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A particle of mass m is at rest at the origin at time t = 0. It is subjected to a force F(t) = $F_{0}e_{−bt}$ in the $×$ dicection. Its speed v(t) is depicted by which of the following curves?

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The vapour pressure of water at $20_{2}C$ is 17.5 mm Hf. If 18 g of glucose $(C_{6}H_{12}O_{6})$ is added to 178.2 g of water at $20_{∘}C$, the vapour pressure of the resulting solution will be

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

The vector $a=αi^+2j^ +βk^$lies in the plane of the vectors $b=i^+j^ $and $c=j^ +k^$and bisects the angle between $b$and $c$. Then which one of the following gives possible values of $αandβ$?

Four species are listed below i. $HCO_{3}$ (ii) $ii<iii<i<iv$ iii. $HSO_{4}$ iv $HSO_{3}F$ Which one of the following is the correct sequence of their acid strength ?

The hydrocarbon which can react with sodium in liquid ammonia is

In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement -1: The number of different ways the child can buy the six ice-creams is $_{10}C_{5}$.Statement -2: The number of different ways the child can buy the six ice-creams is equal to thenumber of different ways of arranging 6 As and 4 Bs in a row.

Relative permittivity and permeability of a material are $ϵ_{r}andμ_{r}$, respectively. Which of the following values of these quantities are allowed for a diamagnetic material ?

A thin rod of length 'L' is lying along the x-axis with its ends at $x=0andx=L$. Its linear density (mass/length) varies with x as $k(Lx )_{n}$, where n can be zero or any positive number. If the position $x_{CM}$ of the centre of mass of the rod is plotted against 'n', which of the following graph best approximates the dependence of $x_{CM}$ on n ?