The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. What is the period of oscillation?

Starting from the origin, a body oscillates simple harmonically with a period of 2 s. After what time will its kinetic energy by 75% of the total energy?

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During the observation, till water is coming out, the time period of oscillation would

If a simple harmonic motion is represented by its time period is

The polymer containing strong intermolecular forces e.g., hydrogen bonding is?

29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl's method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete neutralisation. The percentage of nitrogen in the compound is?

Two simple harmonic motions are represented by the equations and . The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

The functionrepresents

In forced oscillation of a particle the amplitude is maximum for a frequency *w*1 of the force, while the energy is maximum for a frequency *w*2 of the force, then

A particle of mass m is attached to a spring (of spring constant *k*) and has a natural angular frequency An external force F(*t*) proportional tois applied to the oscillator. The time displacement of the oscillator will be proportional to

The total energy of a particle, executing simple harmonic motion is :

x / x^{2} / independent of x / x^{1/2}

where x is the displacement from the mean position.

A particle at the end of a spring executes simple harmonic motion with a period t_{1}, while the corresponding period for another spring is t_{2}. If the period of oscillation with the two springs in series is *T*, then

The bob of a simple pendulum executes simple harmonic motion in water with a period *t*, while the period of oscillation of the bob is t_{0 }in air. Neglecting frictional force of water and given that the density of the bob is (4/3) × 1000 kg/m^{3}. What relationship between *t* and *t _{0}* is true?

A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function of displacement *x*. Which of the following statement is true?

The length of a simple pendulum executing simple harmonic motion is increased by 21%. Then what will be the percentage increase in the time period of the pendulum of increased length?

Two particles *A* and *B* of equal masses are suspended from two massless springs of spring constants *k _{1}* and

*k*, respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of

_{2}*A*and

*B*is

A child swinging on a swing in sitting position stands up, then the time period of the swing will

increase / decrease / remains same /increases if the child is long and decreases if the child is short.

In a simple harmonic oscillator, at the mean position

If a spring has time period *T*, and is cut into *n* equal parts, then the time period of each part will be

In a simple harmonic oscillator, at the mean position

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of

choices available to him is?

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

Then number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

Total number of four digit odd numbers that can beformed using0,1,2,3,5,7 are

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are

Number greater than 1000 but less than 4000 is formed using the digits 0, 2, 3, 4 repetition allowed is

## The real value of 'a' for which sum of square of the roots of the equation assume the least value is

The real value of 'a' for which sum of square of the roots of the equation

assume the least value is

A point oscillates along the x axis according to the law . Draw the approximate plots

(a) of displacement x, velocity projection vx, and acceleration projection wx as functions of time t;

(b) velocity projection vx and acceleration projection wx as func- tions of the coordinate x.

If a young man rides his motorcycle at 25 km/hour, he had to spend Rs. 2 per km on petrol. If he rides at a faster speed of 40 km/hour, the petrol cost increases at Rs. 5 per km. He has Rs. 100 to spend on petrol and wishes to find what is the maximum distance , he can travel within one hour. Express this as an LPP and solve it graphically

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5,760 to invest and has space for at most 20 items. A fan and sewing machine cost Rs. 360 and Rs. 240 respectively. He can sell a fan at a profit of Rs. 22 and sewing machine at a profit of Rs. 18. Assuming that he can sell whatever he buys, how should he invest his money in order to maximize his profit? Trans late the problem into LPP and solve it graphically

Two tailors A and B earn Rs.150 and Rs.200 per day respectively. A can stitch 6 shirts and 4 pants per day while B can stitch 10 shirts and 4 pants per day. Form a linear programming problem to minimize the labour cost to produce at lest 60 shirts and 32 pants

A company has two plants to manufacture motor cycles. 70% motor cycles are manufactured at the first plant, while 30% are manufactured at the second plant. At the first plant, 80% motor cycles are rated of the standard quality while at the second plant, 90% are rated of standard quality. A motor cycle, randomly picked up, Is found to be of standard quality. Find the probability that it has come out from the second plant?

An object starts at the origin in a straight line. Its velocity versus time graph is shown in the figure. Which one of the following choices best gives the proper intervals(s) of time for which the object is moving away from the origin?

Two identical discs of mass m and of radius R touch each other and move with the same velocity perpendicularly to the line segment which joins their centres of mass, along the surface of a horizontal smooth tabletop. There is a third disc of mass M and of radius R at rest, at a point on the perpendicular bisector of the line segment joining the centres of mass of the two moving discs as shown in the figure. The two moving discs collide elastically with the third one, which is at rest. There is no friction between the rims of the discs. What should the ratio of M/m be in order that after the collision the two discs of mass m move perpendicularly to their initial velocity?

A triangular frame consists of three identical rods, each of mass m and length *l*. It rests upright on a horizontal smooth surface with its lower right corner against a stop about which the frame could pivot. A horizontal force of magnitude F is applied to the upper corner of the

frame as shown in the figure. What is the largest value of F may have without causing the frame to pivot upward about the stop?

A particle is moving along straight line such that dot product of its acceleration and velocity is negative. How many times particle can be found at a distance d from the origin?

A uniform, solid cylinder having mass M and radius R is pulled by a horizontal force F acting through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?

An object of mass M starts from rest at the bottom of a fixed incline of height H. A person decides to push the object up the incline in one of two ways with an applied force shown in the diagram. In each of the trials, the object reaches the top of the incline with speed V. How would the work done by the person on the block compare for the two trials? Assume the same constant non-zero coefficient of kinetic friction between the incline and the object for both trials.

The position versus time graph of a particle moving along a straight line is shown. What is the total distance travelled by the particle from t = 0 s to t = 10s?

A wedge of mass M= 10kg, height h= 3m and angle of inclination is at rest at horizontal surface. There is a small point – like object (mass m = 0.5kg) next to the slope as shown in the figure. At what acceleration must wedge be moved in order that the point like object reaches its top in a time t = 5s (Neglect the friction between point like object and wedge)

Ram pushes eight identical blocks on the horizontal frictionless surface with horizontal force F. The force that block-1 exerts at block-2 has magnitude and the force that block-7 exerts on the block-8 is