Which of the following is fully fluorinated polymer?

KMnO4 acts as oxidising agent in acidic medium. The number o moles of KmnO4 that will be needed to react with one mole of sulphide ions in acidic solution is

During the adiabatic process,

Solid carbon dioxide is an  example of

Law of constant composition does not hold true for

The Major product of nitration of benzoic acid is

The reaction, \({ 3ClO }^{ - }(aq)\longrightarrow { ClO }_{ 3 }^{ - }(aq)+2{ Cl }^{ - }(aq),\) is an example of 

When a copper wire is immersed in silver nitrate solution ,the colour of the solution becomes blue,because copper

If 400\(\Omega\) of resistance is made by adding four 100\(\Omega\) resistance of tolerance 5%, then the tolerance of the combination is

If L has the dimensions of length; V that of potential and \({ \epsilon }_{ 0 }\)  is the permittivity of free space, than the quantity \({ \epsilon }_{ 0 }LV\) have the dimensions of

The solution set of (x)² + (x + 1)² = 25, where (x) is the nearest integer greater than or equal to x, is

\(\int { \frac { sinx }{ sin|x-\alpha ) } } dx,\) equals

If \(f(x)=cos[{ \Pi }^{ `2 }]x+cos[{ -\Pi }^{ `2 }]x,\)where [x] stands for the greatest integer function,then

Consider the experiment of rolling a die. Let A be the event of 'getting a prime number and B be the event of 'getting an odd number', then
A and B=

The one which is the measure of the central tendency, is

If -2, 2,1 are direction of a line, then its direction cosines are

\(\left| \vec { a } \times \vec { b } \right| ^{ 2 }+\left| \vec { a } .\vec { b } \right| ^{ 2 }\) =144 and \(\left| \vec { a } \right| =4\) and \(\left| \vec { b } \right| \) is equal to 

Let  \({ f }_{ 1 }\left( x,y \right) \equiv { ax }^{ 2 }+2hxy+b{ y }^{ 2 }=0\)  and let  \({ f }_{ i+1 }\left( x,y \right) =0\)  denotes the equation of the bisectors of  \({ f }_{ i }\left( x,y \right) =0\) for all i = 1, 2, 3, ....
On the basis of above information, answer the following questions:
If f_i+1(x, y) = 0 represents the equation of a pair of perpendicular lines, then \({ f }_{ n+2 }\left( x,y \right) =0\forall n\ge 2\) is same as

If \(\cos { x } +\sin { x } =a\left( -\frac { \pi }{ 2 } <x<-\frac { \pi }{ 4 } \right) \), then cos 2x is equal to

If the two circles x²+y²=r² and (x-5)²+y²=9 intersect in two distinct points,then

In the quadratic equation a x² + bx + c = 0, if \(\Delta ={ b }^{ 2 }-4ac\) and \(\alpha +\beta ,{ a }^{ 2 }+{ \beta }^{ 2 },{ a }^{ 3 }+{ \beta }^{ 3 }\) are in GP, where a, \(\beta\)  are the roots of a x² + bx + c = 0, then

if the coefficients of x⁷ and x⁸ in \(\left( 2+\frac { x }{ 3 } \right) ^{ n }\) are equal then n is

If m and n are two odd positive integers with n2-n² is

Compute \(\cfrac { 7! }{ 5! } \)

If \(\alpha \) and \(\beta \) are the roots of the equation \({ 2x }^{ 2 }-(p+1)x+(p-1)=0\) and \(\alpha -\beta =\alpha \beta \), then what is the value of p 

If a,b,c are distinct real numbers and
​​​​​​​\(\left| \begin{matrix} a & { a }^{ 2 } & { a }^{ 3 }-1 \\ b & b^{ 2 } & { b }^{ 3 }-1 \\ c & { c }^{ 2 } & { c }^{ 3 }-1 \end{matrix} \right| =0\) then

The modulus of the complex number \(z=\frac { (1-i\sqrt { 3 } )(cos\theta +isin\theta ) }{ 2(1-i)(cos\theta -isin\theta ) } \) is

If P={1,2} then the set PxPxP is

The sum of the series 1²+(1²+2²)+(1²+2²+3²)to n terms=...

Isoelectric point is a

The strongest acid amongst the following compound is

Identify B and C in the following reaction series.\(CH_2=CH_2\xrightarrow{Conc. H_2SO_4}\ A\xrightarrow{\Delta/H_2O}\ B\ \xrightarrow{PBr_3}\ C\)

Which of the following on thermal decomposition yields a basic as well as acidic oxide?

The highest oxidation state of Mn is in 

Aluminium is 

Which of the following statements regarding S_N1 reaction shown by alkyl halide is incorrect?

Which of the following metals does not form amalgams?

16.26 milligram  of  a  sample  of an  element  X  contains  1.66 x 10²⁰ atoms. What  is  the  atomic mass  of the  element X ?

The element  X(atomic weight) = 75) and Y (atomic weight =16) combine to give a compound containing 75.8% X. The moleculer formula of the compound is:

\(\beta\)-particle is emitted in radioactivity by

A colloid can be purified by

Match the following and choose the correct option.

When mercuric iodide is added to the aqueous solutions of KI, the

When white phosphorus reacts with caustic soda, the produces are PH₃ and NaH₂PO₂ . This reaction is an example of

Standard electrode potential,E₀ values in volts,of a few metals are given below

Mg²⁺/Mg=-2.37,Zn²⁺/Zn=-0.76;Sn²⁺/Sn =-0.14

Which one of the following conclusions drawn from Which one of the following conclusions drawn from these values is wrong?

The Solubility of BaSO₄ at 20⁰C is 2.23*10^-4g per 100 ml. the solublity product of BaSO₄ would be 

The equilibrium constant in a reversible chemical reaction at a given temperature

In which of the following reactions would \(\Delta\)E be equal to \(\Delta\)H?

Pressure of 1 g of an ideal gas A at \({ 27 }^{ \circ }C\) is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. The ratio between their molecular masses M_A/M_B would be

Which of the following has the highest value of lattice energy?

Uncertainity in position of a minute particle of mas 25g in space is 10^-5m.What is the uncertainity in its velocity in ms^-1?(h=6.6X10^-34Js)

A transverse wave is travelling in a string. Equation of the wave:

Which one of the following graphs represents the behaviour of an ideal gas?

When a charge moves in a uniform magnetic field

The difference between phase and frequency modulation

The unit cell of silicon is a

The binding energy per nucleon of \({ Li }^{ 7 }\)and \({ He }^{ 4 }\) are 5.6 MeV and 7.06 Mev respectively, Then the energy of the reaction : \({ Li }^{ 7 }\)+ P = \(2[_{ 2 }{ He }^{ 4 }]\) is

The photoelectric current at distances \(r_{1}\) and \(r_{2}\) of light source from photoelectric cell are \(I_{1}\) and \(I_{2}\) respectively.

The value of \(I_{1}\over I_{2}\) will be

A source of electromagnetic wave have power output of 800 W. The maximum value of electric field at distance of 4 m from the source is

A parallel monochromatic beam of light is incident normally on a narrow slit.A diffraction pattren is formed on a screen placid perpendicular to the direction of the incident beam. At the first minimum of the diffraction pattren, the phase difference between the rays coiming from the two edges of the slits is

The wavelength of light diminishes \(\mu \) times in a medium. A driver from inside water (\(\mu \)=1.33) looks at an object whose natural colour is green. He sees the object as

Thermocouple is based on the principle of

A cube of side 10 cm has resistance of 50 ohm across two opposite faces.  The electrical conductivity of its material in siements per metre is

The electric potential V at any point (x,y,z) in space is given by V=\(4 {x} ^ { 2 }\) volt.The electric field at (1,0,2) m in \(V{ m }^{ -1 }\)is

When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude 'a' is

One end of a conducting rod is maintained at temperature 50°C and at the other end ice is melting at 0°C. The rate of melting of ice is doubled if:

A ship,floating in clear water of density 1000 kg m^-3,moves, to sea-water of density 1050 kg m^-3 where it floats again.The upthrust on the ship then

Suppose, there existed a planet that went around the sun twice as ast as the earth. What would be its orbital size as compared to that of the earth?

A body having moment of inertia about its axis of rotation equal to 3 kg-m² is rotating with angular velocity equal to 3 rad/sec. Kinetic energy of this rotating body is the same as that of a body of mass 27 kg moving with a speed of:

The kinetic energy acquired by a mass m in travelling a certain distance d, starting from reset, under the action of a constant force is directly proportional to

A person who is at rest on completely frictionless ice covering a lape, could reach shore by

A projectile can have the same range R for two angles of projection. If t₁ and t₂ be the times of flight in the two cases, then what is the product of two times of flight?

A man is at a height of 100 m. He sees a car which makes an angle of π/6 with man's position. If the car moves to a point where angle is π/3, what is the distance moved by it?

Which of the following will have the dimensions of time?

Passing through of points (3, -2) and (-1,4)

If \(tan^{-1}\left\{{\sqrt(1+x^2)}-\sqrt{(1-x^2)}\over \sqrt{(1+x^2)+\sqrt{(1-x^2)}} \right\}=\alpha, \)then x² is equal to

If \(tan^{-1}\left\{{\sqrt(1+x^2)}-\sqrt{(1-x^2)}\over \sqrt{(1+x^2)+\sqrt{(1-x^2)}} \right\}=\alpha, \)then x² is equal to

Assuming that the petrol burnt in a motor boat varies as the cube of its velocity, the most economical speed, when going against a current of c km/h is

If f' (x) = sin x + sin 4x· cos x, then f'\(\left( { 2x }^{ 2 }+\frac { \pi }{ 2 } \right) \)at \(x=\sqrt { \frac { \pi }{ 2 } } \)is equal to

The solution set of the equation log_x2log_2x2=log_4x2 is

The equation |x+1||x-1|=a²-2a-3 can have real solution for x, if a belongs x to

For the statement "19 is a real number or a positive integer" then "Or" is

If \({ sin }^{ -1 }\frac { 14 }{ \left| x \right| } +{ sin }^{ -1 }\frac { 2\sqrt { 15 } }{ \left| x \right| } =\frac { \pi }{ 2 } \) , then the value of x is

The general solution of sec4x - sec2x =2 is 

If e is the eccentricity of the hyperbola \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } -\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) and \(\theta\) is angle between the asymptotes, then cos \(\theta\)/2 is equal to :

Find the equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line Y - 4X + 3 = 0.

If function f(x) is continuous in the interval (a, b) and having same definition between a and b, then we can find \(\int _{ a }^{ b }{ f(x) } \) dx and if f(x) is discontinuous and not having same definition between a and b, then we must break the interval such that f(x) becomes continuous and having same defintion in the breaking intervals.
Now, if f (x) is discontinuous at \(x=c(a<c<b),\) ,then \(\int _{ a }^{ b }{ f(x) } dx=\int _{ a }^{ b }{ f(x) } dx+\int _{ a }^{ b }{ f(x) } dx\) and also if f(x) is discontinuous at x=a in (0,2a),then we can write \(\int _{ a }^{ 2a }{ f(x) } dx=\int _{ 0 }^{ a }{ \{ f(a-x)+ } f(a=x)\} \quad dx\)     
\(\int _{ \pi /2 }^{ 3\pi /2 }{ [2\quad sin\quad x]\quad dx } \) (where [.]   denotes greatest integer function) is equal to

\(\int \) \(\frac { 1 }{ { x }^{ 2 }\left( { x }^{ 4 }+1 \right) ^{ 3/4 } } \) dx is equal to 

The combined resistance R of two resistors R₁ and R₂(R₁,R₂>0)is given by \({1\over R}={1\over R_1}+{1\over R_2}\)
If R₂+R₂=C (a constant) then maximum resistance R is obtained if

If y = \((1+x)(1+{ x }^{ 2 })(1+{ x }^{ 4 })...(1+{ x }^{ 2^{ n } })\), then the value of \(\frac { dy }{ dx } \) at x = 0 is

The function f(x)=sin⁴x+cos⁴x increases, if

\(\lim _{ n\rightarrow \infty }{ \left( \frac { n! }{ \left( mn \right) ^{ n } } \right) ^{ 1/n } } \) (m  ∈ N) is equal to

If e^x+e^f(x)=e, then for f(x)

The solution of the differential equation xdy + (x + y) dx = 0 is

The integral 

\(\int _{ 0 }^{ 1 }{ \frac { { x }^{ a }-1 }{ logx } } dx\) equals

The left hand derivative of \(f\left( x \right) =\left[ x \right] \sin { \pi x } \) at x = k, where k is an integer and [ ] denotes the greatestt integer function is

Thr probabilities of occurance of two events A and B are 0.25 and 0.5 respectively. The probability of their simultaneous occuring is 0.14; then the probability that neither of these occurs, is

The frequency distribution table is given here.

Find the S.D.

The equation of the plane through the line of intersection of the planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0 and parallel to the axis, is

The position vectors of the points A,B,C are \(\left( 2\hat { i } +\hat { j } -\hat { k } \right) ,\left( 3\hat { i } -2\hat { j } +\hat { k } \right) \) and \(\left( \hat { i } +4\hat { j } -3\hat { k } \right) \) respectively. These position 

 If the lines represented by 2x² - 5xy + 2y² = 0 be the two sides of a parallelogram and the line 5x + 2y = 1 be one of its diagonal.
On the basis of above information, answer the following questions:
The ratio of the longer side to smaller side is

If the circles x²+y²+2x+2ky+6=0 and x²+y²+2ky+k=0, intersects ortogonally, then k is

If \({tan 3A\over tan A} = {k}\), then \(sinn 3A\over sin A \),is equal to

If 1.3+3.3²+5.3³+7.3⁴+.. upto n terms is equal to 3+(n-1).3b, then b=

The sum of the series \(1+\frac { 1 }{ { 3 }^{ 2 } } +\frac { 1.4 }{ 1.2 } .\frac { 1 }{ { 3 }^{ 4 } } +\frac { 1.4.7 }{ 1.2.3 } +\frac { 1 }{ { 3 }^{ 6 } } +...is\)

For every positive integer n, 7ⁿ-3ⁿ is divisible by 

The total number of numbers that can be formed by using all the digits 1, 2, 3, 4, 3, 2, 1, so that the odd digits always occupy the odd places, is

The condition that one root of the equation ax²+bx+c=0 may be square of the other, is 

If \(\left| \begin{matrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{matrix} \right| \)=k(a+b+c)³, then k is

If  \(x^2+1=0\Rightarrow x^2=-1 \)  or  \(x=\pm\sqrt{-1}=\pm i\) (iota) is called the imaginary unit.
Also, i²=-1,i³=i².i=(-1)i=-i and i⁴=(i²)²=(-1)²=1
ie, \(i^n+i^{n+1}+i^{n+2}+i^{n+3}=0\forall n\epsilon I(Interger) \) and x³-1=0\(\Rightarrow\)(x-1)(x²+x+1)=0
\(\Rightarrow (x-1)(x-\omega)(x-\omega^2)=0\)
\(\therefore x=1,\omega,\omega^2\)  are the cube roots of unity. ie,\(\omega^n+\omega^{n+1}+\omega{n+2}=0\forall n\epsilon I(interger)\)
Now let z=a+ib if \(|a:b|=\sqrt{3}:1 \ or 1:\sqrt{3}\)
Then, convert z in terms of  \(\omega,\ or\ \omega^2\) .  Also \(|1-\omega|=|1-\omega^2|=\sqrt{3}\)
If \((\omega\ne1)\) is a cube root of unity and \(i=\sqrt{-1}\) , then
\(\left| \begin{matrix} 1 & 1+i+{ \omega }^{ 2 } & { \omega }^{ 2 } \\ 1-i & -1 & { \omega }^{ 2 }-1 \\ -i & -i+\omega -1 & -1 \end{matrix} \right| \) is equal to

State T for true and F for false.
In a class of 140 students, 60 play football, 74 play hockey and 75 play cricket, 30 play hockey and cricket, 18 play football and cricket, 42 play football and hockey and 8 play all the three games. Then
(i) The number of students who do not play any of these three games is 42.
(ii) The number of students who play only cricket is 35.
(iii) The number of students who play football and hockey, but not cricket is 34.

Let A and B are two independent events. The probability that both A and B happen is \(\frac { 1 }{ 2 } \) and the probability that neither A nor B happens is \(\frac { 1 }{ 2 } \) then

Identify the incorrect statement about Al₂(SO₄)₃

In common-emitter circuit, the voltage gain is

The length of the tangent at the point \(t=\frac { \pi }{ 2 } \) on the curve \(x=\left( t+\sin { t } \right) ,y=\left( 1-\cos { t } \right) \) is

Which pair of ions gives ppt. when their dilute aqueous solutions are mixed?

Which of the following can act as both as an antiseptic and disinfectant?

The outer electron configuration of Gd (Atomic number 64) is

In the froth floatation process, for the facilitation of ores, the ore particles float because

Which of the following requires least energy to show photoelectric effect?

Of the following elements, which one has the same oxidation state in all of its compounds?

The following data are given as the standard enthalpies of combination of \(C(s), H_2(g)\) and \(CH_4(g)\) are \(-393.5\ kJ\ mol^{-1},-285.8\ kJ\ mol^{-1}\)  and \(-890.4\ kJ\ mol^{-1}\) respectively at 298 K.  The standard enthalpy of formation of methane \([CH_4(g)] \) is

The pykometric density of sodium chloride crystal is \(2.165\times 10^3\ kgm^{-3}.\) While its X-rays density is \(2.178\times 10^3\ kgm^{-3}\)  The fraction of unoccupied sites in NaCl crystal is

At higher temperature, greater number of molecules have high velocity.

The solid like conducting state of gases with free electrons is called

Which one of the following gases binds (about 200 times) to haemoglobin than oxygen?

Which one of the following is a vat dye?

Which one of the  following is not present in RNA?

Which of the following is used in coating non-sticking frying pans?

2,4 dinitrophenyl hydrazine is called

Which one of the following products is obtained when aniline reacts with bromine water?

In Rosenmund reduction,
\(RCOCl + H_2 \overset {Pd/BaSO_4 }{ \rightarrow } RCHO + HCl\)
BaSO₄ here,

Wax,of which candle is made ,is a mixture of

The product formed when butyne-1 reacts with excess of hydrogen bromide in absence of H₂O₂ would be

In the given heptane \({ ^{ 1 } }C{ H }_{ 3 }-{ ^{ 2 } }C{ H }_{ 2 }-{ ^{ 3 } }C{ H }_{ 2 }-{ ^{ 4 } }C{ H }_{ 2 }-{ ^{ 5 } }C{ H }_{ 2 }-{ ^{ 6 } }C{ H }_{ 2 }-{ ^{ 7 } }C{ H }_{ 3 },\) if one hydrogen is substituted by -OH group to give an optically active alcohol, the substitution should be done at carbon numbered

In spectrochemical series, chlorine lies above water because

Amongst TiF^2-, CoF^3-, Cu₂CI₂ and NiCI₄^2- (At. Nos. Ti=22, Co=27, Cu=29, Ni=28), the colourless species are :

What will be the molarity of a solution which contains 5.85 g NaCl(s) per 500 mL?

Which one of the following pairs of icons have the similar size?

Dichromate ions in alkaline medium exist as

Sodium hydroxide is prepared by the electrolysis of an aqueous solution of

The reaction of ethyl bromide and silver cyanide results in the formation of 

Nitrosifying bacteria conver ammonium compounds into 

Which one of the following metals is extracted by aluminothermic process?

How  many  molecules  of  benzene are  there  in  1 litre  of  benzene? Specific  gravity  of  benzene is  0.88.

The formation of a yellow precipitate by the addition of solution of ammonium molybdate to the sodium extract of an organic compound confirms the presence of

If the half-life for ¹⁴C is 5770 years, the n t_3/4 is 

Emulsion are prepared by

The rate of formation of SO₃ in the following reaction is 100g min^-1 \(2SO_2+O_2\longrightarrow2SO_3\)The rate of disappearance of O₂ is

K_f of water is 1.86 K Kg mol^-1 . If your automobiles radiator holds 1.0 kg of water, how many grams of ethylene glycol (C₂H₆O₂) you must add to get the freezing point of the solution lowered to -2.8^o C ?

In the reaction \({ 2I }^{ - }+{ Cl }_{ 2 }\longrightarrow { I }_{ 2 }+2C{ l }^{ - }\) the reductant is

A certain current liberated 0.504g of hydrogen in 2 hours.The approximate amount of copper deposited in grams by the same current flowing for the same time in a CuSO₄ solution:

If a neutral solution has pK_a=13.36 at 50⁰C, the ph of the solution is

For the equilibrium \(A+B\rightleftharpoons C+D;K_{c}=100\) at Equi.

In thermodynamics a process is called reversible when

Which of the following substances has the highest m.p.?

A pi bond

Energy of an electron in hydrogen atom is given by \(E=-\frac { 13.6 }{ { n }^{ 2 } } eV\). Which one of the following statements is true if n is changed from 1 to 4? Energy will

When two waves of almost equal frequencies n₁ and n₂ are produced simultaneously, then the interval between successive maxima is

For a simple pendulum, when a graph is plotted betwen displacement d, KE=\(1\over 2\)mv² and PE=mgh, taking d along X-axis and \(1\over 2\)mv² and mgh along Y-axis, the graph comes as

For a substance, the average life for \(\alpha-\)emission is 1620yr and for \(\beta-\)emission is 405yr. After how much time, the \(1\over 4\) of the material remains after \(\alpha \ and \ \beta\) emission?

The radiation corresponding to \(3\rightarrow 2\) transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 x 10^-4  T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to

A paramagnetic sample shows a net magnetisation of 8 Am^-1 when placed in an external magnetic field of 0.6 T at a temperature of 4 K. When the same sample is placed in an external magnetic field of 0.2 T at a temperature of 16 K, the magnetisation will be 

A mass M, attached to a horizontal spring, executes SHM with amplitude A1. When the mass M passes through its mean position, then a smaller mass m is placed over it and both of them move together with amplitude A₂. The ratio of (A₁/A₂) is

N molecules, each of mass m, of gas A and 2N molecules, each of mass 2m, of gas B are contained in the same vessel which are maintained at a temperature T.The mean square of the velocity of molecules of B type is denoted by v² and the mean square of the X component of the velocity of A  type is denoted by w² ; then w^2/v² is:

Two rods X and Y having equal lengths. Then, cross-sectional area are A_x and A_y and thermal conductivities K_x and K_y . When the temperature at ends of each rod are are T_x and T_y respectively, the rate of flow of heat through X and Y will b, if  equal 

In an AM wave for audio frequency of 3400 cycle/s, the appropriate carrier frequency will be 

In a p-n junction diode at high value of reverse bias the current rises sharply.The value of reverse bias is known as

In Rutherford's experiment, silver foil is replaced by a copper foil of the same thickness. The number of alpha particles scattered through the same angle per minute in copper foil is proportional to

In a dischange tube at 0.02 mm, there is formation of

An electromagnetic wave crossing through vacuum is given by \(E={ E }_{ 0 }\sin { \left( kX-\omega t \right) } \) . The quantity independent from the wavelength of radiation is

At two points P and Q on screen in Young's double slit experiment, waves from slits S₁ and S₂ have a path difference of 0 and \(\lambda /4\) respectively.The ratio of intensities at P and Q will be

A person cannot see objects clearly beyond 2.0 m. The power of lens required to correct his vision will be

Quantity that remains unchanged in a transformer is

Which of the following substances has negative permeability and very large value of susceptibility?

The e.m.f. in a thermocouple one junction of which is kept at 0⁰C, is given by E=at+bt². The peltier coefficient is

Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1,2), (2,4) and (4,1) shows electrostatic attraction, while pairs (2,3) and (4,5) shows repulsion. Therefore, ball 1 must be,

Solar pond is a device for collecting solar heat. The pond is about one metre deep, filled with saturated salt solution and protected from air current and other disturbances. When exposed to the sun, the temperature at the bottom can go as high as 800eor more. Why is this possible?

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. Ifthe rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is:

A tuning fork is an octave to an organ pipe. It can sound only with

If the spring-mass system is a very high altitude, the natural frequency of longitudinal vibration

A tank 4 m long,3 m broad and 1 m deep is filled with water.The thrust on one of the sides is 1.96 x 10⁴ N.The point of action of this resultant thrust lies at a distance y from the surface of water such that y is

The additional kinetic energy to be provided to a satellite of mass m revolving around a planet of mass M, to transfer it from a circular orbit of radius R 1 to another of radius Rz (R₂ > R₁ ) is

For a rotating body if 'a' is tangential acceleration; \(\vartheta \) linear speed, \(\alpha\) angular acceleration and \(\omega\) angular velocity, then \(\alpha /a\) is

A body of mass m₁ travelling with velocity \(\upsilon\) suffers head on collision with a mass m₂ at rest. Calculate the ratio of the kinetic energy., energy  transfer is complete when

An object is kept on a smooth inclined plane of 1 in I. The horizontal acceleration to be imparted to the inclined plane so that the object is stationary relative to incline is:

If retardation produced by air resistance is g/10, then time of flight of projectile will nearly

The position vector of a particle is, \(\vec { r } =\left( a\cos { \omega t } \right) \hat { i } +\left( a\sin { \omega t } \right) \hat { j } .\)  The velocity of the particle is:

The dimensions of  \(\frac { { e }^{ 2 } }{ 4\pi { \varepsilon }_{ 0 }hc } \)where e, £0, hand care electronic charge, electric permittivity, Planck's constant electronic charge, electric permittivity, Planck's constant

Obtain the equation of the line passing through the intersection of the lines 2x-3y+4=0 and 3x+4y=5, and drawn parallel to y-axis.

The number of the positive integral solutions of \(tan^{-1}x+cos^{-1}\left(y\over \sqrt{(1+y^2)}\right)=sin^{-1}\left(3\over\sqrt{10}\right)\) is

If \(\int _{ \pi /2 }^{ x }{ \sqrt { (3-2{ sin }^{ 2 }t) } +\int _{ 0 }^{ y }{ cos\quad t\quad dt=0, } } then\left( \frac { dy }{ dx } \right) _{ \pi ,\pi }\)is

The number log₂7 is

If ∝,β,⋎,δ are the roots of  x⁴ + x² + 1 = 0, then the equation whose roots are ∝²,β²,⋎²,δ²  is

If \(p\leftrightarrow q\) is true, then which of the following is true?

Find the principal values of \(sin^{-1}(\frac{1}{\sqrt{2}})\)

The maximum and minimum values of cos²x - 6sinxcosx + 3sin²x + 2 are 

If the equation of the sides of a triangle are X + Y = 2, Y = X and \(\sqrt{3}\) Y + X = 0, then which of the following is an exterior point of the triangle?

If function f(x) is continuous in the interval (a, b) and having same definition between a and b, then we can find \(\int _{ a }^{ b }{ f(x) } \) dx and if f(x) is discontinuous and not having same definition between a and b, then we must break the interval such that f(x) becomes continuous and having same defintion in the breaking intervals.
Now, if f (x) is discontinuous at \(x=c(a<c<b),\) ,then \(\int _{ a }^{ b }{ f(x) } dx=\int _{ a }^{ b }{ f(x) } dx+\int _{ a }^{ b }{ f(x) } dx\) and also if f(x) is discontinuous at x=a in (0,2a),then we can write \(\int _{ a }^{ 2a }{ f(x) } dx=\int _{ 0 }^{ a }{ \{ f(a-x)+ } f(a=x)\} \quad dx\)    
\(\int _{ -1 }^{ 1 }{ [|x|]d\left( \frac { q }{ 1+e^{ -1/x } } \right) } \) (where [.]   denotes greatest integer function) is equal to

If function f(x) is continuous in the interval (a, b) and having same definition between a and b, then we can find \(\int _{ a }^{ b }{ f(x) } \) dx and if f(x) is discontinuous and not having same definition between a and b, then we must break the interval such that f(x) becomes continuous and having same defintion in the breaking intervals.
Now, if f (x) is discontinuous at \(x=c(a<c<b),\) ,then \(\int _{ a }^{ b }{ f(x) } dx=\int _{ a }^{ b }{ f(x) } dx+\int _{ a }^{ b }{ f(x) } dx\) and also if f(x) is discontinuous at x=a in (0,2a),then we can write \(\int _{ a }^{ 2a }{ f(x) } dx=\int _{ 0 }^{ a }{ \{ f(a-x)+ } f(a=x)\} \quad dx\)    
\(\int _{ -1 }^{ 1 }{ [|x|]d\left( \frac { q }{ 1+e^{ -1/x } } \right) } \) (where [.]   denotes greatest integer function) is equal to

\(\int{{x+3\sqrt{x^2}+6\sqrt x}\over x(1+3\sqrt{x})}dx\) is equal to

\(\frac { d }{ dx } \left( tan^{ -1 }\left( \frac { \sqrt { x } -\sqrt { a } }{ 1+\sqrt { xa } } \right) \right) ,x,a>0,\) is
 

For all x\(\in \)(0,1)

\(\lim _{ n\rightarrow \infty }{ \sum _{ x=1 }^{ 20 }{ { cos }^{ 2n } } } (x-10)\)  is equal to

If y=f(x)=\(\frac { x+2 }{ x-1 } \), then

The force required to accelerate a train of mass \({ 10 }^{ 6 }\)kg from rest to a velocity of 6m/second in 2 minutes, is

Two forces acting at the point A (-3,0) and B(3,0) form a couple of moment 30 units.If AB is the arm of the couple then magnitude of each of these forces, is 

Integrating factor of \(\frac { dy }{ dx } -y\) = 1,y(0) = 1 is given by

The points of extremum of \(\int _{ 0 }^{ { x }^{ 2 } }{ \frac { { t }^{ 2 }-5t+6 }{ 2+{ e }^{ t } } dt } \) in the [1,2] are

The maximum value of \(\frac { \log { x } }{ x } \), is

Two distinct numbers are selected at random from the first twelve natural numbers. The probability that the sum will be divisible by 3 is

Calculate the mean deviation from the mean of the following data:​​​​​​​​​​​​​​​​​​​​​​​​​​​​

If OABC is a tetrahedron such that OA² + BC² = OB² + CA² = OC² + AB², then

Find the value of \(\lambda \)so that the vectors \(2\hat { i } -4\hat { j } +\hat { k } \) and \(4\hat { i } -8\hat { j } +\lambda \hat { k } \) are parallel

The locus of the centre of the circle which touches two given circles externally,is

If A lies in the third quadrant and 3 tan A - 4 = 0, then 5 sin 2A + 3 sin A + 4 cos A is equal to

The coefficient of x⁴⁹ in the product (x - 1) (x - 3)....(x - 99) is

If p be the sum of the of add terms and Q and of even terms in the expansion of (x + a)ⁿ, then the value of  [(x + a)²ⁿ - (x -a)²ⁿ] equals

Let P(n):"n2-n+41 is a prime number", then 

A is a set containing n elements. A subset P₁ is chosen and A is reconstructed by replacing the elements of P₁. The same process is repeated for subsets P₁, P₂, ...., pm with m > 1. The number of ways of choosing P1, P2,..., P_m, so that \({ P }_{ 1 }\cup { P }_{ 2 }\cup ....\cup { P }_{ m }=A\) is

If one root of the quadratic equation ax²+bx+c=0 is equal to the n^th power of the other then \(({ ac }^{ n })^{ \frac { 1 }{ n+1 } }+({ a }^{ n }c)^{ \frac { 1 }{ n+1 } }+b\), equals

let f(t)=\(\left| \begin{matrix} cost & t & 1 \\ 2sint & t & 2t \\ sint & t & t \end{matrix} \right| \),then \(\underset { t\rightarrow 0 }{ lim } \cfrac { f(t) }{ { t }^{ 2 } } \) is equal to

For positive integers n1, n2 the value of the expression (1+i)ⁿ¹+(1+i³)ⁿ¹+(1+i⁵)ⁿ²+(1+i⁷)ⁿ², where i=\(\sqrt { -1 } \), is a real number,if and only if,

Let A={x,y,z} and B={1,2}. The number of relations from A to B is

For positive integers n1, n2 the value of the expression (1+i)ⁿ¹+(1+i³)ⁿ¹+(1+i⁵)ⁿ²+(1+i⁷)ⁿ², where i=\(\sqrt { -1 } \), is a real number,if and only if,

\(\lim _{ x\rightarrow 0 }{ \frac { x\sqrt { { y }^{ 2 }-(y-x)^{ 2 } } }{ \left( \left( \sqrt { (8xy-{ 4x }^{ 2 } } \right) +\sqrt { (8xy)^{ 3 } } \right) } } \)  is equal to

[A] + H₂SO₄ \(\rightarrow\) [B], a colourless gas having irritating smell
[B] + K₂Cr₂O₇ + H₂SO₄ \(\rightarrow\) green solution
[A] and [B] are

Which statement is not true about enzyme inhibitors?

Which statement is not true about enzyme inhibitors?

Large number of oxidation states are exhibited by the antinoids than those by the lanthanoids, the main reason being

In blast furnace, the highest temperature is in

Which of the following is incorrect regarding ionisation enthalpy?

Identify disproportionation reaction.

Match of the following and choose the correct option

Which of the following is not characteristic of crystalline solids?

For gaseous state, if most probable speed is denoted by C*, average speed by C and mean square speed by C, then for a large number of molecules, the ratios of these speed are

How much of oxygen (in L) is required for the complete oxidation of 1.5 moles of sulphur into sulphur dioxide at STP?

Molecular weight of a tribasic acid is W. Its equivalent weight will be

Primary constituents of photochemical smog are

Which one of the following is an analgesic?

Which of the following is the sweetest sugar?

methyl magnesium bromide reacts with cyanogen chloride to give

In fischer-spier easterification reaction, the order of reactivity of the alcohols follows the sequence

Schiff's base is produced when a primary amine reacts with

Cannizzaro's reaction is given only with 

An alkyl halide can be converted into an alcohol by 

The mainsource of aromatic compounds is

The attacking species in aromatic sulphonation is

which one of the following is lanthanides element?

One mole of \(Co[NH_{3}]_{5}Cl_{3}\) gives 3 moles of ions on dissolution in water. One mole of this reacts with two moles of \(AgNO_{3}\) to give two moles of AgCl. The complex is 

The stability of dihalides of Si, Ge, Sn and Pb increases steadily in the sequence

which one of the following is not a use of mercury ?

Which one the following is the major constituent of gun powder?

Ozone is made from oxygen by

Aluminium is employed as a reducing agent in the reduction of

A metal is burnt in O₂; all the products of the combustion are weighed. It is found that the weight of the metal seems to have increased by 24%. The at.  wt.  of metal would be

An analysis of organic compound gave 74% C,8.65% H and 17.3% N. Its empirical formula is

Which of the radioactive isotopes is used for temperature control in blood disease?

The volume of a colloidal particle, V_c as compared to the volume of a solute particle in a true solution V_s , could be

For the reaction: 2NO(g)+O_{2 \(\rightleftharpoons \) 2NO(g), if the volume of the reaction vessel is diminished to \(\frac { 1 }{ 3 } \) of its volume, the rate of the reaction will change to} 

In comparison to 0.01 M solution of glucose, the depression in freezing point of 0.01 M MgCl₂ is ......

The oxidation number of hydrogen in calcium hydride is

The charge in coulombs of N^-₃ ion is

Which one of the following pairs of solution is not an acidic buffer?

\(K_{p}\) for the reaction
​​​​​​​\(A(g)+2B(g)\rightleftharpoons 2C(g)+D(s) \) is

The enthalpy of vaporisation of water is 186.5 J mol^-1; the entropy of its vaporisation would be

The rates of diffusion of SO₂, CO₂, PCl₃, and SO₃ are in the order

When two ice cubes are pressed over each other,they unite to form one cube.Which of the following forces is responsible to hold them together?

What will be the uncertainty in velocity of a cricket ball of 100 g, if the uncertainty in its position is 1.65 Å?

Waves of displacement amplitude A and angular frequency ധ travel in air with the same velocity. Which of the following waves has the highest intensity?

For a simple pendulum, when a graph is plotted betwen displacement d, KE=\(1\over 2\)mv² and PE=mgh, taking d along X-axis and \(1\over 2\)mv² and mgh along Y-axis, the graph comes as

In the following, which one of the diodes is reverse biased?

A radioactive sample has a disintegration rate of 36X10⁵ disintegrations per minute. The sample itself consisting of 10^-5\(\mu\) mole of the active nuclei. The disintegration constant, \(\lambda\) is given by

The surface of a metal is illuminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV-nm)

At which of the following temperatures would the molecules of a gas have twice the average kinetic energy they have at 27° C?

A cylinder of radius ris filled with water upto a height h, so that thrust on the walls is equal to that on bottom, then it is equal to 

Match the physical quantities given in Column I with their formula in Column II and select correct option in the choices given below.

An electron is injected into a region of uniform magnetic field of induction with its velocity inclined to the field. The path of the electron is a

Till recently, electronic communication was accomplished by sending electrical signals through copper cables. Howeve, optical fibre communication, instead of electrical signals, uses

In the process of fission, the binding energy per nucleon

A proton, a deutron and an \(\alpha \)- particle have same kinetic energies.  Their velocities are in the ratio of

A source has radiating power P uniformly in all the directions. The strength of the electrical vibration at a distance d from the source is

The phenomenon of diffraction can be treated as the phenomenon of interference of light if the number of coherent sources is

The dispersive power of material of a lens of focal length 25 cm is 0.05. The longitudinal chromatic aberration of the lens is

Three metalic loops of copper,platinum and sliver having exactly the same dimension,are rotating in a uniform magnetic field with the same angular velocity.The induced e.m.f is

If a diamagnetic solution is poured into a U-tube and one arm of this U-tube is placed between the poles of a strong magnet, with the meniscus in line with the field, then the level of solution will

A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by \(\Delta \)T in a time t. A number N of similar cells is now connected in series with a wire of the same material and gross-section but of length 2L. The temperature of the wire is raised by the same amount \(\Delta \)T in the same time t. Then value of N is

In a metre bridge experimeter, an unknown resistance P is compared with a known resistance Q.  Then P should best be

If the temperature of a hot body is raised by 5%, then the heat energy radiated would increase by:

70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the same gas through same range (30°C to 35°C) at constant volume is:

A block with a mass M = 0.50 kg is suspended at rest from a spring with spring constant k=200 Nm−1. A  blob of putty (m=0.30 kg) is dropped onto the block from a height of 10 cm; the putty slicks to the block. The total energy of the oscillating system is

Four maximum extension with given load for a given wire and same value of tension,which is true?

A synchronous relay satellite reflects TV signals and transmit.s TV programmes from one part of the world to the other because its:

Two blocks of masses 6 kg and 4 kg are placed on a frictionless surface and connected by a spring. If the heavier mass is given a velocity of 14 m/s in the direction of lighter one, then the velocity gained by the centre of mass will be:

At certain point, the potential and kinetic energies of a body of mass 100 gm projected vertically up are 3.6 \(\times\) 10⁷ erg and 6.2 \(\times\) 10⁷ erg respectively. The maximum height reached by the body and the velocity with which it is projected from the ground are:

A ball is thrown from a point with a speed v_o at an angle of projection θ.From the same point and at the same instant a person starts running with a constant speed v_o /2 to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

The displacement of a particle moving in a straight line depends on time \(x=\alpha t^3+\beta t^2+\gamma t+\delta \).  The ratio of initial acceleration to its initial velocity depends

In the formula, \(X=3Y\ Z^2, X\) and Z have dimensions of capacitance and magnetic induction.  The dimensions of Y in MKS system are

Find the equation of the line through (-2,3)with slope -4

If a, b are positive quantities and, if \(a_1={a+b\over 2},b_1=\sqrt{a_1,b}\) \(a_2={a_1+b_1\over1},b_2\sqrt{a_1b_1}\) and so on, then

If a, b are positive quantities and, if \(a_1={a+b\over 2},b_1=\sqrt{a_1,b}\) \(a_2={a_1+b_1\over1},b_2\sqrt{a_1b_1}\) and so on, then

A cubic f(x)=ax³+bx²+cx+d vanishes at x=-2 and has relative minimum/maximum at x = - 1 and x=\(\frac{1}{3}\) and if \(\int _{ -1 }^{ 1 }{ f(x)dx=\frac { 14 }{ 3 } } \)
The nature of roots of f(x) = 3 is

If  y²=ax²+bx+c, then y³.\(\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \) is

In a triangle ABC, 2a² + 4b² + c² = 4ab + 2ac, then the numerical value of cas B is equal to

If the equation ax²+bx+c=0 and x³+3x²+3x+2=0 have two common roots,then

The converse of the statement
"If sun is not shining, then sky is filled with clouds" is

4 tan^-1\(\frac{1}{5}\)-tan^-1\(1\over70\)+tan^-1\(1\over99\) is equal to

At how many points the curve \(y={ 81 }^{ { sin }^{ 2 }x }+{ 81 }^{ { cos }^{ 2 }x }-30\)  will intersect X-axis in the region \(-\pi \le x\le \pi \)  ? 

The point (at², 2bt) lies on the hyperbola \({x^2\over a^2}-{y^2\over b^2}=1\) for

The locus of the point of intersection of the tangents to the circle x=r cosθ, y=r sinθ at points whose parametric angles differ by ㅠ/3 is

The angle between the lines \(\sqrt{3}\)X + Y = 1 and X + \(\sqrt{3}\)Y = 1 is equal to

If \(\int\ sin^{-1}\ x.cos^{-1}\ x\ dx=f^{-1}(x)\) \([Ax-xf^{-1}(x)-2\sqrt{1+x^2}]+{\pi\over 2}\sqrt{1-x^2} +2x+C\),  then

Statement-I: A window has the shape of a rectangle surmounted by an equilateral triangle. If the perimeter of the window is 12m, then length 1.782m and breadth 2.812 m of the rectangle will produce the largest area of the window.
Statement-II: For maximum or minimum f(x) = 0

The derivative of   \({ sin }^{ -1 }\left( \frac { 2x }{ 1+{ x }^{ 2 } } \right) \)with respect to \(cos^{ -1 }\left( \frac { 1-{ x }^{ 2 } }{ 1+x^{ 2 } } \right) is\) 

Define F(x) as the product of two real functions \(f_2(x)=x,\) \(x\epsilon R\) and \(f_2(x)=\begin{cases} sin\frac { 1 }{ x } ,\quad if\quad x\neq 0 \\ 0,\quad \quad \quad if\quad x=0 \end{cases}\)as \(F(x)=\begin{cases} { f }_{ 1 }(x).{ f }_{ 2 }(x),\quad if\quad x\neq 0 \\ 0,\quad \quad \quad \quad \quad if\quad x=0 \end{cases}\)
Statement I F(x) is continuous on R.
Statement II f₁(x) and f₂(x) are continuous on R.

if \(f(x)=\begin{cases}x+2, x\le -1 \\ cx^2, x>-1\end{cases},\)then find c, if \(\underset { x\rightarrow -1 }{ lim } f(x)\) exists.

Let f(x)=\(\begin{cases} 1+x & 0\le x\le 2 \\ 3-x & 2<x\le 3 \end{cases}\), then fof(x)

The angle of projection of a particle when its range on the horizontal plane is \(4\sqrt { 3 } \) times the greatest height attained is

The resultant of two forces P and Q is \(\sqrt { 3 }\)Q and makes an angle \({ 30 }^{ \circ }\)with the direction of P. then

The differential equation representing the family of the curves y² = 2c ( x + √c )where c is a positive parameter, is of

If \(y=\log _{ \cos { x } }{ \sin { x } } \), then \(\frac { dy }{ dx } \) is equal to

Two dice are thrown. The events P, Q and R are described as follows:
P: getting an odd number on the first die.
Q: getting an even number on the first die.
R: getting atmost 6 as sum of the numbers on two dice.
The total number of outcomes in the event (P or R) is

The frequency distribution table is given here.

Find the variance.

The plane 4x + 7y + 4z + 81 = 0 is rotated through a right angle about its line of intersection with the plane 5x + 3y + 10z = 25. The equation of the plane in its new position is x - 4y + 6z = k, where k is

Let \(\vec { a } \),\(\vec { b } \),\(\vec { c } \) be three unit vectors such that 3 \(\vec { a } \) + 4 \(\vec { b } \) + 5 \(\vec { c } \) = 0. Then which of the following statements is true?

If the angle between the lines represented by 6x² + 5xy - 4y² + 7x + 13y - 3 = 0 is tan^-1(m) and a² + b² - ab - a - b + 1 \(\le \) 0, then 5a + 6b is equal to

The straight line y = x - 2 rotates about a point where it cuts x-axis and becomes perpendicular on the straight line ax + by + c = 0, then its equation is

The minimum and maximum values of \(​​ab\sin { x+b } \sqrt { \left( 1-{ a }^{ 2 } \right) } \cos { x } +c\left( \left| a \right| <1,b>0 \right) \) respectively are

If x, y, z are positive integers then (x+y)(y+z)(z+x) is

Statement I : (x - 2y)⁵ =x⁵ - 10x⁴ y + 40x³ y² - 80x²y³ + 80xy⁴ - 32y⁵
Statement II : (x -y)ⁿ = ⁿC_oXⁿ -ⁿC₁x^n-1y + ⁿC₂x^n-2 y² -ⁿC₃x^n-3y³ + ..+ (-1)ⁿⁿ C_nyⁿ