An elastic string of unstretched length  and force constant  is stretched by a small length . It is further stretched by another small length . The work done in the second stretching is

A shell of mass  moving with velocity  suddenly breaks into 2 pieces. The part having mass  remains stationary. The velocity of the other shell will be

If  then B=

The set S : = { 1, 2, 3 .........12} is to be partitioned into three sets A, B, C of equal size. Thus A  B  C = S, A  B = B  C = A  C = . The number of ways to partition S is -

A one kilowatt motor is used to pump water from a well 10 m deep. The quantity of water pumped out per second is nearly

Assertion (A) : The Remainder obtained when the polynomial  is divided by  Is 1
Reason (R): If  is divided by  then the remainder is f(a)

A ball hits the floor and rebounds after inelastic collision. In this case

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.

Statement II Principle of conservation of momentum holds true for all kinds of collisions.

A mass M  is lowered with the help of a string by a distance h at a constant acceleration g/2. The work done by the string will be

A particle begins at the origin and moves successively in the following manner as shown, 1 unit to the right, 1/2 unit up, 1/4 unit to the right, 1/8 unit down, 1/16 unit to the right etc. The length of each move is half the length of the previous move and movement continues in the ‘zigzag’ manner indefinitely. The co-ordinates of the point to which the ‘zigzag’ converges is –

The greatest possible number of points of intersections of 8 straight line and 4 circles is :

The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows
The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.
The number point of intersection between two circles can be counted by finding the number of ways in which two circles can be selected out of the lot multiplied by 2 as two circles can intersect at most two points.
The number point of intersection between two circles can be counted by finding the number of ways in which one circle and one line can be selected out of the lot multiplied by 2 as one circle and one line can intersect at most two points.

Assertion (A):If ,then A
Reason (R) : 

A force–time graph for a linear motion is shown in figure where the segments are circular. The linear momentum gained between zero and  is

How many different nine digit numbers can be formed from the number 2,2,3,3,5,5,8,8,8 by rearranging its digits so that the odd digits occupy even position ?

Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.

A person predicts the outcome of 20 cricket matches of his home team. Each match can result either in a win, loss or tie for the home team. Total number of ways in which he can make the predictions so that exactly 10 predictions are correct, is equal to :

The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is (repetition is not allowed) :

 Alternatively, we can use the formula for the sum of numbers as

We can also solve this problem by writing all the possible numbers and finding the sum of them which will be time taking and make us confused. We should know that the value of the digits is determined by the place where they were present. We should check whether there is zero in the given digits and whether there are any repetitions present in the numbers. Similarly, we can expect problems to find the sum of numbers formed by these digits with repetition allowed.