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Recent questions tagged isi2015-mma
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91
ISI2015-MMA-91
Suppose a solution of the differential equation $(xy^3+x^2y^7)\frac{\mathrm{d} y}{\mathrm{d} x}=1,$ satisfies the initial condition $y(1/4)=1$. Then the value of $\dfrac{\mathrm{d} y}{\mathrm{d} x}$ when $y=-1$ is $\frac{4}{3}$ $- \frac{4}{3}$ $\frac{16}{5}$ $- \frac{16}{5}$
Suppose a solution of the differential equation $$(xy^3+x^2y^7)\frac{\mathrm{d} y}{\mathrm{d} x}=1,$$ satisfies the initial condition $y(1/4)=1$. Then the value of $\dfra...
Arjun
258
views
Arjun
asked
Sep 23, 2019
Others
isi2015-mma
differential-equation
non-gate
+
–
0
votes
3
answers
92
ISI2015-MMA-92
Consider the group $G=\begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{-1} \end{pmatrix} : a,b \in \mathbb{R}, \: a>0 \end{Bmatrix}$ ... is of finite order $N$ is a normal subgroup and the quotient group is isomorphic to $\mathbb{R}^+$ (the group of positive reals with multiplication).
Consider the group $$G=\begin{Bmatrix} \begin{pmatrix} a & b \\ 0 & a^{-1} \end{pmatrix} : a,b \in \mathbb{R}, \: a>0 \end{Bmatrix}$$ with usual matrix multiplication. Le...
Arjun
1.4k
views
Arjun
asked
Sep 23, 2019
Set Theory & Algebra
isi2015-mma
group-theory
subgroups
normal
non-gate
+
–
3
votes
1
answer
93
ISI2015-MMA-93
Let $G$ be a group with identity element $e$. If $x$ and $y$ are elements in $G$ satisfying $x^5y^3=x^8y^5=e$, then which of the following conditions is true? $x=e, \: y=e$ $x\neq e, \: y=e$ $x=e, \: y \neq e$ $x\neq e, \: y \neq e$
Let $G$ be a group with identity element $e$. If $x$ and $y$ are elements in $G$ satisfying $x^5y^3=x^8y^5=e$, then which of the following conditions is true?$x=e, \: y=e...
Arjun
906
views
Arjun
asked
Sep 23, 2019
Set Theory & Algebra
isi2015-mma
group-theory
+
–
0
votes
1
answer
94
ISI2015-MMA-94
Let $G$ be the group $\{\pm1, \pm i \}$ with multiplication of complex numbers as composition. Let $H$ be the quotient group $\mathbb{Z}/4 \mathbb{Z}$. Then the number of nontrivial group homomorphisms from $H$ to $G$ is $4$ $1$ $2$ $3$
Let $G$ be the group $\{\pm1, \pm i \}$ with multiplication of complex numbers as composition. Let $H$ be the quotient group $\mathbb{Z}/4 \mathbb{Z}$. Then the number of...
Arjun
810
views
Arjun
asked
Sep 23, 2019
Set Theory & Algebra
isi2015-mma
group-theory
non-gate
+
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