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(i) 250ºC — Gas 

(ii) 100ºC — Gas 

(iii) 0ºC — Solid

Modern Periodic Law states that properties of elements are a periodic function of their atomic number. 

In Modern Periodic Table there are18 groups and 7 periods.

Following are the characteristics of the images formed by plane mirrors

• : Size of image is equal to size of object. 
• Image formed is erect. 
• Image formed is virtual. 
•  Image is laterally inverted. 
•  Object distance is equal to image distance.

Charcoal is obtained from wood by destructive distillation of wood. Charcoal is considered a better fuel than wood because 

(i) it has higher calorific value than wood. 

(ii) it does not produce any smoke on burning.

(B) Negative

r = 21 cm

h  = 28 cm

(a) Volume of 1 toy = Volume of cone + Volume of hemisphere

\(=\frac13\pi r^2h+\frac23\pi r^3\)

\(= \frac13\pi r^2(h + 2r)\)

\(= \frac13 \times\frac{22}{7}\times 21\times21\,(28 + 42)\)

= 462 x 70

 = 32340 cm³

\(\therefore\) Volume of 50 toys  = 32340 x 50 cm³ = 1617000 cm³

(b) \(\frac{Volume \,of\, hemisphere}{Volume \, of \, circle} =\cfrac{\frac23\pi r^3}{\frac13\pi r^2h}\)

\(=\frac{2r}{h}\)

\(=\frac{2\times21}{28}\)

\(=\frac32\)

= 3 : 2

Hence, required ratio is 3 : 2.

(a) \(\because N = \sum f_i = 50\) 

\(\frac N 2 = 25\)

Cumulative frequency which is just greater than 25 is 26.

\(\therefore\) 120 - 140 is median class

\(\therefore\) l = 120

cf = 12

f = 14

h = 20

\(\therefore\) Median = \(l + \cfrac{\frac N2-cf}{f}\times h\) 

\(=120 + \frac{25 - 12}{14}\times 20\)

\(=120 + \frac{13}{14}\times 20\)

= 120 + 18.57

= 138.57

\(\therefore\) Median distance travelled by bus = 138.57 Km

(b) Mean = \(\frac{\sum f_Ix_i}{\sum x_i}\)

\(= \frac{7260}{50}\)

\(= \frac{726}{5}\)

= 145.2 

\(\therefore\) Mean distance travelled by bus = 145.2 Km

Decreasing at rate of 72 units/sec.

The smallest prime number is 2 and the smallest composite number is 2².

Hence, required HCF (2², 2) = 2

The value of k is -3/2.

The value of k is 2.

Let  p(x)=x²-2kx-6=0

x = 3 is one root of the quadratic equation

So, Remainder = p(3) = 0

p(3) =0

(3)²-2k(3)-6=0

-6k=-3

So, k=3/6=1/2

so, k=1/2

Smallest prime number = 2 

Smallest composite number = 4 

2 = 2 × 1 

4 = 2 × 2 

HCF (2, 4) = 2

Therefore the HCF of smallest prime number and smallest composite number is 2.

If one root of the equation (݇k -1)x² -10x + 3 = 0 is the reciprocal of the other, then the value of ݇is 4.

(d) the ghost materialising in sections. 

Offsprings produced through asexual reproduction are genetically identical to each other as well as to their parents, while sexually produced offsprings show genetic variations leading to evolution.

R₁ → R₁ – R₂, R₂ → R₂ – R₃ 

Taking (x – y),(y – z) common from R₁ and R₂ 

Then R₁ → R₁ – R₂, R₃ → R₃ – zR₂ 

Then taking (x – z) common from R₁ and expand.

P(4 Heads) 6 Tails

= ¹⁰C₄(1/2)⁴.(1/2)⁶

= 210/2¹⁰ = 105/512

Bt-toxin occurs as an inactive toxin and it is converted into an active toxin due to alkaline pH of the gut which solubilise the crystals. The activated toxin creates pores in the midgut epithelial cells by lysing that causes death of the insect.

C= 1 x 10^-6 

V = 10 

q = CV 

= 1 x 10^-6 x 10 

= 10^-5

The two main reasons to harness non-conventional sources of energy are: 

(i) As, fossil fuels like coal, petroleum, are present in a limited amount which and are likely to finish one day so the need for alternative sources of energy is essential. 

(ii) Use of conventional sources of energy (coal, petroleum etc.)

The angle is 60°.

Properties of electromagnetic waves :

1. Transverse nature
2. Does not get deflected by electric fields or magnetic fields.
3. Same speed in vacuum for all waves.
4. No material medium is required for propagation.
5. They get refracted, diffracted and polarised.

Electric charges present on a plane, kept normal to the direction of propagation of an em waves can be set and energy and momentum from the waves.

Correct Option (b) 24 × 10⁶ Ω ± 10%

When a ball is dropped from a height. Its speed continuously increased due to force of gravity (accelertion due to gravity increase on coming downwards).

When we stop pedalling a bicycle, its speed slows down due to air resistance and force of friction between type of bicycle and surface of road. So retardation force is created which stop the bicycle.

This is because  as gas expands the volume increases, so pressure decreases as (P_V)initial = (P_V)final. So the gas flow so fast that it doesn't get time to interact with moleciles.

Market value is the price at which the bond is traded in the stock exchange.

d) the market price per share of the firm's common stock

In the Discounting technique , the future value of all cash inflow at the end of time horizon at a particular rate of interest is calculated. 

b) maximize the value of the firm's common stock. 

Capitalisation of a firm refers to the composition of its long-term funds and its capital structure.

(c) Rs. 0.50 

A(n) shareholder would be an example of a principal, while a(n) manager would be an example of an agent.

c) the creation of value for shareholders. 

d) individuals buying and selling the stock.

The Activity ratios are primarily measures of return.

(i) Dioecy / production of unisexual flowers (in different plants)

(ii) Self incompatibility

Devices which prevent both autogamy and Geitonogamy in flowering plant are: 

1. In some species, pollen reiease and stigma receptivity are not synchronized. Either the pollen is released before the stigma becomes receptive or stigma becomes receptive before the release of pollen. It prevents autogamy. 

2. Different positioning of the anther and the stigma. As a result, the pollen does not come in contact with the stigma of the same flower. 

Methodology and Technique 

(i) DNA is isolated and extracted from the cell or tissue by centrifugation. 

(ii) By the process of polymerase chain reaction (PCR), many copies are produced. This step is called amplification. 

(iii) DNA is cut into small fragments by treating with restriction endonucleases. 

(iv) DNA fragments are separated by agarose gel electrophoresis. 

(v) The separated DNA fragments are visualised under ultraviolet radiation after applying suitable dye. 

(vi) The DNA is transferred from electrophoresis plate to nitrocellulose or nylon membrane sheet. This is called Southern blotting. 

(vii) Probes are now added which bind to specific nucleotide sequences that are complementary to them. This is called hybridisation. 

(viii) The hybridised DNA fragments are detected by autoradiography. They are observed as dark bands on X-ray film. 

DNA Fingerprinting: 

This technique was discovered by Alec Jaffery in 1985. The technique involves following steps: 

(i) Isolation and extraction of DNA from the cell by centrifugation. 

(ii) By the help of enzyme restriction endonuclease DNA molecules are digested. The fragment also contains VNTRs. 

(iii) The small DNA fragments are separated through gel electrophoresis set-up that contain agarose polymer gel. 

(iv) The separated DNA fragments are transferred from electrophoresis plate to synthetic membranes like nitrocellulose or nylon membrane sheet called southern blotting. 

(v) The DNA probes are added which target a specific nucleotides sequence which is complementary to them and this process is called hybridisation (Southern blotting). 

(vi) The nylon membrane is exposed to an X-ray film and dark orange coloured bands developed at sites where probes have bound to the DNA fragments. This is known as autoradiography. 

On comparing the DNA prints of blood samples A and B, it can be confirmed that the blood sample picked up from the crime scene belongs to the same individual or to two different individuals.

Organisms exhibiting external fertilisation show great synchrony between the sexes , release a large number of gametes into the surrounding medium

In Amoeba, binary fission takes place whereas in yeast cell division occurs by budding.

(c) About 60% of the world GDP.

(b) Dramatic expression.

(b) They used it for mummification.

(a) The science of etymology.

Let us assume, to the contrary, that √3 is rational.

That is, we can find integers a and b (≠0) such that √3 =a/b 

Suppose a and b have a common factor other than 1, then we can divide by the common factor, and assume that a and b are coprime.

So, b√3 =a

Squaring on both sides, and rearranging, we get 3b² = a².

Therefore, a² is divisible by 3, and by Theorem 1.3, it follows that a is also divisible by 3.

So, we can write a = 3c for some integer c.

Substituting for a, we get 3b² = 9c², that is, b² = 3c².

This means that b² is divisible by 3, and so b is also divisible by 3 (using Theorem 1.3 with p = 3).

Therefore, a and b have at least 3 as a common factor.

But this contradicts the fact that a and b are coprime.

This contradiction has arisen because of our incorrect assumption that 3 is rational.

So, we conclude that √3 is irrational.

Let side of square tank = x

and depth = h

Capacity = x²h = 250

Cost function = c = 50x² + 400h²

c = 50x² + 400 x 250 x 250 x^-4

dc/dx = 0, x = 10

h = 2.5

d²c/dx² > 0 local maxima

Total cost of tank is minimum when side is 10 metre and depth of tank = 2.5 metre 

Let us assume, to the contrary that 7 − √5 is irrational 

7 − √5 = p/q, Where p & q are co-prime and q ≠ 0 =√5 = 7q-p/q

7q - p/q is rational = √5 is rational which is a contradiction 

Hence 7 − √5 is irrational