An infinite number of identical circular discs each of radius  are tightly packed such that the centers of the discs are at integer values of coordinates x and y . The ratio of the area of the uncovered patches to the total area is .

It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A. How many days will it take for a raft to drift from A to B (all speeds stay constant ) ?

“ My friend Raju has more than 1000 books “, said Ram . “ Oh no , he has less than 1000 books”, said Shyam .’’ Well , Raju certainly has at least one books “, said Geeta . If only one of these statements is true , how many books does Raju have ?

Of the following , Which is the odd one out ?

A student appearing for an exam is declared 1oto have failed the exam if his /her  score.This implies

Find the next figure ‘D'

N is a four digit number . If the leftmost digit is removed , the resulting three digit number is 1/9 ^th of N. How many such N are possible ?

AB and CD are two chords of a circle subtending 60^o and 120^o respectively at the same point on the circumference of the circle . Then AB:CD

Which of the following inferences can be drawn from the above graph?

What is the minimum number of moves required to transform figure 1 to figure 2 ? A move is defiend as removing a coin and placing it such that it touches two other coins in its new position

The relatiopnship among the numbers in each corner squre is the same as that in the other corner squres . Find the missing

Which of the following best approximates sin (0.5^o )?

What comes next in the sequence ?

Which of the following statements is logically incorrect

How many times strating at 1:00 pm would the minute and hour hands of clock make an angle of 40^o  with each other in the next 6 hour ?

Brothers Santa and Chris walk to school from their house .The former takes 40 minutes While the latter , 30 minutes. One day Santa Started 5 minutes earlier than Chris. In how many minutes would Chirs overtake Santa ?  

The set of numbers (5,6,7,m,6,7,8,n) has an arthimetic mean of 6 and mode (most frequency occuring number ) of 7. Then = mX n =

The diagram shows a block of  marble having the shape of a triangular prism. What is the maximum number slabs of 10X10X5 cm³ Size that can be cut parallel to the face on which the block is resting ?

A soild contains a spherical cavity is filled with a liqued and includes a spherical bubble of gas . The radii of cavity and gas bubble are 2 mm and 1 mm , respetively . What  proportion of the cavity is filled with liquid ?

Fill in the blank : F2 , _______, D8, C16, B32 , A64.

An inverted cone is filled with water at a constant rate. The volume of water inside the cone as a function of time is represented by the curve :

 

A spacecraft flies at a constant height R above a planet of radius R. At the instant the spacecraft is over the north pole, the lowest latitude visible from the spacecraft is :

An experiment consists of tossing a coin 20 times. Such an experiment is performed 50 times. The number of heads and the number of tails in each experiment are noted. What is the correlation coefficient between the two ?

Which of these groups of numbers has the smallest mean ?
Group A : 1, 2, 3, 4, 5, 6, 7, 8, 9
Group B : 1, 2, 3, 4, 6, 6, 7, 8, 9
Group C : 1, 2, 2, 4, 5, 6, 7, 8, 9
Group D : 1, 3, 3, 4, 5, 6, 7, 9, 9

Identical balls are tightly arranged in the shape of an equilateral triangle with each side containing n balls. How many balls are there in the arrangement ?

A shopkeeper has a faulty pan balance with a zero offset. When an object is placed in the left. plan it is balanced by a standard 100 g weight. When it is placed in the right pan it is bálanced by a standard 80 g weight. What is the actual weight of the object ?

A and B start from the same point in opposite directions along a circular track simultaneously. Speed of B is 2 / 3 rd that of A. How many times will A and B cross each other before meeting at the starting point ?

Consider a solid cube of side 5 units. After painting, it is cut into cubes of 1 unit. Find the probability that a randomly chosen unit cube has only one side painted .

How many integers in the set {1, 2, 3, .... 100} have exactly 3 divisors ?

The arithmetic and geometric means of two numbers are 65 and 25, respectively. What are these two numbers ?

The elements of the set {x : x is an integer, x² : 4} can be represent as .....Z..... . Here, Z refers to

If Y = {x : x is a positive factor of the number 2p – 1(2p – 1), where 2p – 1 is a prime number}, then Y can be represent in roster form as

The set {x : x is a positive integer less than 6 and 3x – 1 is an even number} in roster form is

If A B and A B, then

The number of non-empty subsets of the set{1, 2, 3, 4} is

The number of elements of the power set of a set containing m elements is

If A = {x : x = n², n = 1, 2, 3}, then number of proper subsets is

If A = {x : x = 4n + 1, 2 £ n £ 5},then number of subsets of A is

Let A and B be two non-empty subsets of a set X such that A is not a subset of B, then

Which of the following is/are empty set? 
A = {x : x2 + x + 1 = 0 and x Î Z}   B = {x : x is a prime number and 19 < x < 23}

The set {x : x⁴ = 1 and x R} is .....X.... set. Here, X refers to

The universal set for the sets   
A = {x : x² – 5x + 6 = 0} and   
B = {x : x² – 3x + 2 = 0} having least number of elements is

If A = {1, 2, 3}, B = {x € R : x2 – 2x + 1 = 0}, 

If A = (–3, 5) and  B = [–7, 9], then

Yojna a weekly journal

Kurukshetra a journal on rural development is published by

Devaluation of a currency means

In India rural incomes are generally lower than the urban incomes, which of the following reasons account for this
            1. a large number of farmers are illiterate and know little about scientific agriculture
            2. prices of primary products are lower than those of manufactured products
            3. Investments in agriculture has been low when compared to investment in industry

Which of the following programmes aims at the promotion of savings among rural women