If 
and 
are the roots of the equation 
If 
, then for all real x
Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval
If the mean deviation about the median of the numbers a, 2a, ......., 50a is 50, then |a| equals
A man saves ` 200 in each of the first three months of his service. In each of the subsequent months his saving increases by ` 40 more than the saving of immediately previous month. His total saving from the start of service will be ` 11040 after
The coefficient of 
in the expansion of 
is?
A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed v ms-1. The velocity of sound in air is 300 ms-1. If the person can hear frequencies upto a maximum of 10000 Hz, the maximum value of v upto which he can hear the whistle is
An observer moves towards a stationary source of the sound, with a velocity onefifth of the velocity of sound. What is the percentage increase in the apparent frequency?
When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. if the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?
The displacement y of a particle in a medium can be expressed as:
m, where t is in second and x in the meter.
What is the speed of the wave?
A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
A metal wire of a linear mass density of 9.8 g/m is stretched with a tension of 10 kg-wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency u. The frequency u of the alternating source is
The displacement of a particle varies according to the relation 
The amplitude of the particle is
The displacement y of a wave travelling in the x direction is given by
where x is expressed in metre and t in second. The speed of the wavemotion, in ms-1 is
Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it is
A wave 
on a string meets with another wave producing a node at x = 0. Then the equation of the unknown wave is
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?
A wave traveling along thexaxis is described by the equation 
. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then a and b in appropriate units are
The speed of sound in oxygen (O2) at a certain temperature is 460 ms-1. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of
A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
A wave traveling along thexaxis is described by the equation . If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then a and b in appropriate units are
The speed of sound in oxygen (O2) at a certain temperature is 460 ms-1. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of
A string is stretched between fixed points separated by 75 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed v ms-1. The velocity of sound in air is 300 ms-1. If the person can hear frequencies upto a maximum of 10000 Hz, the maximum value of v upto which he can hear the whistle is
An observer moves towards a stationary source of the sound, with a velocity onefifth of the velocity of sound. What is the percentage increase in the apparent frequency?
When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per second are heard. if the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?
The displacement y of a particle in a medium can be expressed as:
m, where t is in second and x in the meter.
What is the speed of the wave?
A tuning fork of known frequency 256 Hz makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
A metal wire of a linear mass density of 9.8 g/m is stretched with a tension of 10 kg-wt between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency u. The frequency u of the alternating source is
The displacement of a particle varies according to the relation The amplitude of the particle is
The displacement y of a wave travelling in the x direction is given by
where x is expressed in metre and t in second. The speed of the wavemotion, in ms-1 is
Length of a string tied to two rigid supports is 40 cm. Maximum length (wavelength in cm) of a stationary wave produced on it is
A wave on a string meets with another wave producing a node at x = 0. Then the equation of the unknown wave is
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