Exams

A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not "guesses" but reliable accounts of the real world. Scientific theories are not ever proved in the sense of being proved to be 100% correct.

Examples of some scientific theories are ::

Evolution, gravity, atomic theory, the germ theory of disease, relativity, quantum theory, electromagnetic theory, layered Earth theory, etc...

Given,

 5sinx + 12cosx ≥ -r 

⇒13513sin x + 1213cos x ≥ -rcosx) ≥ -r 

513= cosA => sinA =1213

=> 13(sinx cosA + sinA cosx) ≥ -r

=> 13(sin(x + A)) ≥ -r

we know that , -1 ≤ sin (angle) ≤ 1

=> 13sin (x + A) ≥ -13 ⇒rmin =13 

The incomes of A and B be 3P and 4P.

Expenditures = Income - Savings

(3P - 100) and (4P - 100)

The ratio of their expenditure = 1:2

(3P - 100):(4P - 100) = 1:2

2P = 100 => P = 50

Their incomes = 150, 200

The servant worked for 9 days instead of 12 days, he should receive 9/12 of his total payment

Let the price of 1 shirt be Rs. S 

i.e., 3/4 (400 + S).

However, the question states that the servant receive Rs. 280 + S where S is the price of the shirt.

By equating the two equations we get 3/4 (400 + S) = 280 + S.

Therefore, Price of the shirt S = Rs. 80.

Nirmala Sitharaman, who took oath as the new Cabinet member in september 2017 under Narendra Modi, has been given the Defence Ministry portfolio. Incidentally, she has become the first dedicated woman defence minister of India and only the second woman to hold the crucial ministry after Indira Gandhi. 

Epiglottis is that prevents food from entering the windpipe. 

It is a cartilageous flap that flaps opens and closes when swallowing. When you swallow, the epiglottis flattens backward to cover the entrance to your larynx and prevent food from entering the lungs and windpipe. The epiglottis returns to its usual position after swallowing.

A place where honey bees are kept in called an Apiary or a bee yard.