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When liquid medicine of density p is to be put in the eye it is done with the help of a dropper. As the bulb on the top of the dropper is pressed, a drop forms at the opening of the dropper. We wish to estimate the size of the drop. We first assume that the drop formed at the opening is spherical because that requires a minimum increase in its surface energy. To determine the size, we calculate the net vertical force due to the surface tension T when the radius of the drop is R. When this force becomes smaller than the weight of the drop, the drop gets detached from the dropper.
If the radius of the opening of the dropper is r, the vertical force due to the surface tension on the drop of radius R (assuming r << R)
The nuclear charge (Ze) is nonuniformly distributed within a nucleus of radius R. The charge density p(r) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction.
For a = 0, the value of d (maximum value of p as shown in the figure) is
Two small equally charged spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x << l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v = a/√x , where a is a constant.
A composite wire of uniform diameter 3.0 mm consists of a copper wire of length 2.2 m and a steel wire of length 1.6 m which is stretched under a load by 0.7 mm. Calculate the load, given that the Young's modulus of elasticity for copper is 1.1 × 10^{11} N m^{–2} and that for steel is 2 × 10^{11} N m^{–2}.
A stepped cylinder, with thread wound around smaller diametre, is released from rest and the cylinder moves down. Then,
When a body of mass M is attached to lower end of wire (of length L) whose upper end is fixed, then the elongation of wire is l. Which of the following statements regarding this is/are correct?
Positive point charges q_{1} and q_{2} are moving with velocities v_{1} and v_{2} as shown in the given figure. Mark the correct statements.
Directions: Mark out the correct statement(s) about wave speed and particle velocity for the transverse travelling mechanical wave on string.
An elliptical cavity is carved within a perfect conductor. A positive charge q is placed at the centre of the cavity. The points A and B are on the cavity surface as shown in the figure. Then
It is observed that only 0.39% of the original radioactive sample remains un decayed after eight hours. Hence
Consider the situation shown in figure and select the correct statement from the following.
In the figure shown AB is rod of length 30 cm and area of crosssection 1 cm^{2} and thermal conductivity 336 S.I. units. The ends A and B are maintained at temperature 20°C and 40°C respectively. A point C of this rod is connected to a box D, containing ice at 0°C, through a highly conducting wire of negligible heat capacity. Find the rate at which ice melts in the box. [Assume latent heat of fusion for ice L_{ice} = 80 cal g^{−1}]
A binary star consists of two stars A (mass 2.2M_{s}) and B (mass 11M_{S}), where M_{s} is the mass of the Sun. They are separated by distance d and are rotating about their centre of mass, which is stationary. The ratio of the total angular momentum of the binary star to the angular momentum of star B about the centre of mass is
When two identical batteries of internal resistance 1 Ω each are connected in series across a resistor R, the rate of heat produced in R is J_{1}. When the same batteries are connected in parallel across R, the rate is J_{2}. If J_{1} = 2.25J,, then the value of R (in Ω) is
A large glass slab (μ = 5/4) of thickness 6 cm is placed over a point source of light on a plane surface. There is a bright circular patch of light on the top surface of the slab with radius R cm. What is the value of R?
A mirror of radius of curvature 20 cm and an object which is placed at a distance of 15 cm are both moving with velocities 1 m s^{−1} and 10 m s^{−1} as shown in diagram. The velocity of the image at this situation is 9v_{P}. Find v_{P}.
In the shown wire frame, each side of a square (the smallest square) has a resistance 2 Ω. The equivalent resistance of the circuit between the points A and B is
A thin string of negligible mass, natural length L has Young's modulus Y. The string hangs from roof with masses m_{1} and m_{2} as shown in the figure. If mass m_{2} is removed gently, the mass m_{1} is just able to bounce back up to point O. Find the ratio m_{2}/m_{1}. (string will not obstruct the motion of mass m_{1} and system is initially in equilibrium)
Directions: The following question is based on the paragraph given below.
The noble gases have closedshell electronic configuration and are monatomic gases under normal conditions. The low boiling points of the lighter noble gases are due to weak dispersion forces between the atoms and the absence of other interatomic interactions.
The direct reaction of xenon with fluorine leads to a series of compounds with oxidation numbers +2, +4 and +6. XeF_{4} reacts violently with water to give XeO_{3}. The compound can also be prepared using XeF_{6} as the starting compound. The compounds of xenon exhibit rich stereochemistry and their geometries can be deduced considering the total number of electron pairs in the valence shell.
The chemical nature of the compounds XeF_{4} and XeF_{6} is expected to be
(1R, 3S)Cis1Bromo3methyl cyclohexane. The product formed in the reaction is
What is the magnetic moment of coordination compound formed during brown ring test?
The equilibrium constant K for the reaction 2HI(g) ⇌ H_{2} (g) + I_{2(g)} at room temperature is 2.85 and that at 698 K is 1.4 × 10^{–2}. This implies that 
Consider the following graph:
From this graph, it is clear that
Which of the following oxides can act both as a reducing agent as well as an oxidising agent?
Among the given options, the compound(s) in which all the atoms are in one plane in all the possible conformations (if any) is/are
Amongst the following, the species having at least one unpaired electrons is/are
[Note  Use Molecular Orbital Theory to be valid in all the options]
Which of the following statements are correct ?
The species observed in the following sequence of reaction:
The correct order of resonance energies of the compounds
The formula of the magnesium salt of a monobasic acid is MgA_{2}.nH_{2}O. (HA is the formula of the acid.) 1 gram of the salt on strong heating leaves behind 0.2 gram of MgO. Given that the molecule mass of the acid is 62, what is the value of n?
How many structural isomers of ester having molecular formula C_{6}H_{12}O_{2} are possible with parent name as methanoate?
For real gases, the graph of PV v/s p at constant temperature is not linear. So, d/P or W/V.P will not be independent of P. (W→ Mass of gas, V → Volume, P → Pressure) yintercept of the graph d/P (g/atmL) v/s P (atm) at 360 K is:
[Given: Molar mass of gas = 60 g/m,
How many isomers of 'x' C_{8}H_{10} when reacts with hot alkaline KMnO_{4} gives only aromatic dicarboxylic acid? How many isomers of 'y' C_{4}H_{8} when reacts with hot alkaline KMnO_{4} to give carbondioxide? What is the sum of 'x' and 'y'?
A hydrocarbon A of molecular weight 54g reacts with an excess of Br_{2} in CCl_{4} to give a compound B whose molecular weight is 539% more than that of A. however on catalytic hydrogenation with excess of H_{2} A forms C whose molecular weight is only 7.4% more than that of A. A reacts with an alkyl bromide of molecular weight 109g in the presence of NaNH_{2} to give another hydrocarbon D, which on reductive ozonolysis, yields diketone E, if the molecular weight of E is xyz then find the value of (x+y+z).
Calculate the number of different hydrocarbons possible, when a mixture of sodium ethanoate and sodium propanoate undergoes kolbe electrolysis.
Out of 3n consecutive integers, three are selected at random. Find the probability that their sum is divisible by 3.
If SK be the perpendicular from the focus S on the tangent at any point P on the ellipse then locus of the foot of the perpendicular K is equal to
The value of where [.] denotes the greatest integer function is
The equations of two ellipses are and where p is a parameter. The locus of the points of intersection of both the ellipses is a set of curves comprising
The internal bisector of ∠A of a triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and side AB at F. If a, b and c represent the sides of ΔABC , then
Let P(x_{1}, y_{1}) and Q(x_{2}, y_{2}), y_{1} < 0, y_{2} < 0 be the end points of the latus rectum of the ellipse x^{2} + 4y^{2} = 4. The equation(s) of parabolas with latus rectum PQ is/are
The vector(s) which is/are coplanar with vectors and perpendicular to the vector is/are
If ∫ x log(1 + x^{2}) dx = ϕ(x) log(1 + x^{2}) + ψ(x), then :
An ellipse intersects the hyperbola 2x^{2} − 2y^{2} = 1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates axes, then
A circle of radius 4cm is inscribed in ΔABC, which touches the side BC at D, if BD = 6cm and DC = 8cm, then which of the following options are correct ?
Directions: The answer to the following question is a single digit integer ranging from 0 to 9.
The harmonic mean of the roots of the equation (5 + √2) x^{2}  (4 + √5) x + 8 + 2√5 = 0 is
Directions: The answer to the following question is a singledigit integer ranging from 0 to 9.
If the system of equations x  ky  z = 0,
kx  y  z = 0,
x + y  z = 0
has a nonzero solution, then possible values of k are ±A. Calculate the value of A.
Directions: The answer to the question is a singledigit integer, ranging from 0 to 9.
Consider the parabola y^{2} = 8x. Let Δ_{1} be the area of the triangle formed by the end points of its latus rectum and the point on the parabola, and Δ_{2} be the area of the triangle formed by drawing tangents at P and at the end points of the latus rectum.
Then Δ_{1}/Δ_{2} is
The integer n for which is a finite nonzero number is
The total number of local maxima and local minima of the function
357 docs148 tests

JEE Advanced Mock Test  4 (Paper II) Test  54 ques 
JEE Advanced Mock Test  5 (Paper I) Test  54 ques 
JEE Advanced Mock Test  5 (Paper II) Test  54 ques 
JEE Advanced Mock Test  6 (Paper I) Test  54 ques 
JEE Advanced Mock Test  6 (Paper II) Test  54 ques 
357 docs148 tests

JEE Advanced Mock Test  4 (Paper II) Test  54 ques 
JEE Advanced Mock Test  5 (Paper I) Test  54 ques 
JEE Advanced Mock Test  5 (Paper II) Test  54 ques 
JEE Advanced Mock Test  6 (Paper I) Test  54 ques 
JEE Advanced Mock Test  6 (Paper II) Test  54 ques 