A tuning fork arrangement (pair) produces 4 beats/sec with one fork of frequency 288 cps. A little wax is placed on the unknown fork and it then produces 2 beats/sec. What is the frequency of the unknown fork?
Tube A has both ends open while tube B has one end closed, otherwise they are identical. What is the ratio of the fundamental frequency of tube A and B?
If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is
A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute.If a1 =a2 =...=a10 =150 and a10, a11,....arein an A.P. with common difference –2, then the time taken by him to count all notes is
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is
For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
In a binomial distribution ,
, if the probability of at least one success is greater than or equal to 9/10 , then n is greater than
If the roots of the equation bx2 +cx+a=0 be imaginary, then for all real values of x. The expression
If the roots of the equation bx2 +cx+a=0 be imaginary, then for all real values of x. The expression
The sum to infinity of the series
One ticket is selected at random from 50 tickets numbered 00, 01, 02, ...., 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, equals
If the mean deviation of number1,1+d,1+2d,...., 1 + 100d from their mean is 255, then the d is equal
If the mean deviation of number1,1+d,1+2d,...., 1 + 100d from their mean is 255, then the d is equal
The remainder left out when 
is devided by 9 is
From 6 different novels and3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. Then the number of such arrangements is
The number of value of x in the interval [0, 3pai] satisfying the equation 
if 
is equal to
In a triangle ABC, let 
If r is the inradius and R is the circumradius of the triangle ABC, then 2(r + R) equals
If in a ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sinA, sinB, sinC are in
The sides of a triangle are sina, cosa and and 
then the greatest angle of tringle is?
If 
then the difference between the maximum and
minimum values of u2 is given by
Let 
such that 
if 
then value of 
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is 60o and when he retires 40 meters away from the tree the angle of elevation becomes 30o. The breadth of the river is
The upper 3/4th portion of a vertical pole subtends an angle tan–1(3/5) at a point in the horizontal plane through its foot and at a distance 40 m from the foot. A possible height of the vertical pole is
The number of solution of tanx + secx = 2cosx in [0, 2p) is
The half-life period of a first order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the chemical reaction will be (log 2 = 0.301)
One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44 u. The alkene is?
Solubility product of silver bromide is 5.0 × 10–13. The quantity of potassium bromide (molar mass taken as 120 g mol–1) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is
At 25°C, the solubility product of Mg(OH)2 is 1.0 × 10–11. At which pH, will Mg2+ ions start precipitating in the form of Mg(OH)2 from a solution of 0.001 M Mg2+ ions ?
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency w. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
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 function
represents
In forced oscillation of a particle the amplitude is maximum for a frequency w1 of the force, while the energy is maximum for a frequency w2 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 to
is 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 / x2 / independent of x / x1/2
where x is the displacement from the mean position.
A particle at the end of a spring executes simple harmonic motion with a period t1, while the corresponding period for another spring is t2. 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 t0 in air. Neglecting frictional force of water and given that the density of the bob is (4/3) × 1000 kg/m3. What relationship between t and t0 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 k1 and k2, respectively. If the maximum velocities, during oscillations, are equal, the ratio of amplitudes of 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