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Recent questions tagged tifrmaths2011

4 votes
3 answers
31
TIFR-2011-Maths-A-10
Let $m \leq n$ be natural numbers. The number of injective maps from a set of cardinality m to a set of cardinality $n$ is $m!$ $n!$ $(n − m)!$ None of the above
Let $m \leq n$ be natural numbers. The number of injective maps from a set of cardinality m to a set of cardinality $n$ is $m!$$n!$ $(n − m)!$ None of the above
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1 votes
1 answer
33
TIFR-2011-Maths-A-8
The sum of the squares of the roots of the cubic equation $x^{3}-4x^{2}+6x+1$ is 0. 4. 16. none of the above
The sum of the squares of the roots of the cubic equation $x^{3}-4x^{2}+6x+1$ is0. 4.16. none of the above
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4 votes
1 answer
34
TIFR-2011-Maths-A-7
The equation $x^{22}\equiv 2$ $\mod 23$ has No solutions $23$ solutions Exactly one solution $22$ solutions
The equation $x^{22}\equiv 2$ $\mod 23$ hasNo solutions$23$ solutionsExactly one solution$22$ solutions
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1 votes
0 answers
35
TIFR-2011-Maths-A-6
The function $f_{n}(x)= n \sin (x/n)$ Does not converge for any $x$ as $n \rightarrow \infty$ Converges to the constant function $1$ as $n \rightarrow \infty$ Converges to the function $x$ as $n \rightarrow \infty$ Does not converge for all $x$ as $n \rightarrow \infty$
The function $f_{n}(x)= n \sin (x/n)$Does not converge for any $x$ as $n \rightarrow \infty$Converges to the constant function $1$ as $n \rightarrow \infty$Converges to t...
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2 votes
1 answer
36
TIFR-2011-Maths-A-5
The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions Infinite number of solutions
The differential equation$\frac{dy}{dx}= y^{1/3}, y(0)=0$ hasA unique solutionNo nontrivial solution Finite number of solutionsInfinite number of solutions
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2 votes
1 answer
37
TIFR-2011-Maths-A-4
The groups $Z_{9}$ and $Z_{3} \times Z_{3}$ are Isomorphic Abelian Non abelian Cyclic
The groups $Z_{9}$ and $Z_{3} \times Z_{3}$ are Isomorphic AbelianNon abelianCyclic
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4 votes
1 answer
38
TIFR-2011-Maths-A-3
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ has An eigenvalue which is purely imaginary At least one real eigenvalue At least two eigenvalues which are not real At least $2$ distinct real eigenvalues
Let $A$ be a $5 \times 5$ matrix with real entries, then $A$ hasAn eigenvalue which is purely imaginaryAt least one real eigenvalueAt least two eigenvalues which are not ...
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1 votes
2 answers
39
TIFR-2011-Maths-A-2
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals. $1$ $0$ $\infty$ Oscillates
$\lim_{x \rightarrow 0} \sin \left(1/x^{2}\right)$ equals.$1$$0$$\infty$Oscillates
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1 votes
2 answers
40
TIFR-2011-Maths-A-1
Consider the sequence $\left \{x_{n} \right \}$ defined by $x_{n}=\frac{\left[nx\right]}{n}$ for $x \in \mathbb{R}$ where $[·]$ denotes the integer part. Then $\left \{x_{n} \right \}$ Converges to $x.$ Converges but not to $x.$ Does not converge Oscillates
Consider the sequence $\left \{x_{n} \right \}$ defined by $x_{n}=\frac{\left[nx\right]}{n}$ for $x \in \mathbb{R}$ where $[·]$ denotes the integer part. Then $\left \{...
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