JEE Main 2004 · 24 Apr 2004 · Offline

Q1.Which one of the following represents the correct dimensions of the coefficient of viscosity?

Q2.A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to

Q3.A ball is released from the top of a tower of height $h$ metres. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?

Q4.If $\vec{A}\times \vec{B}=\vec{B}\times \vec{A}$, then the angle between $A$ and $B$ is

Q5.A projectile can have the same range $R$ for two angles of projection. If $T_1$ and $T_2$ be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

Q6.Which of the following statements is false for a particle moving in a circle with a constant angular speed?

Q7.An automobile travelling with speed of $60\mathrm{km}/\mathrm{h}$, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e $120\mathrm{km}/\mathrm{h}$, the stopping distance will be

Q8.A machine gun fires a bullet of mass 40 g with a velocity $1200{\mathrm{ms}}^{-1}$. The man holding it can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most?

Q9.Two masses $m_1=5\mathrm{kg}$ and $m_2=4.8\mathrm{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when lift free to move?
($\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$)

Q10.A uniform chain of length 2 m is kept on a table such that a length of 60 cm hangs freely from the edge of the table. The total mass of the chain is 4 kg. What is the work done in pulling the entire chain on the table?

Q11.A block rests on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is (take …

Q12.A force $\vec{F}=(5\hat{i}+3\hat{j}+2\hat{k})\mathrm{N}$ is applied over a particle which displaces it from its origin to the point $\vec{r}=(2\hat{i}-\hat{j})\mathrm{m}$. The work done on the particle in joules is

Q13.A body of mass m, accelerates uniformly from rest to ${\mathrm{v}}_1$ in time ${\mathrm{t}}_1$. The instantaneous power delivered to the body as a function of time $t$ is

Q14.A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that

Q15.A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following will not be affected?

Q16.A ball is thrown from a point with a speed $v_0$ at an angle of projection $\theta$. From the same point and at the same instant person starts running with a constant speed $v_0/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angl …

Q17.One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively ${\mathrm{I}}_{\mathrm{A}}$ and ${\mathrm{I}}_{\mathrm{B}}$ such that

Where ${\mathrm{d}}_{\mathrm{A}}$ and ${\mathrm{d}}_{\mathrm{B}}$ ar …

Q18.A satellite of mass $m$ revolves around the earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

Q19.The time period of an earth satellite in circular orbit is independent of

Q20.If $g$ is the acceleration due to gravity on the earth's surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

Q21.Suppose the gravitational force varies inversely as the nth power of distance. Then the time period planet in circular orbit of radius $R$ around the sun will be proportional to

Q22.A wire fixed at the upper end stretches by length by applying a force $F$. The work done in stretching is

Q23.Spherical balls of radius $R$ are falling in a viscous fluid of viscosity $\eta$ with a velocity $v$. The retarding viscous force acting on the spherical ball is

Q24.If two soap bubbles of different radii are connected by a tube,

Q25.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 …

Q26.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

Q27.The total energy of particle, executing simple harmonic motion is

Q28.The displacement $y$ of a particle in a medium can be expressed as $y=10^{-6}\sin (100t+20x+\pi /4)$ m, where $t$ is in seconds and $x$ in meter. The speed of the wave is

Q29.A particle of mass $m$ is attached to a spring (of spring constant $k$) and has a natural angular frequency ${\omega }_0$. An external force $F(t)$ proportional to $\cos \omega t$ ($\omega \ne {\omega }_0$) is applied to the oscillator. The time displacement of the oscillator will …

Q30.In forced oscillation of a particle the amplitude is maximum for a frequency ${\omega }_1$ of the force, while the energy is maximum for a frequency ${\omega }_2$ of the force, then

Q31.One mole of ideal monoatomic gas ($\gamma =5/3$) is mixed with one mole of diatomic gas ($\gamma =7/5$). What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure, to that at constant volume.

Q32.If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$, then the ratio of the radiant energy received on earth to what it was previously will be

Q33.Which of the following statements is correct for any thermodynamic system?
(A) The internal energy changes in all processes.
(B) Internal energy and entropy are state functions.
(C) The change in entropy can never be zero.
(D) The work done in an adiabatic process is always zero.

Q34.Two thermally insulated vessels 1 and 2 are filled with air at temperatures $(T_1,T_2)$, volume $(V_1,V_2)$ and pressure $(P_1,P_2)$ respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will be

Q35.A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

Q36.The temperature of two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are $T_2$ and $T_1$ $(T_2>T_1)$. The rate of heat transfer through the slab, in a steady state …

Q37.A light ray is incident perpendicular to one face of a $90^{\circ }$ prism and is totally internally reflected at the glass-air interface. If the angle of reflection is $45^{\circ }$, we conclude that the refractive index $n$

Q38.A plane convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object?

Q39.The angle of incidence at which reflected light totally polarized for reflection from air to glass (refractive index $n$), is

Q40.The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young's double-slit experiment is

Q41.An electromagnetic wave of frequency $v=3.0$ MHz passes from vacuum into a dielectric medium with permittivity $\epsilon =4.0$. Then

Q42.Two spherical conductor B and C having equal radii and carrying equal charges in them repel each other with a force F when kept apart at some distance. A third spherical conductor having same radius as that of B but uncharged brought in contact with B, then brought in contact wit …

Q43.A charged particle q is shot towards another charged particle Q which is fixed, with a speed $v$ it approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distances of approach would be

Q44.Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium the value of $q$ is

Q45.Alternating current can not be measured by D.C. ammeter because

Q46.The total current supplied to the circuit by the battery is

Q47.The resistance of the series combination of two resistances is S. When they are joined in parallel through total resistance is $P$. If $S=nP$, then the minimum possible value of $n$ is

Q48.An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the length and radii of the wires are in the ratio of $4/3$ and $2/3$, then the ratio of the currents passing through the wire will be

Q49.In a metre bridge experiment null point is obtained at 20 cm from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X<Y$, then where will be the new position of the null point from the same end, if one decides to balance a resistance of 4X ag …

Q50.The thermistors are usually made of

Q51.Time taken by a 836 W heater to heat one litre of water from $10^{\circ }\text{C}$ to $40^{\circ }\text{C}$ is

Q52.The thermo emf of a thermocouple varies with the temperature $\theta$ of the hot junction as $E=a\theta +b{\theta }^2$ in volts where the ratio $a/b$ is $700^{\circ }C$. If the cold junction is kept at $0^{\circ }C$, then the neutral temperature is

Q53.The electrochemical equivalent of a metal is $3.3\times 10^{-7}$ kg per coulomb. The mass of the metal liberated at the cathode when a 3 A current is passed for 2 seconds will be

Q54.A current I ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is

Q55.A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is B. It is then bent into a circular loop of n turns. The magnetic field at the centre of the coil will be

Q56.The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is $54\mu T$. What will be its value at the centre of the loop?

Q57.Two long conductors, separated by a distance $d$ carry current $I_1$ and $I_2$ in the same direction. They exert a force F on each other. Now the current in one of them increased to two times and its direction reversed. The distance is also increased to 3d. The new value of t …

Q58.The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2 s. The magnet is cut along its length into three equal parts and three parts are then placed on each other with their like poles together. The ti …

Q59.The materials suitable for making electromagnets should have

Q60.In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50 V. The voltage across the LC combination will be

Q61.A coil having $n$ turns and resistance $R\Omega$ is connected with a galvanometer of resistance $4R\Omega$. This combination is moved in time $t$ seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

Q62.In a uniform magnetic field of induction $B$ a wire in the form of semicircle of radius $r$ rotates about the diameter of the circle with angular frequency $\omega$. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is $R$ the mean power g …

Q63.In a LCR circuit capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to

Q64.A metal conductor of length 1 m rotates vertically about one of its ends at angular velocity 5 radians per second. If the horizontal component of earth's magnetic field is $0.2\times 10^{-4}\mathrm{T}$, then the e.m.f. developed between the two ends of the conductor is

Q65.According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal vs the frequency of the incident radiation gives straight line whose slope

Q66.The work function of a substance is 4.0 eV. Then longest wavelength of light that can cause photoelectron emission from this substance approximately

Q67.A charged oil drop is suspended in a uniform field of $3\times 10^4\mathrm{V}/\mathrm{m}$ so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge $=9.9\times 10^{-15}\mathrm{kg}$ and $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Q68.A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2:1$. The ratio of their nuclear sizes will be

Q69.The binding energy per nucleon of deuteron $\left({}_1^2\mathrm{H}\right)$ and helium nucleus $\left({}_2^4\mathrm{He}\right)$ is 1.1 MeV and 7 MeV respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

Q70.An $\alpha$-particle of energy 5 MeV is scattered through $180^{\circ }$ by a fixed uranium nucleus. The distance of the closest approach is of the order of

Q71.When npn transistor is used as amplifier

Q72.For a transistor amplifier in common emitter configuration having load impedance of $1\text{ k}\Omega$ ($h_{fe}=50$ and $h_{oe}=25\mu \mathrm{S}=25\times 10^{-6}{\Omega }^{-1}$) the current gain is

Q73.A piece of copper and another of germanium are cooled from room temperature to 77 K, the resistance of

Q74.The manifestation of band structure in solids is due to

Q75.When p-n junction diode is forward biased

Q1.Which of the following sets of quantum numbers is correct for an electron in 4 f orbital?

Q2.Consider the ground state of Cr atom $(Z=24)$. The number of electrons with the azimuthal quantum numbers $l=1$ and 2 are respectively

Q3.Which one the following ions has the highest value of ionic radius?

Q4.The wavelength of the radiation emitted, when in hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant $=1.097\times 10^7{\mathrm{m}}^{-1}$)

Q5.The correct order of bond angles (smallest first) in ${\mathrm{H}}_2\mathrm{S}$, ${\mathrm{NH}}_3$, ${\mathrm{BF}}_3$ and ${\mathrm{SiH}}_4$ is

Q6.Which one the following sets of ions represents the collection of isoelectronic species?

Q7.Among ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{SiO}}_2$, ${\mathrm{P}}_2{\mathrm{O}}_3$ and ${\mathrm{SO}}_2$ the correct order of acid strength is

Q8.The bond order in NO is 2.5 while that in ${\mathrm{NO}}^{+}$ is 3. Which of the following statements is true for these two species?

Q9.The formation of the oxide ion ${\mathrm{O}}^{2-}(\mathrm{g})$ requires first an exothermic and then an endothermic step as shown below
$\mathrm{O}(\mathrm{g})+{\mathrm{e}}^{-}\to {\mathrm{O}}^{-}(\mathrm{g})$ $\Delta {\mathrm{H}}^{\circ }=-142{\mathrm{kJmol}}^{-1}$ …

Q10.The states of hybridization of boron and oxygen atoms in boric acid (${\mathrm{H}}_3{\mathrm{BO}}_3$) are respectively

Q11.Which one of the following has the regular tetrahedral structure?

Q12.Of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one of them?

Q13.As the temperature is raised from $20^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$, the average kinetic energy of neon atoms changes by a factor of which of the following?

Q14.The maximum number of $90^{\circ }$ angles between bond pair of electrons is observed in

Q15.Which one of the following aqueous solutions will exhibit highest boiling point?

Q16.Which among the following factors is the most important in making fluorine the strongest oxidizing halogen?

Q17.In Vander Waals equation of state of the gas law, the constant 'b' is a measure of

Q18.The conjugate base of ${\mathrm{H}}_2{\mathrm{PO}}_4^{-}$ is

Q19.$6.02\times 10^{20}$ molecules of urea are present in 100 ml of its solution. The concentration of urea solution is

Q20.To neutralize completely 20 mL of 0.1 M aqueous solution of phosphorous acid $({\mathrm{H}}_3{\mathrm{PO}}_3)$, the volume of 0.1 M aqueous KOH solution required is

Q21.For which of the following parameters the structural isomers ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}$ and ${\mathrm{CH}}_3{\mathrm{OCH}}_3$ would be expected to have the same values?
(Assume ideal behaviour)

Q22.Which of the following liquid pairs shows a positive deviation from Raoult's law?

Q23.Which one of the following statements is false?
(1) Raoult's law states that the vapour pressure of a components over a solution is proportional to its mole fraction
(2) Two sucrose solutions of same molality prepared in different solvents will have the same freezing point depres …

Q24.What type of crystal defect is indicated in the diagram below?
${\mathrm{Na}}^{+}{\mathrm{Cl}}^{-}{\mathrm{Na}}^{+}{\mathrm{Cl}}^{-}{\mathrm{Na}}^{+}{\mathrm{Cl}}^{-}$
Cl □ ${\mathrm{Cl}}^{-}$ □ ${\mathrm{Na}}^{+}$ □ ${\mathrm{Na}}^{+}$ …

Q25.An ideal gas expands in volume from $1\times 10^{-3}{\mathrm{m}}^3$ to $1\times 10^{-2}{\mathrm{m}}^3$ at 300 K against a constant pressure of $1\times 10^5{\mathrm{Nm}}^{-2}$. The work done is

Q26.In hydrogen - oxygen fuel cell, combustion of hydrogen occurs to

Q27.In first order reaction, the concentration of the reactant decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is

Q28.What is the equilibrium expression for the reaction ${\mathrm{P}}_{4(\mathrm{s})}+5{\mathrm{O}}_{2(\mathrm{g})}\rightleftharpoons {\mathrm{P}}_4{\mathrm{O}}_{10(\mathrm{s})}$ ?

Q29.For the reaction, $\mathrm{CO}(\mathrm{g})+{\mathrm{Cl}}_2(\mathrm{g})\rightleftharpoons {\mathrm{COCl}}_2(\mathrm{g})$ the $\frac{{\mathrm{K}}_{\mathrm{p}}}{{\mathrm{K}}_{\mathrm{c}}}$ is equal to

Q30.The equilibrium constant for the reaction ${\mathrm{N}}_2(\mathrm{g})+{\mathrm{O}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{NO}(\mathrm{g})$ at temperature T is $4\times 10^{-4}$. The value of Kc for the reaction …

Q31.The rate equation for the reaction $2\mathrm{A}+\mathrm{B}⟶\mathrm{C}$ is found to be: rate $=\mathrm{k}[\mathrm{A}][\mathrm{B}]$. The correct statement in relation to this reaction is that the

Q32.Consider the following ${\mathrm{E}}^{\circ }$ values
${\mathrm{E}}_{{\mathrm{Fe}}^{3+}/{\mathrm{Fe}}^{2+}}^{\circ }=0.77\mathrm{V}$
${\mathrm{E}}_{{\mathrm{Sn}}^{2+}/\mathrm{Sn}}^{\circ }=-0.14\mathrm{V}$

Under standard conditions the potential for the reaction …

Q33.For a sparingly soluble salt of the type $\mathrm{A}{\mathrm{B}}_4$ (dissociating as $\mathrm{A}{\mathrm{B}}_4\rightleftharpoons {\mathrm{A}}^{4+}+4{\mathrm{B}}^{-}$) whose molar solubility is $s$ and whose solubility product is ${\mathrm{K}}_{\mathrm{sp}}$, the value of $s$ in terms of ${\mathrm{K}}_{\mathrm{sp}}$ is given b …

Q34.The standard e.m.f of a cell, involving one electron change is found to be 0.591 V at $25^{\circ }\mathrm{C}$. The equilibrium constant of the reaction is ( $F=96,500\mathrm{C}{\mathrm{mol}}^{-1}:R=8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$ )

Q35.The enthalpies of combustion of carbon and carbon monoxide are -393.5 and $-283\mathrm{kJ}{\mathrm{mol}}^{-1}$ respectively. The enthalpy of formation of carbon monoxide per mole is

Q36.The limiting molar conductivities ${\Lambda }^{\circ }$ for $\mathrm{NaCl},\mathrm{KBr}$ and KCl are 126, 152 and $150\mathrm{S}{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$ respectively. The ${\Lambda }^{\circ }$ for NaBr is

Q37.In a cell that utilises the reaction $\mathrm{Zn}(\mathrm{s})+2{\mathrm{H}}^{+}(\mathrm{aq})⟶{\mathrm{Zn}}^{2+}(\mathrm{aq})+{\mathrm{H}}_2(\mathrm{g})$ addition of ${\mathrm{H}}_2{\mathrm{SO}}_4$ to cathode compartment, will

Q38.Which one the following statement regarding helium is incorrect?

Q39.Identify the correct statements regarding enzymes

Q40.One mole of magnesium nitride on the reaction with an excess of water gives

Q41.Which one of the following ores is best concentrated by froth - floatation method?

Q42.Beryllium and aluminium exhibit many properties which are similar. But the two elements differ in

Q43.Aluminium chloride exists as dimer, ${\mathrm{Al}}_2{\mathrm{Cl}}_6$ in solid state as well as in solution of non-polar solvents such as benzene. When dissolved in water, it gives

Q44.The soldiers of Napolean army while at Alps during freezing winter suffered a serious problem as regards to the tin buttons of their uniforms. White metallic tin buttons got converted to grey powder. This transformation is related to

Q45.The ${\mathrm{E}}_{{\mathrm{M}}^{+3}/{\mathrm{M}}^{2+}}^{\circ }$ values for $\mathrm{Cr},\mathrm{Mn},\mathrm{Fe}$ and Co are $-0.41,+1.57,+0.77$ and +1.97 V respectively. For which one of these metals the change in oxidation state form +2 to +3 is easiest?

Q46.Excess of KI reacts with ${\mathrm{CuSO}}_4$ solution and then ${\mathrm{Na}}_2{\mathrm{S}}_2{\mathrm{O}}_3$ solution is added to it. Which of the statements is incorrect for this reaction?

Q47.Among the properties (a) reducing (b) oxidising (c) complexing, the set of properties shown by ${\mathrm{CN}}^{-}$ion towards metal species is

Q48.The coordination number of central metal atom in a complex is determined by

Q49.Which one of the following complexes in an outer orbital complex?

Q50.Coordination compound have great importance in biological systems. In this context which of the following statements is incorrect?

Q51.Cerium $(Z=58)$ is an important member of the lanthanoids. Which of the following statements about cerium is incorrect?

Q52.Which one the following has largest number of isomers?
(R = alkyl group, en = ethylenediamine)

Q53.The correct order of magnetic moments (spin only values in B.M.) among is
(Atomic numbers: $\mathrm{Mn}=25$; $\mathrm{Fe}=26$, $\mathrm{Co}=27$)

Q54.Consider the following nuclear reactions …

Q55.The half - life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is

Q56.The compound formed in the positive test for nitrogen with the Lassaigne solution of an organic compound is

Q57.The ammonia evolved from the treatment of 0.30 g of an organic compound for the estimation of nitrogen was passed in 100 mL of 0.1 M sulphuric acid. The excess of acid required 20 mL of 0.5 M sodium hydroxide solution for complete neutralization. The organic compound is

Q58.Which one of the following has the minimum boiling point?

Q59.The IUPAC name of the compound

Q60.Which one the following does not have ${\mathrm{sp}}^2$ hybridized carbon?

Q61.Which of the following will have meso-isomer also?

Q62.Rate of the reaction

is fastest when Z is

Q63.Amongst the following compound, the optically active alkane having lowest molecular mass is

Q64.Consider the acidity of the carboxylic acids:
(1) PhCOOH
(2) $\mathrm{o}-{\mathrm{NO}}_2{\mathrm{C}}_6{\mathrm{H}}_4\mathrm{COOH}$
(3) $\mathrm{p}-{\mathrm{NO}}_2{\mathrm{C}}_6{\mathrm{H}}_4\mathrm{COOH}$
(4) …

Q65.Which of the following is the strongest base?

Q66.Which base is present in RNA but not in DNA?

Q67.The compound formed on heating chlorobenzene with chloral in the presence concentrated sulphuric acid is

Q68.On mixing ethyl acetate with aqueous sodium chloride, the composition of the resultant solution is

Q69.Acetyl bromide reacts with excess of ${\mathrm{CH}}_3\mathrm{MgI}$ followed by treatment with a saturated solution of ${\mathrm{NH}}_4\mathrm{Cl}$ given

Q70.Which one of the following reduced with zinc and hydrochloric acid to give the corresponding hydrocarbon?

Q71.Which of the following undergoes reaction with $50\%$ sodium hydroxide solution to give the corresponding alcohol and acid?

Q72.Among the following compound which can be dehydrated very easily is

Q73.Which of the following compound is not chiral?

Q74.Insulin production and its action in human body are responsible for the level of diabetes. This compound belongs to which of the following categories?

Q75.The smog is essentially caused by the presence of

Q1.Let $R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}$ be a relation on the set $A=\{1,2,3,4\}$. The relation $R$ is

Q2.The range of the function $f(x)={}^{7-x}{P}_{x-3}$ is

Q3.Let $\mathrm{z},\mathrm{w}$ be complex numbers such that $\overline{\mathrm{z}}+\mathrm{i}\overline{\mathrm{w}}=0$ and arg $\mathrm{zw}=\pi$. Then arg z equals

Q4.If $z=x-iy$ and $z^{\frac{1}{3}}=p+iq$, then $\frac{\left(\frac{x}{p}+\frac{y}{q}\right)}{\left(p^2+q^2\right)}$ is equal to

Q5.If $\left|z^2-1\right|=|z{|}^2+1$, then $z$ lies on

Q6.Let $A=\left(\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right)$. The only correct statement about the matrix $A$ is

Q7.Let $A=\left(\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right)$ and $B=\left(\begin{array}{ccc}4& 2& 2\\ -5& 0& \alpha \\ 1& -2& 3\end{array}\right)$. If $B$ is the inverse of matrix $A$, then $\alpha$ is

Q8.If $a_1,a_2,a_3,\dots ,a_n,\dots$ are in G.P., then the value of the determinant $\left|\begin{array}{ccc}\log a_n& \log a_{n+1}& \log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}& \log a_{n+5}\\ \log a_{n+6}& \log a_{n+7}& \log a_{n+8}\end{array}\right|$, is

Q9.Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation

Q10.If $(1-p)$ is a root of quadratic equation $x^2+px+(1-p)=0$, then its roots are

Q11.Let $\mathrm{S}(\mathrm{K})=1+3+5+\dots +(2\mathrm{K}-1)=3+{\mathrm{K}}^2$. Then which of the following is true?

Q12.How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

Q13.The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is

Q14.If one root of the equation $x^2+px+12=0$ is 4, while the equation $x^2+px+q=0$ has equal roots, then the value of '$q$' is

Q15.The coefficient of the middle term in the binomial expansion in powers of $x$ of $(1+\alpha x{)}^4$ and of $(1-\alpha x{)}^6$ is the same if $\alpha$ equals

Q16.The coefficient of $x^n$ in expansion of $(1+x)(1-x{)}^n$ is

Q17.If ${\mathrm{S}}_{\mathrm{n}}={\sum }_{\mathrm{r}=0}^{\mathrm{n}}\frac{1}{{}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}}$ and ${\mathrm{t}}_{\mathrm{n}}={\sum }_{\mathrm{r}=0}^{\mathrm{n}}\frac{\mathrm{r}}{{}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}}$, then …

Q18.Let $T_r$ be the rth term of an A.P. whose first term is a and common difference is $d$. If for some positive integers $m,n,m\ne n,T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then $a-d$ equals

Q19.The sum of the first $n$ terms of the series $1^2+2\cdot 2^2+3^2+2\cdot 4^2+5^2+2\cdot 6^2+\dots$ is $\frac{n(n+1{)}^2}{2}$ when n is even. When n is odd the sum is

Q20.The sum of series $\frac{1}{2!}+\frac{1}{4!}+\frac{1}{6!}+\dots$ is

Q21.Let $\alpha ,\beta$ be such that $\pi <\alpha -\beta <3\pi$. If $\sin \alpha +\sin \beta =-\frac{21}{65}$ and $\cos \alpha +\cos \beta =-\frac{27}{65}$, then the value of $\cos \frac{\alpha -\beta }{2}$ is

Q22.If $u=\sqrt{a^2{\cos }^2\theta +b^2{\sin }^2\theta }+\sqrt{a^2{\sin }^2\theta +b^2{\cos }^2\theta }$, then the difference between the maximum and minimum values of $u^2$ is given by

Q23.The sides of a triangle are $\sin \alpha ,\cos \alpha$ and $\sqrt{1+\sin \alpha \cos \alpha }$ for some $0<\alpha <\frac{\pi }{2}$. Then the greatest angle of the triangle is

Q24.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 $60^{\circ }$ and when he retires 40 meter away from the tree the angle of elevation becomes $30^{\circ }$. The breadth of the river is

Q25.If $f:R\to S$, defined by $f(x)=\sin x-\sqrt{3}\cos x+1$, is onto, then the interval of $S$ is

Q26.The graph of the function $y=f(x)$ is symmetrical about the line $x=2$, then

Q27.The domain of the function $f(x)=\frac{{\sin }^{-1}(x-3)}{\sqrt{9-x^2}}$ is

Q28.If ${\lim }_{x\to \infty }{\left(1+\frac{a}{x}+\frac{b}{x^2}\right)}^{2x}=e^2$, then the values of $a$ and $b$, are

Q29.Let $f(x)=\frac{1-\tan x}{4x-\pi },x\ne \frac{\pi }{4},x\in \left[0,\frac{\pi }{2}\right]$. If $f(x)$ is continuous in $\left[0,\frac{\pi }{2}\right]$, then $f\left(\frac{\pi }{4}\right)$ is

Q30.If $\mathrm{x}={\mathrm{e}}^{\mathrm{y}+{\mathrm{e}}^{\mathrm{y}+\dots \mathrm{to}\infty }},\mathrm{x}>0$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is

Q31.A point on the parabola $y^2=18x$ at which the ordinate increases at twice the rate of the abscissa is

Q32.A function $y=f(x)$ has a second order derivative $f^{\prime \prime }(x)=6(x-1)$. If its graph passes through the point ( 2,1 ) and at that point the tangent to the graph is $y=3x-5$, then the function is

Q33.The normal to the curve $\mathrm{x}=\mathrm{a}(1+\cos \theta ),\mathrm{y}=\mathrm{asin}\theta$ at ' $\theta$ ' always passes through the fixed point

Q34.If $2a+3b+6c=0$, then at least one root of the equation $a{x}^2+bx+c=0$ lies in the interval

Q35.${\lim }_{n\to \infty }{\sum }_{r=1}^n\frac{1}{n}{e}^{\frac{r}{n}}$ is

Q36.If $\int \frac{\sin x}{\sin (x-\alpha )}dx=Ax+B\log \sin (x-\alpha )+C$, then value of $(A,B)$ is

Q37.$\int \frac{dx}{\cos x-\sin x}$ is equal to

Q38.The value of ${\int }_{-2}^3\left|1-x^2\right|dx$ is

Q39.The value of $\mathrm{I}={\int }_0^{\pi /2}\frac{(\sin \mathrm{x}+\cos \mathrm{x}{)}^2}{\sqrt{1+\sin 2\mathrm{x}}}\mathrm{dx}$ is

Q40.If ${\int }_0^{\pi }xf(\sin x)dx=A{\int }_0^{\pi /2}f(\sin x)dx$, then $A$ is

Q41.If $f(x)=\frac{e^x}{1+e^x},{\mathrm{I}}_1={\int }_{\mathrm{f}(-\mathrm{a})}^{\mathrm{f}(\mathrm{a})}\mathrm{xg}\{\mathrm{x}(1-\mathrm{x})\}\mathrm{dx}$ and …

Q42.The area of the region bounded by the curves $y=|x-2|,x=1,x=3$ and the $x$-axis is

Q43.The differential equation for the family of curves $x^2+y^2-2ay=0$, where $a$ is an arbitrary constant is

Q44.The solution of the differential equation $ydx+\left(x+x^{2}y\right)dy=0$ is

Q45.Let $\mathrm{A}(2,-3)$ and $\mathrm{B}(-2,1)$ be vertices of a triangle ABC. If the centroid of this triangle moves on the line $2x+3y=1$, then the locus of the vertex C is the line

Q46.The equation of the straight line passing through the point $(4,3)$ and making intercepts on the co-ordinate axes whose sum is -1 is

Q47.If the sum of the slopes of the lines given by $x^2-2cxy-7y^2=0$ is four times their product, then c has the value

Q48.If one of the lines given by $6x^2-xy+4c{y}^2=0$ is $3x+4y=0$, then $c$ equals

Q49.If a circle passes through the point $(a,b)$ and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

Q50.A variable circle passes through the fixed point $A(p,q)$ and touches $x$-axis. The locus of the other end of the diameter through $A$ is

Q51.If the lines $2x+3y+1=0$ and $3x-y-4=0$ lie along diameters of a circle of circumference $10\pi$, then the equation of the circle is

Q52.The intercept on the line $\mathrm{y}=\mathrm{x}$ by the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}=0$ is AB . Equation of the circle on AB as a diameter is

Q53.If $a\ne 0$ and the line $2bx+3cy+4d=0$ passes through the points of intersection of the parabolas $y^2=4ax$ and $x^2=4ay$, then

Q54.The eccentricity of an ellipse, with its centre at the origin, is $\frac{1}{2}$. If one of the directrices is $x=4$, then the equation of the ellipse is

Q55.A line makes the same angle $\theta$, with each of the $x$ and $z$ axis. If the angle $\beta$, which it makes with $y$-axis, is such that ${\sin }^2\beta =3{\sin }^2\theta$, then ${\cos }^2\theta$ equals

Q56.Distance between two parallel planes $2x+y+2z=8$ and $4x+2y+4z+5=0$ is

Q57.A line with direction cosines proportional to $2,1,2$ meets each of the lines $x=y+a=z$ and $x+a=2y=2z$. The co-ordinates of each of the point of intersection are given by

Q58.If the straight lines $x=1+s,y=-3-\lambda s,z=1+\lambda s$ and $x=\frac{t}{2},y=1+t,z=2-t$ with parameters $s$ and $t$ respectively, are co-planar then $\lambda$ equals

Q59.The intersection of the spheres $x^2+y^2+z^2+7x-2y-z=13$ and $x^2+y^2+z^2-3x+3y+4z=8$ is the same as the intersection of one of the sphere and the plane

Q60.Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of these are collinear. If the vector $\vec{a}+2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+3\vec{c}$ is collinear with $\vec{a}$ ( $\lambda$ being some non-zero scalar) then …

Q61.A particle is acted upon by constant forces $4\hat{i}+\hat{j}-3\hat{k}$ and $3\hat{i}+\hat{j}-\hat{k}$ which displace it from a point $\hat{i}+2\hat{j}+3\hat{k}$ to the point $5\hat{i}+4\hat{j}+\hat{k}$. The work done in standard units by the forces is given by

Q62.If $\overline{\mathrm{a}},\overline{\mathrm{b}},\overline{\mathrm{c}}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\overline{\mathrm{a}}+2\overline{\mathrm{b}}+3\overline{\mathrm{c}},\lambda \overline{\mathrm{b}}+4\overline{\mathrm{c}}$ and …

Q63.Let $\overline{\mathrm{u}},\overline{\mathrm{v}},\overline{\mathrm{w}}$ be such that $|\overline{\mathrm{u}}|=1,|\overline{\mathrm{v}}|=2,|\overline{\mathrm{w}}|=3$. If the projection $\overline{\mathrm{v}}$ along $\overline{\mathrm{u}}$ is equal to that of …

Q64.Let $\overline{\mathrm{a}},\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be non-zero vectors such that $(\overline{\mathrm{a}}\times \overline{\mathrm{b}})\times \overline{\mathrm{c}}=\frac{1}{3}|\overline{\mathrm{b}}||\overline{\mathrm{c}}|\overline{\mathrm{a}}$. If …

Q65.Consider the following statements:
(a) Mode can be computed from histogram
(b) Median is not independent of change of scale
(c) Variance is independent of change of origin and scale.

Which of these is/are correct?

Q66.In a series of $2n$ observations, half of them equal a and remaining half equal $-a$. If the standard deviation of the observations is 2 , then $|a|$ equals

Q67.The probability that $A$ speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact is

Q68.A random variable $X$ has the probability distribution:

For the events $\mathrm{E}=\{\mathrm{X}$ is a pr …

Q69.The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

Q70.With two forces acting at a point, the maximum effect is obtained when their resultant is 4 N . If they act at right angles, then their resultant is 3 N . Then the forces are

Q71.In a right angle $△\mathrm{ABC},\angle \mathrm{A}=90^{\circ }$ and sides $\mathrm{a},\mathrm{b},\mathrm{c}$ are respectively, $5\mathrm{cm},4\mathrm{cm}$ and $3\mathrm{cm}$ . If a force $\vec{F}$ has moments 0,9 and 16 in N cm . units respectively about vertices …

Q72.Three forces $\vec{P},\vec{Q}$ and $\vec{R}$ acting along $IA$, $IB$ and $IC$, where $I$ is the incentre of a $△ABC$, are in equilibrium. Then $\vec{P}:\vec{Q}:\vec{R}$ is

Q73.A particle moves towards east from a point $A$ to a point $B$ at the rate of $4\mathrm{km}/\mathrm{h}$ and then towards north from $B$ to $C$ at the rate of $5\mathrm{km}/\mathrm{h}$. If $AB=12\mathrm{km}$ and $BC=5\mathrm{km}$, then its average spee …

Q74.A velocity $\frac{1}{4}\mathrm{m}/\mathrm{s}$ is resolved into two components along OA and OB making angles $30^{\circ }$ and $45^{\circ }$ respectively with the given velocity. Then the component along OB is

Q75.If $t_1$ and $t_2$ are the times of flight of two particles having the same initial velocity $u$ and range R on the horizontal, then ${\mathrm{t}}_1^2+{\mathrm{t}}_2^2$ is equal to