Evaluate the following limit: _ x 2 a^ -a^ -

How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?

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Prove that: $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$

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Find the number of non-zero integral solutions of the equation ${\left| {1 - i} \right|^x} = {2^x}$.

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Find the equation of hyperbola having Foci $(\pm 4, 0)$ and the latus rectum is of length $12.$

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Find the equation of the parabola with focus $(2, 0)$ and directrix $x = – 2.$

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Differentiate the following function with respect to $\text{x}$:$\text{x}^3\text{e}^\text{x}$

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If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B= {2, 3, 5, 7}, verify that: (A $\cup$ B)' = A' $\cap$ B'

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A card is drawn at random from a pack of 52 cards, find the probability that the card drawn is:
A black king.

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In a single throw of a die describe the following events:
E = Getting an even number greater than 4

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A bag contains 2 red and white balls. three balls are drawn at random. find the probability that:
All the three balls are red.

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Answer