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Recent questions tagged tifrmaths2019

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TIFR-2019-Maths-A: 11
Let $f$ be a continuous function on $\left [ 0,1 \right ]$. Then the limit $\underset{n\rightarrow \infty }{lim}\int ^{1}_{0}nx^{n} f\left ( x \right )dx$ is equal to $f(0)$ $f(1)$ $\underset{x\in\left [ 0,1 \right ]}{sup} f\left ( x\right )$ The limit need not exist
Let $f$ be a continuous function on $\left [ 0,1 \right ]$. Then the limit $\underset{n\rightarrow \infty }{lim}\int ^{1}_{0}nx^{n} f\left ( x \right )dx$ is equal to $f(...
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36
TIFR-2019-Maths-A: 16
The number of ring homomorphisms from $\mathbb{Z}\left [ x,y \right ]$ to $\mathbb{F}_{2}\left [ x \right ]/\left ( x^{3}+x^{2}+x+1 \right )$ equals $2^{6}$ $2^{18}$ $1$ $2^{9}$
The number of ring homomorphisms from $\mathbb{Z}\left [ x,y \right ]$ to $\mathbb{F}_{2}\left [ x \right ]/\left ( x^{3}+x^{2}+x+1 \right )$ equals $2^{6}$$2^{18}$$1$$2^...
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39
TIFR-2019-Maths-A: 19
Let $C^{\infty }\left ( 0,1 \right )$ stand for the set of all real-valued functions on $\left ( 0,1 \right )$ ... given by $f \mapsto f+\frac{df}{dx}$ is injective but not surjective surjective but not injective neither injective nor surjective both injective and surjective
Let $C^{\infty }\left ( 0,1 \right )$ stand for the set of all real-valued functions on $\left ( 0,1 \right )$ that have derivatives of all orders. Then the map $C^{\inft...
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40
TIFR-2019-Maths-A: 20
A stick of length $1$ is broken into two pieces by cutting at a randomly chosen point. What is the expected length of the smaller piece? $1/8$ $1/4$ $1/e$ $1/\pi$
A stick of length $1$ is broken into two pieces by cutting at a randomly chosen point. What is the expected length of the smaller piece?$1/8$$1/4$$1/e$$1/\pi$
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