If n = 1,2,3, ..., then 4 ... 2^ n-1 is equal to:

If the constant term in the binomial expansion of $\left(\sqrt{x}-\frac{k}{x^{2}}\right)^{10}$ is $405,$ then $|k|$ equals

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The sides of a quadrilateral are all positive integers and three of them are $5,10,20$. How many possible value are there for the fourth side?

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In the expansion of $(1 + x)^n.(1 + y)^n.(1 + z)^n$ the sum of the coefficients of the terms of degree $r$ is:

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The number of different signals which can be given from $6$ flags of different colours taking one or more at a time, is:

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The number of possible outcomes when a coin is tossed $6$ times is.

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If the coefficient of $4^{th}$ term in the expansion of ${(a + b)^n}$ is $56$, then $n$ is

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Let $S_n$ be the sum of all integers $k$ such that $2^n < k < 2^{n+1}$, for $n \geq 1$. Then,$9$ divides $S_n$ if and only if

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If ${x^2} - hx - 21 = 0,{x^2} - 3hx + 35 = 0$$(h > 0)$ has a common root, then the value of $h$ is equal to

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For the lines $2x + 5y = 7$and $2x - 5y = 9,$which of the following statement is true

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$\mathop {\lim }\limits_{x \to 0} \frac{{\tan x - \sin x}}{{{x^3}}} = $

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Answer