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An alkali is titrated against an acid with methyl orange as indicator, which of the following is a correctcombination?

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The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

The normal to the curve, $x_{2}+2xy−3y_{2}=0,at(1,1)$:

In $S_{N}2$ reactions the corect order of reactivity for the following compound :

A projectile is given an initial velocity of $(i^+2j^ )m/s,$ where $i^$ is along the ground and $j^ $ is along the vertical. If $g=10m/s_{2},$ the equation of its trajectory is:

The integral $∫_{2}gx_{2}+g(36−12x+x_{2})dxgx_{2} $ is equal to:

The sum of first 9 terms of the series $11_{3} +1+31_{3}+2_{3} +1+2+31_{3}+2_{3}+3_{3} +.....$is

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by \displaystyle\frac{{{d}{P}}}{{{\left.{d}{x}\right.}}}={100}-{12}\sqrt{{{x}{\dot}}}If the firm employs 25 more workers, then the new level of production of items is

The set of all values of $λ$for which the system of linear equations : $2x_{1}−2x_{2}+x_{3}=λx_{1}$$2x_{1}−3x_{2}+2x_{3}=λx_{2}$$−x_{1}+2x_{2}=λx_{3}$has a non-trivial solution,