If x and y are natural numbers such that $(\frac{1}{x})^\frac{1}{y}=0.\overline{3}$, then the value of XY is

The sum of the squares of two consecutive natural numbers is 61. The numbers are

Which of the following is equal to 1 ?

The sum of digits of a natural number $(10^{n}-1)$ is 4707, where n is a natural number. The value of n is

The last digit in the decimal representation of $(\frac{1}{5})^{2000}$ is

If $\log 2 = 0.3010$, then the number of digits in $4^{50}$ is

If $\log \frac{a^{2}}{b}+\log \frac{b}{a^{2}}=\log(a+b)$, then

$\frac{1}{\log_a^b}\times\frac{1}{\log_c^b}\times\frac{1}{\log_a^c}$ is equal to

The ratio of the areas of a square and a square on its diagonal is

The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is

A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of second square is

An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimensions 20 cm × 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is

A small ring of negligible thickness and radius 2cm moves on a bigger ring of radius 10 cm. How many rotations will the small ring take on the bigger ring to make a complete round ?

The cost of fencing an equilateral triangular park and a square park is the same. If the area of the triangular park is $16\sqrt{3}m^{2}$, the length of the diagonal of the square park is

A closed aquarium of dimensions 30 cm × 25 cm × 20 cm is made up entirely of glass plates held together with tapes. The total length of tape required to hold the plates together (ignore the over lapping tapes) is

Three boys are standing on a circular boundary of a fountain. They are at a equal distance from each other. If the radius of the boundary is 5m, the shortest distance between any two boys is

Rita and Meeta both are having lunch boxes of a cuboidal shape. Length and breadth of Rita’s lunch box are 10% more than that of Meeta’s lunch box, but the depth of Rita’s lunch box is 20% less than that of Meeta’s lunch box. The ratio of the capacity of Rita’s lunch box to that of Meeta’s lunch box is

On a particular day of a trade fair, 35000 visitors had visited the fair. The amount collected at the entrance counter was Rs. 9,50,000. The entrance fee was at the rate of Rs. 40 for an adult and Rs.20 for a child. If 10% of the visitors had used free passes, the number of children who visited the fair is

Three spheres of radii 3cm, 4cm and 5cm are melted to form a new sphere. The radius of the new sphere is

The mean of 30 observations was calculated as 150. Later, it was pointed out that value of one of the observations was wrongly taken as 135 instead of 165. The correct mean is

In a class of 45 students, 30 are boys and remaining are girls. If the mean weight of girls is 45 kg and that of boys is 52 kg, then the mean weight of entire class (in kg) is nearest to

The mean of the first 10 even natural numbers is

The median of $6, 7, x - 2, x, 17$ and $20$, (written in ascending order) is 16. Then the value of x is

A number lying between 10 and 100 is seven times the sum of digits. If 9 is subtracted from it, the digits of the number are reversed. The number is

One-third of a certain sum is invested at 3% per annum; one-sixth of the sum is invested at 6% per annum and remaining sum at 8% per annum. If the annual simple interest from all these investments is Rs. 600, the original sum is

If the compound interest on a certain sum of money for 2 years at 4% per annum compounded annually is Rs. 102, then the simple interest on the same sum of money at the same interest rate and for the same period is

One of the factor of the expression $X^{2}-Y^{2}-Z^{2}+2YZ+X+Y-Z$ is

If $a + b + c = 0$, then a factor of the expression $(a+b)^{3}+(b+c)^{3}+(c+a)^{3}$ is

If the length of a rectangule is reduced by 10% and its breadth is increased by 10%, then the area

The sum of the present ages of a father and his son is 99 years. When the father was as old as his son is now, his age was four times the age of the son at that time. The ratio of the present ages of the son and the father is

If an article is sold for Rs. x, there is a loss of 15%. If the same article is sold for Rs. y, there is a profit of 15%. The ratio of (y - x) to (y + x) is

If $\sqrt{x+\frac{x}{y}}=x\sqrt{\frac{x}{y}}$, where x and y are positive real numbers, then y is equal to

A number when divided by 195 leaves a remainder 47. If the same number is divided by 15, the remainder will be

If a : b = 3 : 4; b : c = 4 : 7, then $\frac{a+b+c}{c}$ is equal to

Two trains of lengths 120 m and 90 m are running with speeds of 80 km/hr and 55 km/hr, respectively, towards each other on parallel lines. If they are 90 m apart, after how many seconds they will cross each other completely?

A person goes from town A to town B with a speed of 60 km/h and return to A with a speed of 40 km/h. His average speed for the whole journey is

Twelve men can complete a work in 8 days. Three days after they started the work, it was decided to complete the remaining work in 4 days. How many more men should be employed so that the remaining work can be completed in 4 days?

Efficiency of A is twice as that of B. If they work together, they can complete a job in 18 days. If A alone does the job, in how many days he will complete the job?

Two pipes A and B can fill a tank in 24 hours and 30 hours respectively. If both pipes are opend together, the time taken to fill the tank is

If $\frac{4}{9}th$ of a bucket is filled in one minute, the rest of it will be filled in

Statement: The cotton crop continues to be poor even after the introduction of improved variety of cotton seeds.
Assumptions:
I. The yield of cotton was expected to increase after introduction of improved variety of seeds.
II. The yield of cotton was adequate before the introduction of new variety of seeds.

Statement: No budgetary provision for the purpose of appointing additional faculty would be made in the context of institute’s changed financial priorities.
Assumptions:
I. Appointment of faculty requires funds.
II. There are areas other than appointment of faculty which require more financial attention.

Statement: The office building needs repairing just as urgently as it needs internal as well as external painting.
Assumptions:
I. Efficiency of people working in the office cannot be improved unless office building is repaired.
II. Repairing and painting of office building require funds.

Statement: An opportunity to carry out reforms in elections to the Parliament and State Legislatures has been lost when we rejected most of the recommendations of Goswami Committee for partisan reasons.
Assumptions:
I. Goswami Committee made certain good recommendations to improve the existing election system.
II. Most of the decisions in our country are taken with partisan considerations.

Statement: Shri Roy, retired IAS official has taken over as the new Director of the All India Nuclear Research Institute. It is now expected that the administration of the institute will improve.
Assumptions:
I. The Institute had no Director before Shri Roy.
II. Director is supposed to look after the administration of the Institute.

Which of the following is true of any day’s valid program set operation?

If the program sets ‘R’ and ‘W’ are to be operated on the first day, which of the following could be the other programs on that day?

If the program sets operated on a day is P, Q, W, T, U each of the following could be the next day’s program set except

Which of the following could be the set of programs to be operated on the first day of a month?

If ‘R’ is operated at third place in a sequence, which of the following cannot be the second program in that sequence?

Statements: Some apples are watermelons. All watermelons are fresh. Some potatoes are fresh.
Conclusions:
I. Some apples are fresh.
II. Some potatoes are apples.
III. Some watermelons are potatoes.
IV. Some watermelons are apples.

Statements: All pens are pencils. Some pens are erasers. Some erasers are clips.
Conclusions:
I. Some clips are pens.
II. No clip is a pen.
III. Some erasers are pencils.
IV. No eraser is a pencil.

Statements: Some books are papers. Some papers are plastic. No plastic is black.
Conclusions:
I. Some papers are not black.
II. All papers are not black.
III. Some papers are black.
IV. Some books are black.

Statements: Some doors are windows. All windows are black. Some black are brown.
Conclusions:
I. Some windows are brown.
II. All doors are black.
III. Some doors are black.
IV. No window is brown.

Statements: All teachers are doctors. All doctors are engineers. All engineers are typists.
Conclusions:
I. Some typists are teachers.
II. All doctors are typists.
III. Some engineers are teachers.
IV. All doctors are teachers.

Statement: Air export volumes have increased substantially over the past decade causing backlogs and difficulties for air cargo agents because of increased demand for space and service.
Courses of Action:
I. Airlines and air cargo agents should jointly work out a solution to combat the problem.
II. The reasons for the increase in the volume of air export should be found out.

Statement: The world conference on “Education of All” took place in Thailand in 1990. Widely attend conference endorsed the Framework for Action for Meeting the Basic Learning Needs of all Children.
Course of Action:
I. India should suitably implement the Action points of this conference.
II. India should also immediately organize this type of conference.

Statement: About 30 to 40% of children who are enrolled, do not attend school on any given day.
Course of Action:
I. More schools should be started
II. Reasons for their absenteeism should be found out.

Statement: Although the Indian economy is still heavily dependent on agriculture, its share in global agricultural trade is less than the share of agricultural exports to total exports.
Course of Action:
I. Efforts should be made to increase our agricultural production.
II. The exports of non-agricultural commodities should be reduced.

Statement: Huge amount of resources are required to develop tourist places in a country like India which is endowed with vast coastal lines, rivers, forests, temples, etc.
Courses of Action:
I. More tourist-resorts along the coastal line only should be started.
II. The tourist-potential of India should be exploited.

How many daughters does ‘L’ have?
P. R’s father has three daughters.
Q. ‘T’ is R’s sister and daughter of L.

Who is the brother of C?
P. D is the daughter of M.
Q. M is the father of C.

A library contains only English, Hindi and Telugu novels. How many Telugu novels are there in the library?
P. Of the one thousand novels is the library, fifty per cent novels are in English and Hindi.
Q. The number of Hindi novels is double the number of English novels.

“You must renew your driving licence within ten days from the date of expiry”.
What is the exact date before which the licence must be renewd?
P. The statement was uttered on 17th February.
Q. It was a leap year.

The area of a playground is 484 sq. metres. What is its perimeter?
P. It cots Rs. 912 to put a fence around the playground.
Q. The playground is a perfect square.

Four of the following five are alike in a certain way and so form a group. Which
one of the following does not belong to the group?

Raman starts walking towards West. After walking 10 metres he turns towards North. After walking 20 metres he turns towards East and walk 10 meters. How far is he from him original position and in which direction?

Anxiety causes ulcer. However, some who are happy-go-lucky type also suffer from ulcer. Which of the following would strengthen the association of anxiety and ulcer?

Role conflict and ambiguity are the most widely examined source variables in managerial stress research. Research in this area is extremely homogeneous, as anywhere from 50% to 85% of this literature employs scales developed by APA. Based on the above information, which of the following can be concluded?

‘A’ is taller than ‘B’. ‘C’ is taller than ‘D’, ‘D’ is taller than ‘E’. To determine who among them is the tallest, which of the following further information, if any, is required?

Statements:
1. According to an authentic report, several militants were hiding in area X.
2. In spite of a thorough search they could not be found.
RI. The locals were providing them with a cover.
RII. When they came to know about the search, they moved on to another area.

Statements:
1. Many officers were transferred at a very short notice by the Chief Secretary.
2. Only those officers, who kept the Chief Secretary in good humour were not transferred.
RI. The Chief Secretary is a jolly person.
RII. The transfers were based on personal feelings of the Chief Secretary.

Statements:
1. Party ‘X’ lost elections in a certain area.
2. Lack of enthusiasm in the party workers was very noticeable.
RI. The party workers play a major role during election campaign.
RII. Had the workers been the devoted type, the party was sure to win the elections.

Statements:
1. Only those buildings fell down during heavy rains which had faulty designs or inferior material.
2. The heavy rains wiped a whole colony.
RI. The houses in the colony had faulty designs.
RII. An inferior kind of building material was used during construction.

Statements:
1. If a person dies while he is in police custody, the policeman are summoned by the Court.
2. If atrocities are proved, they are punished by law.
RI. Law is very considerate for the criminals.
RII. No person can die a natural death while he is in police custody.

(A) No wealthy persons are vagrants.
(B) All lawyers are wealthy persons.
(C) Some lawyers are vagrants.
(D) Some wealthy persons are not vagrants.
(E) No lawyers are vagrants.
(F) All lawyers are vagrants.

(A) All voters are residents.
(B) Some voters are citizens.
(C) All citizens are residents.
(D) No citizen is a resident.
(E) All voters are citizens.
(F) Some residents are voters.

(A) Some preachers are persons of unfailing vigor.
(B) Some intellectuals are persons of unfailing vigor.
(C) No preacher is an intellectual.
(D) Some persons of unfailing vigor are not preachers.
(E) All preachers are persons of unfailing vigor.
(F) Some intellectuals are not preachers.

(A) All students are the people who saw the game.
(B) All persons who saw the game are persons who were at dance.
(C) Some students were persons who were at the dance.
(D) Some persons who saw the game are students.
(E) Some students are not the persons who saw the game.
(F) No one who was at the dance saw the game.

(A) Some intellectuals are shy and retiring people.
(B) Some shy and retiring people are successful politicians.
(C) No intellectuals are successful politicians.
(D) All shy and retiring people are intellectuals.
(E) Some successful politicians are intellectuals.
(F) No shy and retiring people are successful politicians.

The royal court of Alauddin was graced by the great poet

Match the facts of List-1 with List-2 and then answer which choice is correct?

The name of India’s first aircraft carrier is

Which of the following is associated with the manufacture of guided missiles?

National Highway No. 3 runs from

The first nuclear test was conducted in India in the year

Which State grows nearly 30 per cent of world opium?

A list of national languages can be traced in the ................... Of the Indian Constitution.

Which one of the following provides constitutional guarantee of personal freedom?

Which one of these countries is not in Scandinavia?

What is the official language of the Argentina?

Falkland Islands are in

The French Revolution gave its modern meaning to the term

The Iran-Iraq war started for exclusive possession of

‘Dirham’ is the currency of

OPEC stands for

A light-year is a unit of

The main masses of land above sea level are called

The Mineral resource which has made Middle East of vital importance to the
world to-day is

Which one of the following match with ‘Khetri, Jharia, Kudermukh, Kolar
respectively?

The Alpine races mostly live in the Indian States of

Which of the following factors influence the climate of India?

What is the distance of running in a marathon race?

‘Prince of Wales Cup’ is associated with the game of

‘Quessberry Rules’ is the name given to the rules in

Who was the first recipient of Nehru Award for International Understanding?

Which of the following Indians was awarded ‘Legion D Award’, the highest civilian
award of France?

C.Funk’s name has been associated with the research of which of the following?

Who defined democracy as a “Government of the people, by the people and for
the people”?

Who said, “give me somewhere to stand, and I will move the world”?

Ben Hur, the world famous epic, is written by

Poliomyelitis is caused by

A person in normal health requires per day

The fourth estate is

‘Hertz’ is a unit of

A ‘bear’ on the Stock Exchange is a speculator

The function of DNA in the body is

Which of the following is called a ‘red planet’?

In a human body, the basic building block are

Which feature film was screened in the UN in Nov. 2006?