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Ask QuestionPosted by Khilesh Maskare 1 year, 8 months ago
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Preeti Dabral 1 year, 8 months ago
The Venn diagram for {tex}(A \cap B)'{/tex}The shaded portion represents {tex}(A \cap B)'{/tex}
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Preeti Dabral 1 year, 8 months ago
Certain pteridophytes produce two kinds of spores. This phenomenon is called heterospory.
Heterospory is the crucial step in evolution. This ultimately led to seed development in gymnosperms and angiosperms.
Examples: Selaginella, Salvinia.
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Preeti Dabral 1 year, 10 months ago
धनराम मोहन को अपना प्रतिद्वंद्वी इसलिए नहीं समझता था क्योंकि वह जानता था कि मोहन एक बुद्धिमान लड़का है। वह मास्टर जी के कहने पर ही उसको सजा देता था। धनराम मोहन के प्रति स्नेह और आदर का भाव रखता था। शायद इसका एक कारण यह था कि बचपन से ही उसके मन में जातिगत हीनता की भावना बिठा दी गई थी
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Preeti Dabral 1 year, 11 months ago
The title of the chapter ‘The Birth’ is perfect. The theme of the story is about a young doctor, Andrew dealing with a critical birth case. The baby is born lifeless. He takes certain decisions that prove quite successful. Not only he succeeds in saving the mother who is in critical condition after the delivery, but also succeeds in reviving the child. So the baby born lifeless is born again owing to the efforts of the dedicated doctor. Hence the title is perfectly appropriate and justified.
Posted by Op Ankit 1 year, 11 months ago
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Preeti Dabral 1 year, 11 months ago
{tex}\begin{aligned} & \text { Let } y=f(x)=\operatorname{cosec} x \\ & \therefore f(x+h)=\operatorname{cosec}(x+h) \\ & \therefore \frac{d y}{d t}=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\ & =\lim _{h \rightarrow 0} \frac{\operatorname{cosec}(x+h)-\operatorname{cosec} x}{h} \\ & =\lim _{h \rightarrow 0} \frac{1}{h}\left[\frac{1}{\sin (x+h)}-\frac{1}{\sin x}\right] \\ & =\lim _{h \rightarrow 0} \frac{\sin x-\sin (x+h)}{h \cdot \sin x \cdot \sin (x+h)} \\ & =\lim _{h \rightarrow 0} \frac{2 \cos \left(\frac{2 x+h}{2}\right) \sin \left(-\frac{h}{2}\right)}{h \cdot \sin x \sin (x+h)} \\ & =-\lim _{h \rightarrow 0} \frac{\cos \left(x+\frac{h}{h}\right)}{\sin x \cdot \sin (u+h)} \cdot \lim _{h \rightarrow 0} \frac{\sin \frac{h}{2}}{h / 2} \\ & =-\frac{1 \cos x}{\sin x \cdot \sin x} \cdot \lim _{z \rightarrow 0} \frac{\sin z}{z} \\ & {\left[z=\frac{h}{2} \text {; Then, } z \rightarrow 0 \text { when } \Rightarrow h \rightarrow 0\right]} \\ & =\frac{-\cos x}{\sin x \cdot \sin x} \cdot 1 \\ & =-\frac{\cos x}{\sin x} \cdot \frac{1}{\sin x} \\ & =-\operatorname{cosec} x . \cot x \\ & \therefore \frac{d y}{d x}=-1 \operatorname{csec} x \cdot \cot x \\ & \end{aligned}{/tex}
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Preeti Dabral 1 year, 8 months ago
This statement was made by Rajendra to Prof. Gaitonde in the text The Adventure by Jayant Vishnu Narlikar. Rajendra made this statement in the context of Prof. Gaitonde experiencing a different version of the outcome of the Battle of Panipat. Prof Gaitonde was a historian and he was invited in a seminar to speak on the Battle of Panipat. He was to make a point that if in the battle of Panipat the Marathas emerged victorious then what would have happened. Interestingly, Prof. Gaitonde happened to experience the very hypothesis as reality. He entered a different level of consciousness and was witnessing events like the Battle of Panipat in an altogether different version. In the History books, the Marathas are mentioned as being a loser in the battle but in his experience, the Marathas emerged victoriously. Prof. Gaitonde was unable to understand this phenomenon. It is in this context, Rajendra tried to offer a scientific explanation to rationalize Prof. Gaitonde's experience. He meant to say that what Prof. Gaitonde experienced was not imaginative or fantastic but was also real. He tried to explain this in light of the catastrophic theory. According to this theory, there can be many alternative realities simultaneously existing. An observer sees only one of the alternatives. By applying this theory, Rajendra tried to explain the outcome of the Battle of Panipat as revealed to Prof. Gaitonde. The catastrophic theory has been developed by observing the outcome of experiments on small systems like atom and their constituent particles. The behavior of these systems cannot be predicted definitely even if all the physical laws governing those systems are known.
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