For the following questions answer them individually
Simplify the following.
$$\frac{\sin^3 \alpha + \cos^3 \alpha}{\sin \alpha + \cos \alpha}$$
If a = 17 ,b = 13, then find the value of the expression $$(a^3 - b^3 - 3a^2b + 3ab^2).$$
Simplify the given expression.
$$18 \div 3 of 2 \times 5 + 72 \div 18 of 2 \times 3 - 4 \div 8 \times 2$$
The ages of Gyanendra and Arbind are in the ratio 6 : 5. If the sum of their ages is 55 years, then what will be the ratio of their ages after seven years from now?
The following sentence has been divided into parts. One of them may contain an error.
Select the part that contains the error from the given options. If you don't find any error, mark 'No error' as your answer.
The availability of funds will be / ensured if they all tried to / submit the proposals on time.
Select the option that can be used as a one-word substitute for the given group of words.
A person who does not believe that God or Gods exist.
Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.
A.But the question that perturbs Ruskin's mind is what social pressure can be exercised against a dishonest person.
B.The merchant, for instance, must supply perfect and pure things to the people.
C.Ruskin believes that in every civilised society there exist five intellectual professions, namely the soldier, the pastor, the physician, the lawyer and the merchant.
D.Persons belonging to these professions are expected to perform their duty honestly.
Sentences of a paragraph are given below in jumbled order. Arrange the sentences in the correct order to form a meaningful and coherent paragraph.
A. But she has no idea an aunt and uncle are waiting for her.
B. 'The Strange Child' is the story of a young girl who believes she is the only one on the planet.
C. Her parents simply vanished into thin air one day.
D. She travels the world in search of Nevada because she aspires to reside in the Mojave Desert.