Instructions

For the following questions answer them individually

Question 22

Give below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : If the volumes of two cubes are in the ratio of 3:27 then their surface areas are in the ratio of 4:9.

Reason R : If the surface areas of two cubes are in the ratio $$S_1 : S_2$$, then their volumes are in the ratio $$S^{\frac{2}{3}}_1 : S^{\frac{2}{3}}_2$$

In the light of the above statements. choose the correct answer from the options given below :

Question 23

If the high and base radius of a cone are increased by 50% and 25% respectively then the ratio between the volume of a given cone and the new cone is

Question 25

If one root of quadratic equation $$2x^2 - 3x + (2k + 1) = 0$$ is five times the other then the value of k is:

Question 26

A sample of soil weighs 27.8 g and has a volume of 15.20 cm$$^3$$. If the dry mass of sample is 24.57 cm? and the specific gravity of soil grains is 2.7. its void ratio should be equal to ___________

Question 27

Identify the correct expression that may be used to determine the submerged unit weight ($$\gamma'$$) of soil. (V = Total volume of soil sample; $$V_s$$ = Volume of solids; $$\gamma_w$$ = Unit weight of water; $$\gamma_d$$ = Dry unit weight of soil; G = Specific gravity of soil grains)

Question 28

Given below are two statements:

Statement I : The gain in strength of soil with passage of time after it has been remoulded is called Thixotropy.

Statement II : Thixotropy indicates how much shear strength will be regained after a pile has been driven and left in place for some time.

In the light of the above statements, choose the correct answer from the options given below:

Question 29

Liquid limit, plastic limit and shrinkage limit for a soil sample are given as 40%. 25% and 12% respectively. If the natural water content of the soil is 28%. then the consistency index will be about ______________

Question 30

A sand deposit comprises of three distinct horizontal layers of equal thickness. The hydraulic conductivity of the topmost layer, middle layer and the third layer is 0.002 cm/s, 0.01 cm/s, and 0.001 cm/s respectively. The equivalent value of vertical hydraulic conductivity of this sand deposit is about _______________