class 12

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JEE Main

Among the following, correct statement is :

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The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is :

A solid body of constant heat capacity $J/_{∘}C$ is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. (ii) Sequentially keeping in contact 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature $100_{∘}C$ to final temperature $200_{∘}C$. Entropy change of the body in the two cases respectively is :

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $σ$ at equilibrium position. The extension $x_{0}$ of the spring when it is in equilibrium is:

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

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$and $l_{2}=m_{2}+n_{2}$is

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement- I: Higher the range, greater is the resistance of ammeter. Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

If $∫f(x)dx=ψ(x)$, then $∫x_{5}f(x_{3})dx$is equal to

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: