JEE 2020: Weekly Quiz 10 (14.07.2019) for JEE & BITSAT Exams

Question 1

Select the interval for which

satisfies Rolle’s theorem.

Question 2

If the function

follows Rolle’s Theorem in the range

, find the value of c.

Question 3

For which interval Rolle’s theorem is valid for

?

Question 4

If

satisfies Rolle’s theorem in

,find the value of a,b. The total of a and b is 9.

Question 5

Find the value of c for which

holds Rolle’s Theorem in the interval

.

Question 6

If Rolle's theorem for f(x) = e^x (sinx - cosx) is verified on [π/4 , 5π/4] then the value of c is

Question 7

The coordinates of the feet of normals drawn from the point (14,7) to the curve y² – 16x – 8y = 0 are

Question 8

The curves a

+ b

= 1 and c

+ d

= 1 cut each other orthogonally if,

Question 9

Slopes of tangents through (7,1) to the circle

+

= 25 satisfy the equation

Question 10

The sum of the squares of the intercepts on the axes of the tangent at any point on the curve

is

Question 11

The dissociative chemisorptions of X₂ (g) on a metal surface follows Langmuir adsorption isotherm. The ratio of the rate constant of the adsorption and desorption processes is 9 atm^-1. The fractional surface coverage of X(adsorbed) at 1.0 atm pressure is:

Question 12

At 273K and 10 bar the Langmuir adsorption of as gas on a solid surface gave the fraction of surface coverage as 0.01. The Langmuir adsorption isotherm constant___________ bar^-1

Question 13

In the freundlich adsorption isotherm, the y-intercept of log(x/m) - log(c) graph turns out to be
(Here, x = mass of adsorbate, m = mass of adsorbent, p = Equilibrium pressure of adsorbate, c = Equilibrium concentration of adsorbate in solution):

Question 14

Select correct statement from the following -

Question 15

Which of the following is a lyophilic colloid

Question 16

Adsoption of CO charcoal at 273K follow Langmuir isotherm. A plot of p (kPa)/V (cm³) versus p (kPa) is linear with a slope of 0.01 and y- intercept of 0.5. The equilibrium constant, K(kPa^-1), for the adsorption is :

Question 17

The values of ΔH and ΔS for the reaction, C_(graphite) +CO₂(g)→2CO(g) are 170 kJ and 170 JK^-1, respectively. This reaction will be spontaneous at

Question 18

Standard entropies of X₂, Y₂ and XY₃ are 60, 40 and 50JK^-1mol^-1 respectively. For the reaction

to be at equilibrium, the temperature should be

Question 19

Which one of the following is a free radical substitution reaction?

Question 20

Different quantities are used to determine whether a reaction is spontaneous or not. The quantity that helps us to connect the energy released during a reaction to its degree or disorderness is:

Question 21

If 𝒱_rms = root mean square speed of molecules,

𝒱_av = average speed of molecules.

𝒱_mp = most probable speed of molecules,

𝒱 = speed of sound in a gas

Then, identify the correct relation between these speeds.

Question 22

If one mole of a monatomic gas (γ = 5/3) is mixed with one mole of a diatomic gas (γ = 7/5), the value of γ for the mixture is :

Question 23

Which of the following quantities is the same for all ideal gases at the same temperature ?

Question 24

When an ideal diatomic gas is heated at constant pressure the fraction of the heat energy supplied which increases the internal energy of the gas is:

Question 25

For a solid with a small expansion coefficient,

Question 26

Fig shows a process on a gas in which pressure and volume both change. The molar heat capacity for this process is C.

Question 27

For an ideal gas, the heat capacity at constant pressure is larger than that at constant volume because

Question 28

The molar heat capacity for the process shown in fig. is

Question 29

Four curves A, B, C and D are drawn in the fig. for a given amount of gas. The curves which represent adiabatic and isothermal changes are

Question 30

In the following P-V diagram of an ideal gas, two adiabates cut two isotherms at T₁ and T₂. The value of V_B/V_C is

AB → T₁, DC → T₂