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x and y displacements of a particle are given as x(t) = a sinωt and y(t) = a sin2ωt. Its trajectory will look like :
If a body moving in a circular path maintains constant speed of 10 ms-1, then which of the following correctly describes relation between acceleration and radius ?
A block of mass m =10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed v/10 after being dropped from height H, then neglecting energy losses and taking g = 10 ms-2 , the value of H is close to :
Momentum conservation 0.05V=10V0
None of the options match.
A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance (x/2) from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 ms-1 . The total initial energy of the spring is :
A uniform solid cylindrical roller of mass 'm' is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is 'a' and it is rolling without slipping then the value of 'F' is :
Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then :
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then :
If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter cm then the Reynolds number for the flow is (density of water =103 kg/m3 and viscosity of water = 10-3 Pa.s) close to :
If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by :
Excess pressure =
An ideal gas goes through a reversible cycle a → b → c → d has the V - T diagram shown below. Process d → a and b → c are adiabatic.
The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :
In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as Tq . A good estimate for q is :
A simple harmonic oscillator of angular frequency 2 rad s-1 is acted upon by an external force F = sint N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to :
A bat moving at 10 ms-1 towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound = 320 ms-1)
A thin disc of radius b = 2a has a concentric hole of radius 'a' in it (see figure). It carries uniform surface charge 'σ' on it. If the electric field on its axis at height 'h' (h << a) from its centre is given as 'Ch' then value of 'C' is :
Shown in the figure are two point charges +Q and -Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ1 is the surface charge on the inner surface and Q1 net charge on it and σ2 the surface charge on the outer surface and Q2 net charge on it then :
If the capacitance of a nanocapacitor is measured in terms of a unit 'u' made by combining the electronic charge 'e', Bohr radius 'a0', Planck's constant 'h' and speed of light 'c' then :
Suppose the drift velocity vd in a material varied with the applied electric field E as . Then V - I graph for a wire made of such a material is best given by :
A 10V battery with internal resistance 1Ω and a 15V battery with internal resistance 0.6Ω are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to :
A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width 'd'. If 'α' be the angle of deviation of proton from initial direction of motion (see figure), the value of sin α will be :
A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization (magnetic moment/volume), then is:
When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self - inductance of the coil is :
In the circuits (a) and (b) switches S1 and S2 are closed at t=0 and are kept closed for a long time. The variation of currents in the two circuits for t ≥ 0 are roughly shown by (figures are schematic and not drawn to scale) :
An electromagnetic wave travelling in the x-direction has frequency of 2 x 1014 Hz and electric field amplitude of 27 Vm-1 .From the options given below, which one describes the magnetic field for this wave ?
You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :
A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum py in the y-direction then for a majority of electrons passing through the slit (h is Planck's constant) :
A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is θ, then θ is close to :
de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to (|e| = 1.6 x 10-19 C, me = 9.1 x 10-31 kg, h = 6.6 x 10-34 Js) :
If one were to apply Bohr model to a particle of mass 'm' and charge 'q' moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth level will be :
In an unbiased n-p junction electrons diffuse from n - region to p - region because :
Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as :
If the zero error is -0.03cm, then mean corrected diameter is :
A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is : (atomic mass, Ba = 137 amu, Cl = 35.5 amu)
Which of the following is not an assumption of the kinetic theory of gases ?
If the principal quantum number n = 6, the correct sequence of filling of electrons will be :
After understanding the assertion and reason, choose the correct option.
Assertion : In the bonding molecular orbital (MO) of H2, electron density is increased between the nuclei.
Reason : The bonding MO is, which shows destructive interference of the combining electron waves.
The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively. The longest wavelength of light capable of breaking the C - C bond is (Avogadro number = 6.02 x 1023, h = 6.62 x 10-34Js):
A solution at 20°C is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively :
Gaseous N2O4 dissociates into gaseous NO2 according to the reaction
At 300 K and 1 atm pressure, the degree of dissociation of N2O4 is 0.2. If one mole of N2O4 gas is contained in a vessel, then the density of the equilibrium mixture is :
A variable, opposite external potential (Eext) is applied to the cell
Zn|Zn2+ (1 M) || Cu2+ (1 M) | Cu, of potential 1.1 V.
When Eext < 1.1 V and Eext > 1.1 V, respectively electrons flow from :
When Eext<1.1 V, the electrons will flow from anode to cathode, the cell will act as the galvanic cell.
when Eext>1.1 V, electrons will flow from cathode to anode and the cell will act as electrolytic cell.
The reaction 2N2O5(g) → 4NO2(g) + O2(g) follows first order kinetics. The pressure of a vessel containing only N2O5 was found to increase from 50 mm Hg to 87.5 mm Hg in 30 min. The pressure exerted by the gases after 60 min. will be (Assume temperature remains constant) :
The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them:
In the long form of the periodic table, the valence shell electronic configuration of 5s2 5p4 corresponds to the element present in :
In the isolation of metals, calcination process usually results in :
Permanent hardness in water cannot be cured by :
The correct order of thermal stability of hydroxides is :
The least number of oxyacids are formed by :
The geometry of XeOF4 by VSEPR theory is :
An aqueous solution of a salt X turns blood red on treatment with SCN- and blue on treatment with K4 [Fe(CN)6 ]. X also gives a positive chromyl chloride test. The salt X is :
Which molecule/ion among the following cannot act as a ligand in complex compounds ?
The correct statement on the isomerism associated with the following complex ions,
(b) [Ni(H2O)4(NH3)2]2+ and
(c) [Ni(H2O)3 (NH3)3]2+ is :
Photochemical smog consists of excessive amount of X, in addition to aldehydes, ketones, peroxy acetyl nitrile (PAN), and so forth. X is :
1.4 g of an organic compound was digested according to Kjeldahl's method and the ammonia evolved was absorbed in 60 mL of M/10 H2SO4 solution.The excess sulphuric acid required 20 mL of M/10 NaOH solution for neutralization. The percentage of nitrogen in the compound is :
The optically inactive compound from the following is :
A compound A with molecular formula C10H13Cl gives a white precipitate on adding silver nitrate solution. A on reacting with alcoholic KOH gives compound B as the main product. B on ozonolysis gives C and D. C gives Cannizaro reaction but not aldol condensation. D gives aldol condensation but not Cannizaro reaction. A is :
In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which α - hydrogen has been replaced by halogen. This reaction is known as :
Arrange the following amines in the order of increasing basicity.
Match the polymers in column-A with their main uses in column-B and choose the correct answer :
Complete hydrolysis of starch gives :
The cation that will not be precipitated by H2S in the presence of dil HCl is :
In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements :
(a) 5% families own both a car and a phone.
(b) 35% families own either a car or a phone.
(c) 40,000 families live in the town.
The largest value of r for which the region represented by the set is contained in the region represented by the set is equal to :
If 2 + 3i is one of the roots of the equation 2x3 - 9x2 + kx - 13 = 0, k ∈ R, then the real root of this equation :
The least value of the product xyz for which the determinant is non-negative, is :
If A = , then which one of the following statements is not correct ?
The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :
Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :
If the coefficients of the three successive terms in the binomial expansion of (1 + x)n are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is :
The value of is equal to :
The distance, from the origin, of the normal to the curve, x = 2 cost + 2t sint, is:
If Rolle's theorem holds for the function, at the point x = 1/2 , then 2b + c equals :
Let the tangents drawn to the circle, x2 + y2 =16 from the point P(0, h) meet the x-axis at points A and B. If the area of ΔAPB is minimum, then h is equal to :
The integral is equal to :
For x > 0, let f(x) = . Then is equal to:
The area (in square units) of the region bounded by the curves y + 2x2 = 0 and y + 3x2 = 1, is equal to :
If y(x) is the solution of the differential equation and y(0) = 0, then y(-4) is equal to :
The points (0, 8/3) , (0,3) and (82, 30):
Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If L1 is the line perpendicular to L and passing through the point (-2,1), then the point of intersection of L and L1 is :
If y + 3x = 0 is the equation of a chord of the circle, x2 + y2 - 30x = 0, then the equation of the circle with this chord as diameter is :
If the tangent to the conic, y - 6 = x2 at (2,10) touches the circle, x2 + y2 + 8x - 2y = k (for some fixed k) at a point (α, β) ; then (α, β) is
An ellipse passes through the foci of the hyperbola, 9x2 - 4y2 = 36 and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is 1/2 , then which of the following points does not lie on the ellipse ?
If the points (1, 1, λ) and (-3, 0, 1) are equidistant from the plane, 3x + 4y - 12z + 13 = 0, then λ satisfies the equation :
If the shortest distance between the lines and x + y + z + 1 = 0 = 2x- y + z + 3 is 1/√3 , then a value of α is :
Let and be two unit vectors such that .If then is equal to :
Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :
A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs. 54 and per day mean wage of all the workers is Rs.60, then per day mean wage of the night shift workers (in Rs.) is :
In a ΔABC, and Then the ordered pair (∠A, ∠B) is equal to :
If x > 1, then f (5) is equal to :
The contrapositive of the statement "If it is raining, then I will not come", is :