List of practice Questions

The table below shows the age-wise distribution of the population of Reposia. The number of people aged below $35$ years is $400$ million.

Age Group Percentages

Age group	Percentages
Below 15 years	30.00
15 – 24	17.75
25 – 34	17.00
35 – 44	14.50
45 – 54	12.50
55 – 64	7.10
65 and above	1.15

If the ratio of females to males in the ‘below 15 years’ age group is $0.96$, find the number of females (in millions) in that age group.

The number 1982 in the decimal system when written in the base 12 is:

$x$ is number of numbers between 100 and 200 such that $x$ is odd and $x$ is divisible by 3 but not by 7. What is $x$?

The three sides of a triangle have lengths $a, b, c$. If $a^2 + b^2 + c^2 = ab + bc + ca$, then the triangle is:

The expression $N = 55^3 + 17^3 - 72^3$ is exactly divisible by:

If a function $f(x)$ satisfies the equation \[ f\left(x + \frac{1}{x}\right) = x^2 + \frac{1}{x^2}, \quad x \neq 0 \] then $f(x)$ equals:

$a_1=1,\ a_{n+1} = 2a_n + 5$, find $a_{100}$.

A truck travelling at 70 km/h consumes 30% more fuel than another travelling at 50 km/h. If the truck at 50 km/h has a fuel efficiency of 19.5 km/litre, how many km can the 70 km/h truck travel on 10 litres of fuel?

In the sciences, even questionable examples of research fraud are harshly punished.
A. But no such mechanism exists in the humanities - much of what humanities researchers call research does not lead to results that are replicable by other scholars.
B. Given the importance of interpretation in historical and literary scholarship, humanities researchers are in a position where they can explain away deliberate and even systematic distortion.
C. Mere suspicion is enough for funding to be cut off; publicity guarantees that careers can be effectively ended.
D. Forgeries which take the form of pastiches in which the forger intersperses fake and real parts can be defended as mere mistakes or aberrant misreading.
6. Scientists funding data have no such defences.

The concept of a ‘nation-state’ assumes a complete correspondence between the boundaries of the nation and the boundaries of those who live in a specific state.
A. Then there are members of national collectivities who live in other countries, making a mockery of the concept.
B. There are always people living in particular states who are not considered to be (and often do not consider themselves to be) members of the hegemonic nation.
C. Even worse, there are nations which never had a state or which are divided across several states.
D. This, of course, has been subject to severe criticism and is virtually everywhere a fiction.
6. However the fiction has been and continues to be at the basis of nationalist ideologies.

Let $n$ be the number of different $5$-digit numbers, divisible by $4$, using the digits 1, 2, 3, 4, 5, 6 without repetition. Find $n$.

A circle of radius 1 has 7 sectors $S_1, S_2, \dots, S_7$, adjacent to each other. Total area of all 7 sectors = one eighth of area of circle. The $j$-th sector’s area is twice the $(j-1)$-th sector’s area. Find the angle subtended by $S_1$ at the center.

Rearrange the following sentences to form a coherent paragraph:
A. The likelihood of an accident is determined by how carefully the motorist drives and how carefully the pedestrian crosses the street.
B. An accident involving a motorist and a pedestrian is such a case.
C. Each must decide how much care to exercise without knowing how careful the other is.
D. The simplest strategic problem arises when two individuals interact with each other, and each must decide what to do without knowing what the other is doing.

Let $x, y$ and $z$ be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

A student observed an algae with chlorophyll a, b and phycoerythrin, it should belong to

Mg is a component of

Hair are found in the inflorescences of Zea mays are the modification of:

For all $x\,\in\,(0,1)$

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

Choose the word from the four alternatives (1), (2), (3) and (4) that is most nearly similar in meaning to the word given in CAPITAL letters.
CLOUT

Choose the word from the four alternatives (1), (2), (3) and (4) that is most nearly similar in meaning to the word given in CAPITAL letters.
FOMENT

Choose the word from the four altermatives (1), (2), (3) and (4) that is most nearly opposite in meaning to the word given in CAPITAL letters.
SEDENTARY

Choose the word from the four altermatives (1), (2), (3) and (4) that is most nearly opposite in meaning to the word given in CAPITAL letters.
COMPASSIONATE

Choose the word from the four altermatives (1), (2), (3) and (4) that is most nearly opposite in meaning to the word given in CAPITAL letters.
RUDIMENTARY