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\(\underset{x\rightarrow0}{lim}\) \((\frac{1^x+2^x+3^x+...+n^x}n)^{n/x}\) (1^∞ type)

= Exp  \((\underset{x\rightarrow0}{lim}\) \(n/x\times(\frac{1^x+2^x+3^x+...+n^x}n-1))\)

= Exp  \((\underset{x\rightarrow0}{lim}\) \(\frac{1^x+2^x+3^x+...+n^x-n}x)\)

= Exp  \((\underset{x\rightarrow0}{lim}\) \(\frac{1^xlog\,1+2^xlog\,2+3^xlog\,3+...+n^xlog\,n}1)\) (By using D.L.H. Rule)

= Exp  \(\{\underset{x\rightarrow0}{lim}\) 2^x log 2 + 3^x log 3 + .... + n^x log n} (∵ log 1 = 0)

= Exp {log 2 + log 3 + ... + log n}

= Exp {log (2 x 3 x 4 x ... x n)} (∵ log A + log B = log AB)

= 1 x 2 x 3 x 4 x ... x n (∵ e^{log x} = x)

= n!

Hence, \(\underset{x\rightarrow0}{lim}\) \((\frac{1^x+2^x+3^x+...+n^x}n)^{n/x}\) = n!

\(\lim\limits_{x\to0}\frac{x(5^x-2^x)}{cos5x - cos3x}\) (0/0 type)

= \(\lim\limits_{x\to0}\frac{(5^x-2^x)+(5^xlog5-2^x log2)x}{-5sin5x+3sin3x}\) (By using D.L.H. Rule)

= \(\lim\limits_{x\to0}\frac{(5^x-2^x)+(5^xlog5-2^x log2)x}{3(3x)-5(5x)}\) (If θ is very small then sin θ = θ)

= - \(\lim\limits_{x\to0}\frac{(5^x-2^x)+(5^xlog5-2^x log2)x}{16x}\)

= -\((\lim\limits_{x\to0}\frac{(5^x-2^x)}{16x}+\lim\limits_{x \to 0}\frac{5^xlog5-2^xlog2}{16})\) 

= - \((\lim\limits_{x \to 0}\frac{5^xlog5-2^xlog2}{16}+\frac{log5-log2}{16})\) (\(\because\) a^o = 1 & by D.L.H. Rule)

 = -\((\frac{log5/2}{16}+\frac{5/2}{16})\) 

 = -2/16 log (5/2)

 = -1/8 log(5/2)

Hence, \(\lim\limits_{x \to 0}\frac{x(5^x-2^x)}{cos5x-cos3x}=-\frac{1}8log\frac52\)

\(\lim\limits_{x\to 0}\) x log sin² x (0 x \(\infty\) type)

 = \(\lim\limits_{x\to 0}\) \(\frac{log sin^2x}{1/x}\) (\(\infty\)/\(\infty\) type)

 = \(\lim\limits_{x\to 0}\) \(\cfrac{\frac{2sinxcosx}{sin^2x}}{-\frac1{x^2}}\) (By D.L.H. Rule)

 = \(\lim\limits_{x\to 0}\) \(\frac{-2x^2}{sin^2x}.sin x.cos x\)

 = -2(\(\lim\limits_{x\to 0}\) \(\frac{x}{sin x}\))² . \(\lim\limits_{x\to 0}\) sin x cos x

 = -2 .1². 0 . 1 (\(\because\lim\limits_{x\to 0}\frac{x}{sin x}=1\))

 = 0

\(\therefore\) \(\lim\limits_{x\to 0}\) x log sin²x = 0

The definition of a prime number is a number that is divisible by only one and itself. The smallest prime number is 2, which is also the only even prime.

Correct answer is: (d) 1/9

P(perfect Square)=5/45=1/9

Given:

The number of student opted Physics, n(A) = 20

The number of student opted Maths, n(B) = 17

The number of student opted both, n(A∩B) = 12

The number of student opted other subject = 10

Formula used:

n(A∪B) = n(A) + n(B) – n(A∩B)

Calculation:

n(A∪B) = n(A) + n(B) – n(A∩B)

⇒ n(A∪B) = 20 + 17 – 12

⇒ n(A∪B) = 25

Total number of student opted maths and the physics = 25

Number of student in the class = 25 + 10 = 35

∴ The number of student in the class is 35

Correct posture of konasana:- Kona is the Sanskrit word for angle. This pose serves as a warm up pose for more complicated angle pose like Baddha Konasana etc.

Posture- Stand erect with your hands on both the side Palms should be touching the thighs. Separate your legs until about 2-3 feet apart. Raise both hands upto shoulder level. Stretch them out and align them parallel to your shoulder. Inhale and bend to your right slide, sliding the right hand down the right thigh and raising the left hand straight up. Try to stretch the right hand more and touch the right ankle with your fingers. Keep the left hand straight without bending the elbow. Bring down the left hand and place it on your waist. Hold the posture for a few seconds. Exhaling return to the standing position with your feet. Repeat the same steps on the other side alternating the hands.

Benefit:- 

1. This pose is helpful in relieving back pain and increase the flexibility of the spine. 

2. It reduces fat from waist & hips. 

3. Body gets into shape. Arm muscles gets toned up.

Bohr’s Model of an atom, the postulates are 

1. Electrons revolve around the nucleus of an atom in a certain definite path called Orbit or stationary state of shell. 

2. The shells are having different energy levels denoted as K, L, M, N 

3. As long as the electron remains in an orbit, they neither absorb nor emit energy. 

4. The electron can move only in that orbit in which angular momentum is quantized, i.e., the angular momentum of the electron is an integral multiple of h/2π.

Correct posture & benefits of “Sarvangasana” is as under:- Lie on the ground with feet together, raise the trunk so that the weight of the body is bears by shoulders.

The waist is supported by hands and the body is kept absolute straight from the shoulder to the feet.

Benefit:- 

1. Relives the body from bad odors of sweat. 

2. It improves digestion. It is recommended for reducing waist line. 

3. It ensure full flow of blood to the heart and the brain which in turn prevents premature greying. 

4. Precautionary heart patient & patient of HBP should not perform.

Glycemic index is a guide used to classify carbohydrate containing foods.

Six principles of Indenting are:

1. The Indents are made well in advance for regular items keeping in view the earlier sales trends/ fresh bookings/ forecast, etc. 

2. For grocery and dry items the store request is made for 4-5 days together. 

3. For fresh items and perishable items it is generated for each day. 

4. The chef in charge will see what is left in the freezers, refrigerators, kitchen store and then the indent is raised. 

5. Indents are made in triplicate. Original copy along with the 2nd copy goes to store and third copy of the same goes to accounts/ F & B Control department.

Four factors affecting indenting are:

1. Portion size 

2. Day of function 

3. Type of guest: Age group, religion. 

4. Number of expected guests and number of guaranteed guests

-the rise of blood glucose occurring after a meal

-multi-grain Roti has low GI of 27

Body treatment named ‘reflexology’ :- Reflexology is a non invasive presume point massage done on the soles of the feet where there are reflex zones correspoinding to all internal organs in the human body. Pressure is applied according to the body map on the feet which is correlation to the body are guided by meridians. 10 longitude and 3 transverse zones. Reflexology reduces physical, emotional and psychological stress and tension which result in relaxation in the body. Reflexology improves the assimilation of nutrients to enhance the provision of nourishment for healthy functioning. It improves the circulation of the blood and lymph and strengthens the functioning of the immune system. Reflexology can be practiced over the hands feet and on ears. It relaxes, improves circulation and promotes a general feeling of wellness.

Objective of food cost accounting are:

1.To know cost: It is through the mechanism of cost accounting that costs of products or services are ascertained. 

2.To fix the selling price: only if one knows the total cost than one can fix the selling price of a dish. 

3. Cost controlling: The chef/Restaurant manager/ cost accountant while fixing the selling price of a dish must know its exact recipe. 

4. Preparation of account and control of food cost- The Restaurant manager/ cost accountant review the production ,sales and operating results ,stocks of raw material and finished food and other items are valued at cost price or market price which ever is lower. 

5.Operating polices: It helps management in formulating operating policies like what should be the food cost, whether to bake bakery products in house or out source.

Symptoms of obesity: Obese, clumsy, unsymmeterical, excessive sweating, body ache & excessive sleep.

-lasts for not more than 2 weeks in duration. 

-persons recovers completely after the fever.

Five Indian breads along with their methods of cooking are:

1. Pao bun-Baking 

2. Tandoori Naan-Tandoor 

3. Luchi-Deep frying 

4. Dhakai Parantha-Shallow frying 

5. Chapati-Broiling

Methods of cooking are:

1. Dry heat: Broiling or grilling , Baking and roating. 

2. Moist heat: Boiling, steaming brasing, and stewing.

3. Use of oil : Frying.

Brick powder

short stature or low height

retardation of physical growth

Three dry methods of cooking along with example 

• Baking-Food cooked with dry heat. 

Example-cake 

• Grilling-Food is cooked on an open grooved griddle over heat source 

Example-Grilled Chicken 

• Broiling-Food is cooked over dry heat 

Example-broiling of Indian spices

-reduction in antibody production

-therefore the disease fighting capacity is lowered

1) Toasting- Generally applied for bread slices which are browned from both sides by keeping them between two grilles. 

2) Baking- A dry method of cooking, it combines steam which is generated while food is cooked

Elementary canal is known as the food pipe.

Reiki is a natural healing therapy to be done with the energy given by hands.

Cooking by dry heat includes baking and Roasting / grilling.

Hydro therapy is done with water.

Heavy diet and lack of exercise results in the disorder named diabetes.

It controls and coordinates all the cellular functions.

1. false 

2. false

The transpiration driven ascent of xylem sap depends mainly on the following physical properties of water:

• Cohesion – the mutual attraction between water molecules. 
• Adhesion – the attraction of water molecules to polar surfaces (such as the surface of tracheary elements). 
• Surface Tension – water molecules are attracted to each other in the liquid phase more than to water in the gas phase. 

These properties give water high tensile strength, i.e., an ability to resist a pulling force, and high capillarity, I ‘.e., the ability to rise in thin tubes. In plants capillarity is aided by the small diameter of the tracheary elements – the tracheids and vessel elements.

Prokaryotic cell

Fluidy by lipids and functional specificity by proteins

(a) lt has 80S type of ribosome present in the mitochondria.

Ribosome are called ribonucleoprotein particles of the cell.

Mitochondria – synthesis of ATP

(b) Rough Endoplasmic Reticulum (RER) is easily observed in the cell

Under constant temperature the volume of liquid varies inversely to pressure. Moreover, if greater pressure is applied then it will change the state of the matter from liquid to solid at a given temperature. Any liquid will abide by these laws.

Every activity requires energy. Root pressure develops due to activity of living cells of the root.

It is the model of the plasma membrane consists of proteins and phospholipid bilayer. It is otherwise known as protein and iceberg in a sea of lipids. Singer and Nicolson

When a pressure greater than atmospheric pressure is applied to pure water or a solution, its water potential is increased.

Golgi body is associated with secretory activity.