)$. Let $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ be the linear map which sends a vector $v$ to its reflection with respect to the line through $(0,0)$ and $(\cos \theta, \sin \theta)$. Then the ... $\left(\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right)$
Let $\theta \in(0, \pi / 2)$. Let $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ be the linear map which sends a vector $v$ to its reflection with respect to the line thr...
admin
80
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
28
TIFR Mathematics 2024 | Part A | Question: 15
For a polynomial $f(x, y) \in \mathbb{R}[x, y]$, let $X_{f}=\left\{(a, b) \in \mathbb{R}^{2} \mid f(a, b)=1\right\} \subset \mathbb{R}^{2}$. Which of the following statements is correct? If $f(x, y)=x^{2}+4 x y+3 y^{2}$, ... then $X_{f}$ is compact If $f(x, y)=x^{2}-4 x y-y^{2}$, then $X_{f}$ is compact None of the remaining three statements is correct
For a polynomial $f(x, y) \in \mathbb{R}[x, y]$, let $X_{f}=\left\{(a, b) \in \mathbb{R}^{2} \mid f(a, b)=1\right\} \subset \mathbb{R}^{2}$. Which of the following statem...
admin
79
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
29
TIFR Mathematics 2024 | Part A | Question: 16
What is the number of distinct subfields of $\mathbb{C}$ isomorphic to $\mathbb{Q}[\sqrt[3]{2}]$? $1$ $2$ $3$ Infinite
What is the number of distinct subfields of $\mathbb{C}$ isomorphic to $\mathbb{Q}[\sqrt[3]{2}]$?$1$$2$$3$Infinite
admin
85
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
30
TIFR Mathematics 2024 | Part A | Question: 17
Let $\mathbb{F}_{3}$ denote the finite field with 3 elements. What is the number of one dimensional vector subspaces of the vector space $\mathbb{F}_{3}^{5}$ over $\mathbb{F}_{3}$? $5$ $121$ $81$ None of the remaining three options
Let $\mathbb{F}_{3}$ denote the finite field with 3 elements. What is the number of one dimensional vector subspaces of the vector space $\mathbb{F}_{3}^{5}$ over $\mathb...
admin
109
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
31
TIFR Mathematics 2024 | Part A | Question: 18
For a positive integer $n$, let $a_{n}, b_{n}, c_{n}, d_{n}$ be the real numbers such that \[ \left(\begin{array}{ll} 1 & 1 \\ 1 & 0 \end{array}\right)^{n}=\left(\begin{array}{ll} a_{n} & b_{n} \\ c_{n} & ... the following numbers equals $\lim _{n \rightarrow \infty} a_{n} / b_{n}$ ? $1$ $e$ $3 / 2$ None of the remaining three options
For a positive integer $n$, let $a_{n}, b_{n}, c_{n}, d_{n}$ be the real numbers such that\[\left(\begin{array}{ll}1 & 1 \\1 & 0\end{array}\right)^{n}=\left(\begin{array}...
admin
86
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
32
TIFR Mathematics 2024 | Part A | Question: 19
Consider the complex vector space $V=\{f \in \mathbb{C}[x] \mid f$ has degree at most 50 , and $f(i x)=-f(x)$ for all $x \in \mathbb{C}\}$. Then the dimension of $V$ equals $50$ $25$ $13$ $47$
Consider the complex vector space$V=\{f \in \mathbb{C}[x] \mid f$ has degree at most 50 , and $f(i x)=-f(x)$ for all $x \in \mathbb{C}\}$.Then the dimension of $V$ equals...
admin
119
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
33
TIFR Mathematics 2024 | Part A | Question: 20
Let $S$ denote the set of sequences $a=\left(a_{1}, a_{2}, \ldots\right)$ of real numbers such that $a_{k}$ equals 0 or 1 for each $k$. Then the function $f: S \rightarrow \mathbb{R}$ defined by \[ f\left(\ ... }}{10}+\frac{a_{2}}{10^{2}}+\ldots \] is injective but not surjective surjective but not injective bijective neither injective nor surjective
Let $S$ denote the set of sequences $a=\left(a_{1}, a_{2}, \ldots\right)$ of real numbers such that $a_{k}$ equals 0 or 1 for each $k$. Then the function $f: S \rightarro...
admin
147
views
admin
asked
Jan 19
Others
tifrmaths2024
+
–
0
votes
0
answers
34
HEY ,Bad Request Your browser sent a request that this server could not understand. Size of a request header field exceeds server limit. Apache/2.4.41 (Ubuntu) Server at aptitude.gateoverflow.in Port 443
mih7r
133
views
mih7r
asked
Jan 15
0
votes
1
answer
35
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
403
views
admin
asked
Jan 12
Others
tifr2024
+
–
0
votes
1
answer
36
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
243
views
admin
asked
Jan 12
Others
tifr2024
+
–
0
votes
0
answers
37
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
131
views
admin
asked
Jan 12
Others
tifr2024
+
–
0
votes
1
answer
38
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
156
views
admin
asked
Jan 12
Others
tifr2024
+
–
0
votes
1
answer
39
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
197
views
admin
asked
Jan 12
Others
tifr2024
+
–
0
votes
0
answers
40
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
124
views
admin
asked
Jan 12
Others
tifr2024
+
–
Page:
« prev
1
2
3
4
5
6
7
...
80
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register