List of practice Questions

The set of natural numbers is partitioned into subsets $S_1 = \{1\}$, $S_2 = \{2, 3\}$, $S_3 = \{4, 5, 6\}$, $S_4 = \{7, 8, 9, 10\}$ and so on. The sum of the elements of subset $S_{50}$ is:

A square is drawn by joining the midpoints of the sides of a given square. A third square is drawn inside the second square in the same way and this process is continued indefinitely. If a side of the first square is 8 cm, the sum of the areas of all the squares thus formed (in sq.cm) is:

The roots of the equation $a x^2 + 3x + 6 = 0$ will be reciprocal to each other if the value of $a$ is:

A car after traveling 18 km from a point A developed some problem in the engine and speed became $\frac{4}{5}$ of its original speed. As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after traveling 30 km from A, then it would have reached B only 36 minutes late. The original speed of the car (in km/h) and the distance between points A and B (in km) is:

If $n$ is any positive integer, then $n^3 - n$ is divisible:

The value of $\frac{(1 - d^3)}{(1 - d)}$ is:

Gopal went to a fruit market with a certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 10% of the money for taxi fare. If he buys 20 mangoes, then the number of oranges he can buy is:

Consider the following steps:
1. Put $x = 1$, $y = 2$
2. Replace $x$ by $xy$
3. Replace $y$ by $y + 1$
4. If $y = 5$ then go to step 6 otherwise go to step 5
5. Go to step 2
6. Stop
Then the final value of $x$ equals:

In a stockpile of products produced by three machines M1, M2 and M3, 40% and 30% were manufactured by M1 and M2 respectively. 3% of the products of M1 are defective, 1% of products of M2 defective, while 95% of the products of M3 are not defective. What is the percentage of defective products in the stockpile?

From any two numbers $x$ and $y$, we define $x * y = x + 0.5y - xy$. Suppose that both $x$ and $y$ are greater than 0.5. Then $x * x>y$ if:

Consider a function $f(k)$ defined for positive integers $k = 1, 2, $; the function satisfies the condition
$f(1) + f(2) + + f(k) = p( p^{k-1} )$ Where $p$ is a fraction i.e. $0<p<1$. Then $f(k)$ is given by:

116 people participated in a singles tennis tournament of knockout format. The players are paired up in the first round, winners of the first round are paired in the second round, and so on till the final is played between two players. If after any round, the number of players is odd, one player is given a bye (he skips that round and plays the next round with the winners). Find the total number of matches played in the tournament.

There were $x$ pigeons and $y$ mynahs in a cage. One fine morning $p$ of them escaped to freedom. If the bird keeper, knowing only that $p = 7$, was able to figure out without looking into the cage that at least one pigeon had escaped, then which of the following does not represent a possible $(x, y)$ pair?

The remainder when $26^{60}$ is divided by 5 equals:

Mr. X enters a positive integer Y in an electronic calculator and then goes on pressing the square repeatedly. Then:

What is the sum of the following series:
$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + + \frac{1}{100 \times 101}$

The value of $(1 - x) + \frac{1}{1 + x} + \frac{2}{1 + x^2} + \frac{4}{1 - x^6}$

Let $a, b$ be any positive integers and $x = 0$ or $1$, then:

There are six boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a white ball or a black ball in such a manner that at least one box contains a black ball and all the boxes containing black balls are consecutively numbered. The total number of ways in which this can be done equals:

The unit price of product P1 is non-increasing and that of product P2 is decreasing. Which product will be costlier 5 years hence?
I. Current unit price of P1 is twice that of P2.
II. 5 years ago, unit price of P2 was twice that of P1.

How long did Mr. X take to cover 5000 km journey with 10 stopovers?
I. The $i^{th}$ stopover lasted $i^2$ minutes.
II. The average speed between any two stopovers was 66 kmph.

Choose the set of three statements which are most logically related:
Statements:
A. Some beliefs are uncertain.
B. Nothing uncertain is worth dying for.
C. Some belief is worth dying for.
D. All beliefs are uncertain.
E. Some beliefs are certain.
F. No belief is worth dying for.

If R is an integer between 1 & 9, P - R = 2370, what is the value of R?
I. P is divisible by 4.
II. P is divisible by 9.

A man distributed 43 chocolates to his children. How many of his children are more than five years old?
I. A child older than five years gets 5 chocolates.
II. A child 5 years or younger in age gets 6 chocolates.

Ramu went by car from Calcutta to Trivandrum via Madras, without any stoppages. The average speed for the entire journey was 40 kmph. What was the average speed from Madras to Trivandrum?
I. The distance from Madras to Trivandrum is 0.30 times the distance from Calcutta to Madras.
II. The average speed from Madras to Trivandrum was twice that of the average speed from Calcutta to Madras.