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Experimentally it was found that a metal oxide has formula $M_{0.98}O.$ Metal M, is present as $M_{2+}andM_{3+}$ in its oxide. Fraction of the metal which exists as $M_{3+}$ would be:

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Let $α$and $β$be the roots of equation $x_{2}−6x−2=0$. If $a_{n}=α_{n}−β_{n},forn≥1$, then the value of $2a_{9}a_{10}−2a_{8} $is equal to:

Arrange the following compounds in order of decreasing acidity:

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

The standard Gibbs energy change at 300 K for the reaction $2A⇔B+C$ is $2494.2J.$ At a given time, the composition of the reaction mixture is $[A]=21 ,[B]=2and[C]=21 .$ The reaction proceeds in the : $[R=8.314J/K/mol,e=2.718]$

A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of $CO_{2}.$ The empirical formula of the hydrocarbon is:

Let a and b be the roots of equation $px_{2}+qx+r=0,p=0.$. If p, q, r are in A.P. and $α1 +β1 =4$, then the value of $∣α−β∣$ is

If the vectors $AB=3i^+4k^$ and $AC=5i^−2j^ +4k^$are the sides of a triangle ABC, then the length of the median through A is

If z is a complex number of unit modulus and argument q, then $arg(1+z1+z )$equal