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since alpha and beta are roots of the given equation ,so it will satisfy the given eqution.

so,1/(a.alpha+b)= -c/alpha and 1/(a.beta+b)= -c/beta.

Velocity of A = 3v

Velocity of B = 2v

Velocity of C = 1v

Then 

\(AB:BC\)

\(= 3 \times 2:2\times 1\)

\(= 6:2\)

\(= 3:1\)

a. eliminates certain areas of stitching 

b. Less skilled labour is required 

c. it increases productivity

i. Aim & Objectives 

ii. Class size

iii. Age group 

iv. Equipment available 

v. Learning outcomes

Given that required plane passes through points P(2, 4, 2) and Q(2, 3, 5) and parallel to a line whose direction ratios are 3, -2, 1.

Now, direction ratios of line AB are 0, -1, 3

Let the direction ratios of normal to the plane are A, B and C.

Since, point P and Q lie on plane, therefore line joining points P and Q is perpendicular to normal.

∴ 0 x A + (-1) x B + 3 x C = 0 (condition of two perpendicular lines)

⇒ -B+3C = 0

⇒ B=3C .....(i)

Since, given plane is parallel to line 3i - 2j + k

∴ Normal to plane is perpendicular o line 3i - 2j + k

∴ 3A-2B+C = 0

⇒ 3A-6C+C = 0 (from(i))

⇒ 3A = 5C

⇒ A = 5C/3 .....(ii)

Hence, the direction ratios of normal to required plane are 5C/3, 3C, C or 5, 9, 3. (By putting C=3)

Therefore, the equation of the plane is 5x+9y+3z = d, where d is perpendicular distance of origin from plane.

Since, point (2, 4, 2) lies on plane.

∴ d = 2 x 5 + 4 x 9 + 2 x 3

= 10+36+6

= 52

∴ Equation of required plane is 5x+9y+3z = 52.

Equation of line joining the points 2i+j+3k and 4i+2j+3k is r = a+λ(b-a)

⇒ r = (2i+j+3k) + λ((4-2)i + (2-1)j + (3-3)k

⇒ xi+yj+zk = (2+2λ)i + (1+λ)j + 3k (∵ r = xi+yj+zk)

⇒ x = 2+2λ, y = 1+λ, z = 3

Hence, locus of arbitrary point on line joining points (2, 1, 3) and (4, 2, 3) is given by.

(x, y, z) = (2(1+2λ)), 1+λ, 3j

Since, line meets the plane, therefore equation of arbitrary point on line satisfies equation of plane.

∴ 5 x 2(1+λ) + 9 x (1+λ) + 3 x 3 = 52

⇒ 10+10λ+9+9λ+9 = 52

⇒ 19λ = 52-28 = 24

⇒ λ = 24/19

∴ point which lies on both line and plane is (x, y, z) = (86/19, 43/19, 3).

Hence, plane meets the line at (86/19, 43/19, 3).

Let

A = \(\begin{bmatrix} cos \theta & -sin \theta \\[0.3em] sin \theta& \cos \theta\\[0.3em] \end{bmatrix}\)

B = \(\begin{bmatrix} e^{i\theta} &0 \\[0.3em] 0 & e^{-i \theta} \end{bmatrix}\)

Let eigen values of matrix A is \(\lambda\)₁ & \(\lambda\)₂.

And also let eigen values of matrix B is \(\mu\)₁ & \(\mu\)₂.

\(\because\) Trace of any matrix is equal to sum of diagonal elements.

\(\therefore\) Trace of matrix A is  \(\lambda\)₁ +  \(\lambda\)₂ = cos\(\theta\) + cos\(\theta\) = 2 cos\(\theta\)

(\(\because\) Trace of matrix = sum of eigen values of that matrix)

And trace of matrix B is \(\mu\)₁ + \(\mu\)₂ = e^{\(i \theta\)} + e^{\(-i \theta\)} 

 \(\mu\)₁ + \(\mu\)_{2 =} ( cos\(\theta\) + i sin\(\theta\)) + (cos\(\theta\) - i sin\(\theta\)) = 2cos\(\theta\)

Thus,  \(\lambda\)₁ +  \(\lambda\)₂ = \(\mu\)₁ + \(\mu\)₂ .........(1)

Now |A| = \(\begin{bmatrix} cos \theta & -sin \theta \\[0.3em] sin \theta& \cos \theta\\[0.3em] \end{bmatrix}\) = cos²\(\theta\) + sin²\(\theta\) = 1.

Thus \(\lambda\)₁ \(\lambda\)₂ = 1 (\(\because \)|A| = Product of eigen values of matrix A)

And |B| = \(\begin{bmatrix} e^{i\theta} &0 \\[0.3em] 0 & e^{-i \theta} \end{bmatrix}\) =  e^{\(i \theta\)} . e^{\(-i \theta\)} - 0

=  \(e^{i\theta - i \theta}\) = e⁰ = 1.

Thus,  \(\mu\)₁ \(\mu\)₂ = 1

Then,   \(\lambda\)₁ \(\lambda\)₂ =  \(\mu\)₁ \(\mu\)₂.

Now, ( \(\lambda\)₁ - \(\lambda\)₂)² =  ( \(\lambda\)₁ + \(\lambda\)₂)² + 4 \(\lambda\)₁\(\lambda\)₂

₌ \(\big(\)\(\mu\)₁ + \(\mu\)₂\(\big)\)² + 4 \(\mu\)₁\(\mu\)₂

₌   \(\big(\)\(\mu\)₁ - \(\mu\)₂\(\big)\)²

^{\(\Rightarrow\)}  \(\lambda\)₁ - \(\lambda\)₂ =  \(\mu\)₁ - \(\mu\)₂ ..........(2)

or  \(\lambda\)₁ - \(\lambda\)₂ = -( \(\mu\)₁ - \(\mu\)₂) =  \(\mu\)₂ - \(\mu\)₁ ......... (3)

Case - I 

By adding equation (1) and (2), we get.

2\(\lambda\)₁ = 2 \(\mu\)₁ \(\Rightarrow\) \(\lambda\)₁ =  \(\mu\)₁

Then form equation (1) we get \(\lambda\)₂ = \(\mu\)₂.

Case II

By adding equations (1) and (3), we get

2 \(\lambda\)₁ = 2\(\mu\)₂ \(\Rightarrow\) \(\lambda\)₁ = \(\mu\)_2.

Then from equation (1), we get \(\lambda\)₂ = \(\mu\)₁

Hence, eigen values of both matrices A and B are same.

Therefore, both matrices A and B are similar matrices 

Hence, both given matrices are similar over the field of complex numbers for any real value of \(\theta\).

Given s∝tⁿ ⇒ S = ktⁿ

Velocity v = \(\frac{ds}{dt}\) = \(\frac{d}{dt}\) (ktⁿ) = knt^n-1

a = \(\frac{dv}{dt}\) = \(\frac{d}{dt}\) (Knt^n-1).Kn(n-1)t^n-2

⇒ \(\frac{a}{(n-1)}\) = knt^n-2

⇒\(\frac{a}{(n-1)}\)x ns = knt^n-2n.s

= knt^n-2.nktⁿ

= k²n²t^2n-2

= (Knt^n-1)² = v² [∵ v = Knt^n-1]

∴ \(\frac{nas}{(n-1)}\) = v²

Answer: b) Drug bio transformation in the organism 

The Screening Test of the Bayley Scales of Infant and Toddler Development, Third Edition (Bayley-III Screening Test) is an individually administered instrument designed to briefly assess the cognitive, language, and motor functioning of infants and young children between 1 month and 42 months of age. The primary purposes are to determine quickly whether a child is progressing according to normal expectations and to determine if further, more comprehensive evaluation is needed. The Bayley-III Screening Test items are a subset of the cognitive, language, and motor items of the Bayley Scales of Infant and Toddler Development, Third Edition (Bayley-III; Bayley, 2006). The Bayley-III Screening Test can be used to identify young children’s degree of risk for developmental delay and to assist the practitioner in determining whether further evaluation is necessary. By administering the Bayley-III Screening Test, the practitioner can obtain information with which to compare the child to his or her peers in just a few minutes. This approach to assessment enables practitioners to identify challenges early and to recommend interventions at the earliest possible time. The Bayley-III Screening Test is not designed to identify the degree of impairment or specific strengths or weaknesses in cognition, language, or motor functioning, nor should it be used to provide a diagnosis of developmental delay. When in-depth assessment of cognition, language, or motor functioning is indicated by the Bayley-III Screening Test, the full Bayley-III scales should be used to assist in the diagnosis of disorder and to identify areas of relative strength and weakness.

Emotions are a very important determinant of personality. Emotional factors have a huge bearing on a person’s personal and social adjustment. There are many aspects of emotions like dominant emotions, emotional balance, emotional deprivation, excessive love and affection, emotional expressions, emotional catharsis and emotional stress which affect the development of personality directly and indirectly.

Different people are ruled by different predominant emotions in them. It is seen that some people, by nature are happy and cheerful people, while some are forever gloomy and fearsome. These emotions are predominant in them. The happy people will be hopeful even when they face serious, problems while the sad people will feel depressed or fearful even during celebrations or happy moments.

Thus, the ruling emotion in a person determines how he behaves or feels in different situations. Emotionalllv balanced people (whose pleasant emotions are more than the unpleasant ones) are able to adjust well socially and personally.

If a person experiences too many problems and obstacles in life, over time he will develop negative feelings like fear, anger, jealousy, etc. which will affect his adjustment process throughout life and develop pathological traits. If emotions like love, happiness and curiosity are not present in one’s life, it will again affect his adjustments in life.

The influence that the absence of the positive emotions in one’s life has depends on how long the person the person was deprived of the emotion, at what age and to what degree. if a child does not get love and affection, he will be emotionally insecure. Such children grow up to become rebellious adolescents and adults because of the strained relationship with their parents or other family members in early childhood.

 Bombay duck  is found in sea.

Bee keeping is called Apiculture.

CHEWING GUM is made from chicle.

1. Every urbanite knows that the bright lights of the city make it impossible to see all the stars in a night sky.

2. Cinzano and his team have found that many people’s eyes now never get to the stage where they are fully adapted to darkness.

3. Breast cancer, depression and other ailments are some health hazards caussed due to light pollution.

4. It is lighting from office towers that confuses migratory birds.

5. Most of us don’t know that the bright lights might also be making us sick.

Correct option is C) isn’t cold enough

1. Boy Modi helped his father sell tea to buy the basic needs of life.

2. His brother carried on his tea stall near a bus terminal.

3. Boy Modi came in contact with the patriots when he became a member of RSS and attended the Shakha.

4. Seeing his good governance in Gujarat as the Chief Minister, the BJP made him the Chairman of the Election Committee.

5. Mr Modi has been in close touch with the poor people and experienced the pain of proerty himself. So he is a man of the masses.

Correct option is C) have you been doing

Respected Principal Sir, 

Respected teachers and my dear schoolmates! The general election of 2014 withnessed a new trend in the Indian politics. For the first time in the history of free India, the people elected a common man–a man of the street as their Prime Minister. He has risen from the masses. He knows and understands the pangs of poverty. He has slept under a leaking roof and knows how hunger pricks at the empty stomach. He, therefore, knows the troubles and misfortune of the common man.

He himself is a great patriot and is honest to the core. He intends to bring good health, prosperity and good days to the remotest huts in the Indian villages. But we find unhealthy criticism on the lips of some of the politicians and the authorities that flourished on scams and ill-earned money. There may be some selfish fanatics among his supporters. They spread hatred and enmity among the various creeds to hinder development. Let us pray to God that goodness may prevail upon wickedness and the poorest Indian should feel good. 

Thanks.

Correct option is B) Neither

Respected Principal Sir, 

Respected teachers and my schoolmates! We have often mentioned that a healthy mind resides in a healthy body. It is equally true of the nation’s mind. If our surroundings are neat and clean, we feel more enthusiastic and energetic to perform our duties. After cleaning our surroundings, we have to clean our conscience. Employers with clean conscience will work sincerely. They will not accept bribe. They will not be the victims of scams.

The ministerial body with clean conscience will refuse to misuse public money. The administrative machinary working under such body of honest ministers will follow suit. Conscience becomes clean with good education, good company and by eating the bread earned with the sweat of brow.

Very soon, good days willl come. Country will get rid of poverty, illness, hunger and tyranny of injustice. As our honourable Prime Minister Sri Narendra Modi is emphasizing on ‘Clean India’, we should try our best to make India clean and attractive.

Correct option is B) Can

Correct option is C) will be closed

Correct option is B) out

Correct option is A) in

Correct option is C) will have been destroyed

Correct option is A) was looking / rang

Correct option is C) racket

Correct option is A) racked up

Correct option is (1) Aldopentose ​​​​​​

This is seliwanoff test use to identify Aldose and Ketose. Ketose rapidly dehydrated and give dark Red color with resorcinol & HCI but Aldose give light pink colour.

Correct option is B) raking it in

Correct option is B) raw