Area of the region bounded by y = |x| and y=2 in sq. units is

The area bounded by , axis of abscissa and two ordinates corresponding to two points of minima of the function y = f(x) is

The area bounded by and is

The area enclosed between the curve and the co-ordiante axes is

The area (in square units) of the region bounded by

is

The area bounded between the parabolas and , and the straight line y = 2 is

The area bounded by the curves and is

The area bounded by the curves y=cosx and y=sin x between the ordinates x=0 and

The area under the curve with boundaries as X-axis and the ordinates x = 0, x = 3 in sq. units is

The area (in square units) bounded by the curves , x-axis and lying in the first quadrant is

A body is thrown vertically up to reach its maximum height in t seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is

Calculate rms speed of O2 at 273 K and 1 * 10^5Pa pressure. The density of O2 under these conditions is 1.42 kg m–3.

Calculate the pressure exerted on the walls of a 3 litre flask when 7 gms of N2 are introduced into the same at 27°C.

Explain the following

a) Although Au is soluble in aqua-regia, Ag is not

b) Zinc and hot copper is used for recovery of Ag from the complex [Ag(CN)2]–

c) Aluminium metal is frequently used as a reducing agent for extraction of metal such as chromium manganese etc.

d) Partial roasting of sulphide ore is done in the metallurgy of copper.

Cinnabar (HgS) and galena (PbS) on roasting often gives their respective metals but zinc blende (ZnS) does not. Explain.

Aluminium cannot be prepared by the electrolysis of aqueous solution of its salts. Why?

Write short notes on Amalgamation , Hydrometallurgy, Self reduction, Electrolytic reduction?

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

The line L given by passes through the point (13, 32). The line K is parallel to L and has the equation

.Then the distance between L and K is?

The area bounded by the curves y = cosx and y = sinx between the ordinates x = 0 and x = 3π/2 is

Solution of the differential equation cosxdy = y(sinx – y)dx, 0 < x < p/2 is

Consider the system of linear equations

x1 + 2x2 + x3 = 3

2x1 + 3x2 + x3 = 3

3x1 + 5x2 + 2x3 = 1

The system has

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 (O_{2}) 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 (O_{2}) 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