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#### Write laws of refraction. Explain the same with the help of ray diagram, when a ray of light passes through a rectangular glass slab.

Laws of refraction:

1. The incident ray, the normal to any refracting surface at the point of incidence, and the refracted ray all lie in the same plane called the plane of incidence or plane of refraction.
2. The ratio of the sine of the angle of incidence to the angle of refraction is always constant.

or

= refractive index of the second medium with respect to the first medium.

For a glass slab as shown in figure

i = angle of incidence

r1 = angle of reflection

$\frac{sini}{sinr_1}=\frac{\mu_g}{\mu_{air}}$

#### Two stones are thrown vertically upwards simultaneously with their initial velocities u1and u2 respectively. Prove that the heights reached by them would be in the ratio of u12 : u22 (Assume upward acceleration is –g and downward acceleration to be +g ).

The height reached by any stone can be calculated by using the third equation of motion.

$v^2=u^2+2as$

We can use the fact, that at the highest point the velocity will be zero. The acceleration due to gravity will retard the particles.

Therefore, the height raised for any particle will be given as:

$\\0^2=u^2+2as\\\Rightarrow h=\frac{u^2}{2g}$

Therefore

$\frac{h_1}{h_2}=\frac{u_1^2}{u_2^2}\\$

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#### Obtain a relation for the distance travelled by an object moving with uniform acceleration in the interval between 4th and 5th seconds.

Distance travelled in nth second by any particle is equal to the difference of distances travelled in n seconds and n -1 seconds.

For example. distance travelled in the fourth second is the difference of distance travel in four seconds and three seconds.

Hence, by using the second equation of motion we can find out the distance travelled in nth second.

If the initial velocity is zero,

In that case, the distance travelled in the fourth second and fifth second will be in the ratio of 7:9.

#### How are the activities of gastro-intestinal tract regulated?

Activities of digestive system regulate both Harmon and neural reflexes

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#### In which plant will you look for mycorrhiza and coralloid roots? Also, explain what these terms mean.

Mycorrhiza, which is also known as ‘fungus-root’, is basically a mutually beneficial relationship between that of plant root and a fungus. In most cases, the fungus grows within the roots of the plants and helps the plant to absorb water and nutrients, and in return, the plant provides the fungus with food. E.g., Pinus. In some cases, the fungus could be harmful to the plants.

Coralloid Roots: These roots are associated with nitrogen-fixing cyanobacteria. In coralloid roots, the nodules are formed in large numbers, in the roots giving them coralloid appearance. E.g. Cycas and plants of Leguminosae.

#### How are the male and female gametophytes of pteridophytes and gymnosperms different from each other

The size of gametophyte of of pteridophytes quite large compare  to gymnosperm's gametophytes. Gametophyte of pteridophytes are photosynthetic in nature while gametophyte of  gymnosperms are are not photosynthetic in nature

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#### Comment on the lifecycle and nature of a fern prothallus

Fern, which is a type of pteridophytes; reveals a haplo-diplontic state. In this situation, both the stages of gametophytic and sporophytic are multicellular. The diploid sporophyte is represented by a prepotent and independent, photosynthetic, vascular plant body. The haploid gametophyte, which is also independent in nature, but the duration of its life is shorter than that of the sporophytes.

#### Differentiate betweena. Bract and Bracteoleb. Pulvinus and petiolec. Pedicel and peduncled. Spike and spadixe. Stamen and staminoidf. Pollen and pollenium

Ans:

a. The bracteolate is found between the bract and flower while a bract is found towards the base of the pedicle.

b. Petiole is a subcylindrical stalk that connects the lamina with the leaf base while Pulvinus is a swollen leaf base which is found in leguminous plants.

c. The Peduncle is a stalk of the whole inflorescence while a pedicle is the stalk of a flower.

d. Spadix is covered by several large bracts known as spates while in spike sessile flowers are attached on an elongated peduncle.

e. Every stamen represents a male reproductive organ and androecium is composed of stamens. Staminode is a sterile stamen.

f. Polonium is defined as the group of pollen grains while a pollen is a male gametophyte of angiosperms.

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#### The rhizome of ginger is like the roots of other plants that grow underground. Despite this fact, ginger is a stem and not a root. Justify.

The rhizome of ginger is like the roots of other plants that grow underground. Despite this fact, ginger is a stem and not a root. Because ginger is not a root but steam as it has internodes and nodes that roots do not possess.

#### Tendrils of grapevines are homologous to the tendril of pumpkins but are analogous to that of a pea. Justify the above statement.

Tendrils of pumpkins are homologous to the tendrils of grapevines because both originate from the same part of the plan i.e., the stem despite having different functions. But the tendrils of grapevines and tendrils of pumpkins are analogous to that of a pea because the function of tendrils on pumpkin is to creep while in grapevines it is to climb.