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Recent questions tagged tifrmaths2012

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31
TIFR-2012-Maths-A: 1
True/False Question: If $H_{1}$ & $H_{2}$ are subgroups of a group $G$ then $H_{1} .H_{2}=\left \{ h_{1} h_{2}\in G \mid h_{1}\in H_{1},h_{2}\in H_{2}\right \}$ is a subgroup of $G$.
True/False Question:If $H_{1}$ & $H_{2}$ are subgroups of a group $G$ then $H_{1} .H_{2}=\left \{ h_{1} h_{2}\in G \mid h_{1}\in H_{1},h_{2}\in H_{2}\right \}$ is a subg...
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32
TIFR-2012-Maths-A: 2
True/False Question: There exist polynomials $f\left ( x \right )$ and $g\left ( x \right )$, with complex coefficients, such that $\left ( \frac{f\left ( x \right )}{g\left ( x \right )} \right )^{2}=x$.
True/False Question:There exist polynomials $f\left ( x \right )$ and $g\left ( x \right )$, with complex coefficients, such that $\left ( \frac{f\left ( x \right )}{g\le...
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33
TIFR-2012-Maths-A: 3
True/False Question: Let $f$ be real valued, differentiable on $\left ( a,b \right )$ and ${f}'\left ( x \right )\neq 0$ for all $x \in \left ( a,b \right )$. Then $f$ is $1-1$.
True/False Question:Let $f$ be real valued, differentiable on $\left ( a,b \right )$ and ${f}'\left ( x \right )\neq 0$ for all $x \in \left ( a,b \right )$. Then $f$ is ...
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34
TIFR-2012-Maths-A: 4
True/False Question: The inequality $\sum _{n=0}^{\infty }\frac{\left ( log \: log2 \right )^{n}}{n!}> \frac{3}{5}$ holds.
True/False Question:The inequality $\sum _{n=0}^{\infty }\frac{\left ( log \: log2 \right )^{n}}{n!} \frac{3}{5}$ holds.
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35
TIFR-2012-Maths-A: 5
True/False Question: Every subgroup of order $74$ in a group of order $148$ is normal.
True/False Question:Every subgroup of order $74$ in a group of order $148$ is normal.
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37
TIFR-2012-Maths-A: 7
True/False Question: The inequality $\sqrt{1+x}< 1+x/2$ for $x\in \left ( -1, 10 \right )$is true
True/False Question:The inequality$$\sqrt{1+x}< 1+x/2$$for $x\in \left ( -1, 10 \right )$is true
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38
TIFR-2012-Maths-A: 8
True/False Question: If $n$ is not a multiple of $23$ then the remainder when $n^{11}$ is divided by $23$ is $\pm 1$( mod $23$).
True/False Question:If $n$ is not a multiple of $23$ then the remainder when $n^{11}$ is divided by $23$ is $\pm 1$( mod $23$).
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39
TIFR-2012-Maths-A: 9
True/False Question: Suppose $A$ is a nilpotent matrix and $I$ is the identity matrix. Then $\left ( I+A \right )$ is invertible.
True/False Question:Suppose $A$ is a nilpotent matrix and $I$ is the identity matrix. Then $\left ( I+A \right )$ is invertible.
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40
TIFR-2012-Maths-A: 10
True/False Question: The equations $x_{1}+\frac{1}{2}x_{2}+\frac{1}{3}x_{3}=1$ $x_{1}+\frac{1}{4}x_{2}+\frac{1}{9}x_{3}=1$ $x_{1}+\frac{1}{8}x_{2}+\frac{1}{27}x_{3}=1$ has no solution.
True/False Question:The equations$$x_{1}+\frac{1}{2}x_{2}+\frac{1}{3}x_{3}=1$$$$x_{1}+\frac{1}{4}x_{2}+\frac{1}{9}x_{3}=1$$$$x_{1}+\frac{1}{8}x_{2}+\frac{1}{27}x_{3}=1$$h...
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