List of practice Questions

For a given chemical reaction
\(γ_1A + γ_2B → γ_3C + γ_4D\)
Concentration of C changes from 10 mmol dm^–3 to 20 mmol dm^–3 in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm^–3 s^–1. Therefore, the rate of reaction is _____ mmol dm^–3 s^–1. (Nearest Integer)

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If \(σ^2 \) is the variance of X, then 100 σ² is equal to ____.

Directions: In the question two statements are given which are followed by four conclusions (1), (2), (3) and (4). Choose the conclusions which logically follow from the given statements.
Statements: All pens are instruments. Some green things are instruments.
Conclusions: 
(1) All pens are green.
(2) All green things are pens.
(3) Some instruments are green.
(4) All instruments are pens.

Automation, however essential it may be to maximise a country's economic production and minimise its costs, should be rejected. The health care industry wants to increase revenues while reducing costs. Hence, it proposes greater automation of health care. This radical automation of health care would cause patients to lose trust in the system as the health care they would receive would lack the personal touch that, according to several studies, patients desire.
Which of the following expresses the main point of the argument?

Directions: In the question there is a statement followed by two conclusions, numbered I and II. You have to assume everything in the statement to be true, then consider the two conclusions together and decide which of them logically follows from the information given in the statement.
Statements: Government has spoiled many top ranking financial institutions by appointing bureaucrats as directors of these institutions.
Conclusions:
I. Government should appoint directors of the financial institutions taking into consideration the expertise of the person in the area of finance.
II. The director of the financial institution should have expertise commensurate with the financial work carried out by the institution.

Directions: Answer the question based on the following diagram.

The rectangle represents bachelors.
The square represents Delhi metropolis.
The circle represents English language.
The triangle represents tourists.
Which of the following is not true?

Directions: The question presents a situation and asks you to make a judgment regarding that particular circumstance. Answer the question solely on the basis of the information given.
Illegal adulterated and local alcohol that is largely in supply in the city has become a matter of concern for the citizens and administration. A meeting was called up, which involved local people as well, to discuss the situation. The local people claimed that the administration is not doing enough to deal with the situation. You are representing the administration in the meeting. What should be your reaction to these claims?

The integers \(1, 2 ... 40\) are written on the blackboard. The following operation is then repeated 39 times. In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number \(a+b-1\) is written. What will be the number left on the board at the end?

Given the quadratic equation \(x^2 – (A – 3)x – (A – 7) = 0\), for what value of A is the sum of squares of the roots 0?

A question is followed by two statements, numbered (1) and (2). Using the information provided and general knowledge, decide whether the information given is sufficient to solve the problem.
Is \(x^2-y^2\) even?
(1) \(x+y\) is even.
(2) \(x-y\) is odd.

Sumeet spends 10% of his salary on his child’s education, 20% of the remainder on rent and 25% of the balance on garments. Finally, he is left with $ 5,400. What is his salary?

Directions: Choose the word or pair of words that best completes the relationship to the given pair:
allusion: reference:: ________:_________

Directions: Choose the set of prepositions whose meaning and sequence best fits the 3 given sentences.
1. After the burglary, the office bought a sophisticated security system as an insurance ________any such losses. 
2. She put ________ a brave front at the end of the meeting. 
3. Sunil decided to avail himself _________the opportunity to go to Australia for training.
(A) on
(B) of
(C) at
(D) against
(E) up
(F) with

Directions: In the given question, the sentence has four underlined words or phrases. Identify the one underlined work or phrase that must be changed in order to make the sentence correct. Mark E for no error.
Though they were written almost a year after they separated, Salim and Javed’s stories were published on the same day.

Directions: Rearrange the jumbled sentences to show the appropriate sequence.
(A) For example, when the early homo sapiens left their homes in search for food, they would risk death and injury from dangerous animals. 
(B) Throughout human history, the universe has presented an innumerable amount of dangers to explorers. 
(C) Today, many adventure enthusiasts seek to find the thrills and adrenaline rush which their ancestors had experienced in the wild. 
(D) The tradition of humans going out to experience the dangers of unknown nature still exists.

Let the relation R is defined in N by \(a \mathbb{R} b\), if \(3a+2b = 27\) , then R is

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is

Which of the following is not an irrational number?

The correct order of melting point is

The figure shows different paths for going from A to B. The directions of the paths are indicated by arrows. No node can be visited twice. What is the total number of different paths to go from A to B?

Class XII students were asked to prepare one litre of buffer solution of pH \(8.26\) by their Chemistry teacher. The amount of ammonium chloride to be dissolved by the student in \(0.2\) M ammonia solution to make one litre of the buffer is (Given : \(pK_b\) \((NH_3)\) = \(4.74\), Molar mass of \(NH_3\) = \(17\) g \(mol^{–1}\), Molar mass of \(NH_4Cl\) = \(53.5\) \(g\) \(mol^{–1}\))

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be