Let g(x) = 1 + x - [x] and f(x) = l - 1, ;x 0 .then for all x, ;f(g(x)) is equal to

Let g(x) = 1 + x - [x] and f(x) = l - 1, ;x < 0 0, ; ;x = 0, ; 1,…

If $f(x) = x^4+ \lambda x^3 +x^2$ $(\lambda \in R)$ has local maximum at $\frac{1}{2} ,$ then absolute minimum value of $f(x)$ is -

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The sum of all positive integers $n$ for which $\frac{1^3+2^3+\ldots+(2 n)^3}{1^2+2^2+\ldots+n^2}$ is also an integers is

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The sum to $20$ terms of the series $2.2^2-3^2+2.4^2-5^2+2.6^2-\ldots \ldots$ is equal to $........$.

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If $< {a_n} >$ is an $A.P$. and $a_1 + a_4 + a_7 + .......+ a_{16} = 147$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to

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Let $[x]$ denote the largest integer not exceeding $x$ and $\{x\}=x-[x]$. Then, $\int \limits_0^{2012} \frac{e^{\cos (\pi\{x\})}}{e^{\cos (\pi\{x\})}+e^{-\cos (\pi\{x\})}} d x$ is equal to

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The unit vector perpendicular to the vectors $6i + 2j + 3k$ and $3i - 6j - 2k,$ is

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If the $9^{th}$ term of an $A.P.$ be zero, then the ratio of its $29^{th}$ and $19^{th}$ term is

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${\cot ^{ - 1}}\left[ {\frac{{\sqrt {1 - \sin x} + \sqrt {1 + \sin x} }}{{\sqrt {1 - \sin x} - \sqrt {1 + \sin x} }}} \right] = $

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The temperature $T(t)$ of a body at time $t = 0$ is $160^{\circ} F$ and it decreases continuously as per the differential equation $\frac{ dT }{ dt }=- K ( T -80)$, where $K$ is positive constant. If $T (15)=120^{\circ} F$, then $T(45)$ 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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STD 12 - 1. relation and function — JEE STD 11 Science — Question

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