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A planet of mass M is revolving around sun in an elliptical orbit. If dA is the area swept in a time dt, angular momentum can be expressed as
A particle is projected upward from the surface of earth (radius = R) with a speed equal to the orbital speed of a satellite near the earth’s surface. The height to which it would rise is
A spherical hole is made in a solid sphere of radius R. The mass of the original sphere was M.The gravitational field at the centre of the hole due to the remaining mass is
Three particles P, Q and R placed as per given figure. Masses of P, Q and R are √3 m, √3 m and m respectively. The gravitational force on a fourth particle ‘S’ of mass m is equal to
A uniform ring of mass M and radius R is placed directly above uniform sphere of mass 8M and of same radius R. The centre of the ring is at a distance of d = √3R from the centre of sphere. The gravitational attraction between the sphere and the ring is
A cylindrical tank has a hole of diameter 2r in its bottom. The hole is covered wooden cylindrical block of diameter 4r, height h and density ρ/3.
Situation I : Initially, the tank is filled with water of density ρ to a height such that the height of water above the top of the block is h_{1} (measured from the top of the block).
Situation II : The water is removed from the tank to a height h_{2} (measured from the bottom of the block), as shown in the figure.
The height h_{2} is smaller than h (height of the block) and thus the block is exposed to the atmosphere.
Q. Find the minimum value of height h_{1} (in situation 1), for which the block just starts to move up?
A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container.
As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are 20 mm and 1 mm respectively. The upper end of the container is open to the atmosphere.
Q. If the piston is pushed at a speed of 5 mms^{–1}, the air comes out of the nozzle with a speed of
A piece of copper having a rectangular crosssection of 15.2 mm × 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain? Take Young's modulus of copper as 42 × 10^{9}Pa
If the elastic limit of copper is 1.5 × 10^{8} N/ m^{2}, determine the minimum diameter a copper wire can have under a load of 10.0 kg if its elastic limit is not to be exceeded.
A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?
Water is flowing continuously from a tap having an internal diameter 8 × 10^{3}m. The water velocity as it leaves the tap is 0.4 ms^{1}. The diameter of the water stream at a distance 2 × 10^{1} m below the tap is close to
[AIEEE 2011]
A jar is filled with two nonmixing liquids 1 and 2 having densities respectively. A solid ball, made of a material of density , is dropped in the jar. It comes to equillibrium in the position shown in the figure.
Which of the following is true for
[AIEEE 2008]
There are two identical small holes on the opposite sides of a tank containing a liquid. The tank is open at the top. The difference in height between the two holes is h. As the liquid comes out of the two holes, the tank will experience a net horizontal force proportional to
Two soap bubbles with radii come in contact. Their common surface has a radius of curvature r. Then
At what temperature is the r.m.s velocity of a hydrogen molecule equal to that of an oxygen molecule at 47°C?
The temperature of the 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 is with f equal to
Heat generated through a resistive wire will increase _______ times in unit time, if current in the wire becomes twice.
A sphere of mass m and diameter D is Heated by temperature ΔT , if Coefficient of linear expansion is α what will be the change in the Surface Area
For any material, density ρ , mass m and volume V are related by ρ = m/V and B is coefficient of volume expansion then which one is true
A wire of length 2.5 m and area of cross section 1×10^{–6} m^{2} has a mass of 15 kg hanging on it. What is the extension produced? How much is the energy stored in the standard wire if Young’s modulus of wire is 2×10^{11} Nm^{–2}.
A man can jump 1.5m on earth. Calculate the approximate height he might be able to jump on a planet whose density is one quarter of the earth and where radius is one third that of the earth.
Find the height of the geostationary satellite above the earth assuming earth as a sphere of radius 6370 km.
A circular hole of diameter 2.00 cm is made in an aluminium plate at 0 ^{0} C .what will be the diameter at 100^{0} C?
Linear expansion for aluminium = 2.3 x 10^{3} / ^{0} C
A gas is contained in a cylinder with a moveable piston on which a heavy block is placed. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 102 kg. When 2140 J of heat flows into the gas, the internal energy of the gas increases by 1580 J. What is the distance s through which the piston rises? (Round off answer to 2 decimal places)
A metal in a compound can be displaced by another metal in the uncombined state. Which metal is a better reducing agent in such a case?
The oxidation number of P in Ba(H_{2}PO_{2})_{2}, Ba(H_{2}PO_{3})_{2} and Ba(H_{2}PO_{4})_{2} are respectively
The complex [Fe(H_{2}O)_{5}NO]^{2+} is formed in the ringtest for nitrate ion when freshly prepared FeSO_{4} solution is added to aqueous solution of followed by the addition of conc. H_{2}SO_{4}. NO exists as NO^{+ }(nitrosyl).
Q. Magnetic moment of Fe in the ring is
How much heat will be required at constant pressure to form 1.28 kg of CaC_{2} from CaO(s) & C(s) ?
Given :
Δ_{f}H°(CaO, s) = 152 kcal/mol
Δ_{f}H°(CaC_{2}, s) = 14 kcal/mol
Δ_{f}H°(CO, g) = 26 kcal/mol
The enthalpy of neutralisation of a weak acid in 1 M solution with a strong base is 56.1 kJ mol^{1}. If the enthalpy of ionization of the acid is 1.5 kJ mol^{1} and enthalpy of neutralization of the strong acid with a strong base is 57.3 kJ equiv^{1}, what is % ionization of the weak acid in molar solution (assume the acid to be monobasic) ?
From the following data, the heat of formation of Ca(OH)_{2(s)} at 18°C is ………..kcal:
The pK_{a} of a weak acid, HA, is 4.80. The pK_{b} of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be 
[AIEEE2008]
In aqueous solution the ionization constants for carbonic acid are K_{1} = 4.2 x 10^{7} and K_{2} = 4.8 x 10^{11} Selection the correct statement for a saturated 0.034 M solution of the carbonic acid.
[AIEEE2010]
How many litres of water must be added to litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?
[AIEEE2013]
For the following electrochemical cell reaction at 298 K,
E^{°}cell = 1.10 V
We know that the relationship between K_{c} and K_{p} is K_{p} = K_{c} (RT)^{Δn}
What would be the value of Δn for the reaction NH_{4}Cl (s) ⇔ NH_{3} (g) + HCl (g)
For the equilibrium,
at 1000 K. If at equilibrium p_{CO} = 10_{} then total pressure at equilibrium is
Ammonium carbamate dissociates as,
In a closed vessel containing ammonium carbamate in equilibrium with its vapour, ammonia is added such that partial pressure of NH_{3} now equals the original total pressure. Thus, ratio of the total pressure to the original pressure is
A 0.10 M solution of a weak acid, HX, is 0.059% ionized. Evaluate K_{a} for the acid.
AgCI(s)is sparingly soluble salt,
AgCl (s) Ag^{+}(aq) + Cl^{}(aq)
There is
Solubility product of silver bromide is 5.0 x 10^{13}. The quantity of potassium bromide (molar mass taken as 120 g mol^{1}) to be added to 1 litre of 0.05 M solution of silver nitrate to start the precipitation of AgBr is
[AIEEE2010]
Which one of the following is the approximate pH of 0.01 M solution of NaOH at 298 k?
If ΔU and ΔW represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?
What is the oxidation state of S in H_{2}SO_{4} & H_{2}SO_{3}?
Calculate the standard heat of formation of propane, if its heat of combustion is −2220.2 KJmol^{−1} the heats of formation of CO_{2} (g) and H_{2}O(1) are −393.5 and −285.8 kJ mol^{−1} respectively.
For the reaction at 298 K: 2A +B → C
ΔH = 400 J mol^{−1}; ΔS = 0.2 JK^{−1}mol^{−1}
Determine the temperature at which the reaction would be spontaneous.
The reaction between gaseous sulfur dioxide and oxygen is a key step in the industrial synthesis of sulfuric acid:
2SO_{2}(g) + O_{2}(g) ⇌ 2SO_{3}(g)
A mixture of SO_{2} and O_{2} was maintained at 800 K until the system reached equilibrium. The equilibrium mixture contained 5.0 × 10^{−2} M SO_{3}, 3.5 × 10^{−3} M O_{2}, and 3.0 × 10^{−3} M SO_{2}. Calculate K and K_{p} at this temperature.
Calculate the value of ∆U and ∆H on heating 128.0 g of oxygen from 0o C to 1000 C. CV and CP on an average are 21 and 29 J mol1 K^{1}. (The difference is 8Jmol1 K^{1} which is approximately equal to R)
If the coefficients of (r +1)th term and (r + 3)th term in the expansion of (1+x)^{2n} be equal then
In the expansion of (1+x)^{60}, the sum of coefficients of odd powers of x is
The circumcentre of the triangle with vertices (0, 0), (3, 0) and (0, 4) is
The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12), then orthocentre of this triangle is
Area of a triangle whose vertices are (a cos q, b sinq), (–a sin q, b cos q) and (–a cos q, –b sin q) is
The point A divides the join of the points (–5, 1) and (3, 5) in the ratio k : 1 and coordinates of points B and C are (1, 5) and (7, –2) respectively. If the area of ΔABC be 2 units, then k equals
If A(cosa, sina), B(sina, – cosa), C(1, 2) are the vertices of a ΔABC, then as a varies, the locus of its centroid is
Two perpendicular tangents to the circle x^{2}+y^{2} = r^{2} meet at P. The locus of P is
The locus of a variable point whose distance from the point (2, 0) is 2/3 times its distance from the line x = 9/2 is
The locus of a point such that two tangents drawn from it to the parabola y^{2} = 4ax are such that the slope of one is double the other is
T is a point on the tangent to a parabola y^{2} = 4ax at its point P. TL and TN are the perpendiculars on the focal radius SP and the directrix of the parabola respectively. Then
Tangents are drawn from the points on the line x – y + 3 = 0 to parabola y^{2} = 8x. Then the variable chords of contact pass through a fixed point whose coordinates are
From the focus of the parabola y^{2} = 8x as centre, a circle is described so that a common chord of the curves is equidistant from the vertex and focus of the parabola. The equation of the circle is
In an examination, ten students scored the following marks: 60, 58, 90, 51, 47, 81, 70, 95, 87, 99. The range of this data is
Two vertices of a triangle are (3,−2) and (−2, 3) and its orthocentre is (−6, 1). The coordinates of its third vertex are
Let ,Q,R and S be four points on the ellipse 9x^{2} + 4y^{2} = 36. Let PQ and RS be mutually perpendicular and pass through the origin. If , where p and q are coprime, then p + q is equal to :
If one of the lines of my^{2} + (1  m^{2})xy  mx^{2} = 0 is a bisector of the angle between the lines xy = 0, then m(m > 0) is
The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a oneyear old child. If the average age of the family now is λ, then the number of divisors of λ are
If the sum of the coefficients of all even powers of x in the product (1 + x + x^{2} + … + x^{2n}) (1 – x + x^{2} – x^{3} + … + x^{2n}) is 61, then find the value of n.
Find the coefficient of x^{4} in the expansion of (1 + x + x^{2})^{10} .
If the sum of the series
is α/β, where α and β are coprime, then α + 3β is equal to __________.
357 docs148 tests

JEE Main Part Test  3 Test  75 ques 
JEE Main Part Test  4 Test  75 ques 
JEE Main Part Test  5 Test  75 ques 
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Schedule and Syllabus of JEE Mock Test Series Doc  1 pages 
357 docs148 tests

JEE Main Part Test  3 Test  75 ques 
JEE Main Part Test  4 Test  75 ques 
JEE Main Part Test  5 Test  75 ques 
JEE Main Part Test  6 Test  75 ques 
Schedule and Syllabus of JEE Mock Test Series Doc  1 pages 