A quadratic polynomial, whose zeroes are -3 and 4, is (a) x²- x + 12 (b) x² + x + 12 (c) (? 2 ) 2 − ? 2 − 6 (d) 2x² + 2x – 24

  x² - x + 12=0

(x - 4) (x + 3)= 0

x = 4 , -3

So, answer (a)

Steps of construction:

1. Draw circle with centre O and radius OA = 5 cm, .
2. Mark another point B on the circle such that ∠AOB = 120°, supplementary to the angle between the tangents. Since the angle between the tangents to be constructed is 60°.

          ∴ ∠AOB = 180° – 60° = 120°.  

      3.Construct angles of 90° at A and B and extend the lines so as to intersect at point P.

      4. Thus, AP and BP are the required tangents to the circle.

Griffin is a brilliant scientist, as he discovers how to make himself invisible. But he seems to enjoy the feeling of power which he gets out of his invisibility. The power to hurt anybody without getting noticed can give sadistic pleasure to some people. A true scientist should make discoveries for the larger benefit of society, not just for his own benefit.

Multi-Party System If several parties compete for power and more than two parties have a reasonable chance of coming to power either on their own strength or in alliance with others, we call it a multi-party system.
(i) Multi-party system allows a variety of interests and opinions to enjoy political representation.
(ii) Here people have an opportunity to make a choice between several candidates.
Demerits
(i) This system often appears very messy.
(ii) This system sometimes leads to political instability.

DNA copying is otherwise known as DNA replication which is the process of producing 2 identical copies of DNA from one original DNA molecule during cell division. DNA copying is important because it generates variation during sexual reproduction which leads to evolution. Also, DNA copying helps in transfer of information or characters from the parents to the offsprings.

Area of shaded region=π theta/360°(R²-r²)
=22×40°/7×360°(14²-7²)
=22/7×9(196-49)
=22×147/7×9
=22×7/3
=154/3cm²

Homologous series is a series of compounds with similar chemical properties and some functional group differing from the successive member by CH2. Carbon chains of varying length have been observed in organic compounds having the same general formula. Such organic compounds that vary from one another by a repeating unit and have the same general formula form a series of compounds. Alkanes with general formula CnH2n+2, alkenes with general formula CnH2n and alkynes with general formula CnH2n-2 form the most basic homologous series in organic chemistry. The successive members vary from each other by a CH2 unit. For example in CH4 and C2H6, the difference is -CH2 unit and the difference between C2H6 and C3H8   is also -CH2 unit. So CH4, C2H6, and C3H8 are homologs. The same thing can be observed in case of alkenes in which the first member is ethene and the successive members are C3H6, C4H8, and C5H10. They differ from each other by a –CH2 unit. Alkene formula is written as CnH2n. 

The diameter of three concentric circles are in the ratio of 1 : 2 : 3
Let the diameter of the three circles be 1 cm, 2 cm and 3 cm respectively.
So, the radii of three concentric circle will be
1/2 cm , 2/2 cm = 1 cm and 3/2 cm
Ratio of their areas = πr₁² : πr₂² : πr₃²
= π*(1/2)² : π*1² : π*(3/2)²
= 1/4 : 1 : 9/4
So the ratio of their respective ratios are 1/4 : 1 : 9/4

Area of sectors = 

= 39.25 cm2

Since, 14 cm, 48 cm and 50 cm is a Pythagorean triplet, it is a right 

Area = 

Area of shaded portion = (336 - 39.25) cm2

= 296.75 cm2

Let the speed of train be "x km/hr" and speed of taxi be "y km/hr"

here , distance travelled in both cases is same ,

Total distance = 300 + 200 = 260 + 240 = 500 km

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Case 1 :-

Time taken by train to travel 300 km = distance/speed
= 300/x

Time taken by taxi to travel 200 km = 200/y

so,
300/x + 200/y = 5.5 hour

Let 1/x = a , 1/y = b

300 a + 200 b =5.5 -----> (1)

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Case 2 :-

Time taken by train to travel 260 km = 260/x
Time taken by taxi to travel 240 km = 240/x

It is said , that , it took 6 min more ,


6min = 0.1 hour

time taken = 5.5 + 0.1 = 5.6 hours

so ,

260/x + 240/y = 5.6

260a + 240b = 5.6 ----> (2)
-------------------------------------------------------------

Solving equations 1 and 2,

260a + 240b = 5.6 ---------> multiply by 5


300 a + 200 b =5.5 ---------> multiply by 6

========================
1300 a + 1200b = 28
1800a + 1200b = 33
----------------------------------
500a = 5

a = 5/500
= 1/100



260a + 240b = 5.6

260/100 + 240b = 5.6

2.6 + 240b = 5.6

240b = 3

b = 3/240
= 1/80

-----------------------------------------------

we know that

1/a = x , 1/b = y

hence,


x = 100
y = 80


speed of train = 100 km/hr
speed of taxi = 80 km/hr
 

Given , a circle with centre O and radius 8 cm. An external point P from where  a tangent is drawn to meet  the circle at T. 
as OP = 10 cm ; radius OT = 8 cm  As  OT⊥PT = 8 cm 
In right ΔOTP, we  have 
OP2=OT2+PT2 
102=82+PT2
PT2=100−64=36 
So, PT = 6 
Therefore , length of tangent = 6 cm

(a) Fragmentation is defined as the process of breaking up of body on maturation into two or more smaller pieces. Each piece of the body results in development of new individuals. The multicellular organism which reproduces by fragmentation is spirogyra. 

(b) Regeneration is defined as the process of growing a full organism from its body part. The examples of regeneration are: Hydra and Planaria. When the body of Planaria is cut into number of pieces, the each and every body piece can regenerate and results in formation of a complete Planaria. The regeneration of an organism occurs by the process of growth and development The cells of body part which has been cut down gets divides and makes a ball of cells. These multiple cells result in formation of tissues and forms organs again and results in regeneration of another Planaria. It can be explained with the help of the following diagram:

The copying of DNA during reproduction is important because:

• The replication of DNA ensures that each daughter cell formed at the end of cell division, receives equal amount of DNA.
• If DNA won't be copied then the daughter cells won't receive all necessary genes.
• There may be absence of important proteins which are encoded by DNA, if DNA won't be replicated.
• Copying of DNA may result in recombination which will lead to evolution.
• Transfer of genetic material from one generation to other makes the organisms to have similar functions.
• Stability of population is maintained.