If m, n are any two odd positive integer with n< m,then the largest positive integers which divides all the numbers of the type m^2 - n^2 is:

If m, n are any two odd positive integer with n< m,then the large…

If the sum of the coefficients in the expansion of $(x - 2y + 3 z)^n,$ $n \in N$ is $128$ then the greatest coefficie nt in the exp ansion of $(1 + x)^n$ is

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The value of $\mathop {\lim }\limits_{x \to 0} \,\frac{{(1 - \cos 2x)\sin 5x}}{{{x^2}\sin 3x}}$ is

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Let $\alpha $ and $\beta $ are roots of $5{x^2} - 3x - 1 = 0$ , then $\left[ {\left( {\alpha + \beta } \right)x - \left( {\frac{{{\alpha ^2} + {\beta ^2}}}{2}} \right){x^2} + \left( {\frac{{{\alpha ^3} + {\beta ^3}}}{3}} \right){x^3} -......} \right]$ is

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A relation $\phi$ from C to R is defined by $\text{x }\phi\text{ y}\Leftrightarrow|\text{x}|=\text{y}.$ Which one is correct?

$(2+3\text{i})\ \phi\ 13$
$3\phi\ (-3)$
$(1+\text{i})\ \phi\ 2$
$\text{i}\ \phi\ 1$

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${6^{th}}$ term in expansion of ${\left( {2{x^2} - \frac{1}{{3{x^2}}}} \right)^{10}}$ is

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p ∧ (q ∧ r) is logically equivalent to.

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Let $A=\{1,2,3, \ldots .7\}$ and let $P(1)$ denote the power set of $A$. If the number of functions $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{P}(\mathrm{A})$ such that $a \in \mathrm{f}(\mathrm{a}), \forall \mathrm{a} \in \mathrm{A}$ is $\mathrm{m}^{\mathrm{n}}, \mathrm{m}$ and $\mathrm{n} \in \mathrm{N}$ and $\mathrm{m}$ is least, then $\mathrm{m}+\mathrm{n}$ is equal to__________.

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In the expansion of the following expression $1 + (1 + x) + {(1 + x)^2} + ..... + {(1 + x)^n}$ the coefficient of ${x^k}(0 \le k \le n)$ is

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If $a + 2b + 3c = 6$, then the greatest value of $abc^2$ is (where $a,b,c$ are positive real numbers)

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A point equidistant from the lines $4x + 3y + 10 = 0$, $5x - 12y + 26 = 0$ and $7x + 24y - 50 = 0$ is

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