Class 11th

An ideal gas is a theoretical or hypothetical gas that obeys the ideal gas law perfectly. That is, PV=nRT. 

Vernier calipers are instruments for making accurate linear measurements. They are commonly used to measure the diameter of a sphere or the depth of a hole. Its precision comes from a sliding Vernier scale that runs along a fixed main scale. 

There are two types of errors in measurements. One is a systematic error, which comes from a fault in the measuring device. The other is a random error in measurement, which is caused by a sudden change in the environment.  

$36x^2+36y^2-108x+120y+c=0$

$\Rightarrow x^2+y^2-3x+\frac{10}{3}y+\frac{c}{36}=0$              

The circle not interesting either axes

$\therefore g^2<c\&f^2<c$               

  $\Rightarrow \frac{9}{4}<\frac{c}{36}\Rightarrow c>81-\left(i\right)\&\frac{25}{9}<\frac{c}{36}\Rightarrow c>100......\left(ii\right)$            

(i)  $\cap$ (ii) -> c > 100 .(iii)

Point of intersection between x – 2y – 4 = 0 & 2x – y – 5 = 0 is (2 - 1) lies inside the circle.

$\therefore 4+1-6-\frac{10}{3}+\frac{c}{36}<0\Rightarrow c<156.......\left(iv\right)$         

-> $\left(iii\right)\cap \left(iv\right)$ 100 < c < 156

Strength = 0.72 g/L

Using ;

$Molarity=\frac{Strength}{Molarmassofsolute}$              

$M=\frac{0.72}{180}M$              

= 4 * 10^-3 M

Ans. is 4.

Theoretically; 1 mol benzene gives 1 mol toluene

Moles of benzene = $\frac{10}{78}mol$

Moles of toluene (Theoretical) = $\frac{10}{78}mol$

Mole of toluene (observed) = $\frac{9.2}{92}=0.1mol$

% yield = $\frac{0.1}{\frac{10}{78}}*100$

= 78%

Acyclic isomers of pentene are :-

So; total isomers are 6

K_p = 47.9      T = 288 K

K_C =?                    R = 0.083 L bar/K mol

$N_2{O}_4\left(g\right)?2N{O}_2\left(g\right)$           

Using

$K_p=K_C{\left(RT\right)}^{\Delta ng}$              

Here ;

$\Delta ng=1$                

49.7 = K_C (0.083 * 288)¹

K_C = 2

Sign conventions are important because all kinematic variables can be positive or negative. You must first choose your coordinate system and positive direction, then consistently apply signs. For example, if you are choosing upward as positive in free-fall problems, gravity becomes negative (a = -g), upward initial velocity is positive, and downward displacement is negative. The equations of motion work for any situation, as long as you substitute values with proper signs. Incorrect conventions lead to wrong answers.