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A tank of uniform crosssection is completely filled with ice. The height of ice is H and its mass is m. When the entire ice melts, the work done by gravity is
(ρ_{ice} = 0.9 gm/cc, ρ_{water} = 1 g/cc and g represents acceleration due to gravity)
A hydrogen like species having atomic number Z = 2, in ground state, is excited by means of electromagnetic radiation of frequency 1.315 × 10^{16} Hz. How many spectral lines will be observed in the emission spectrum?
(Planck’s constant h = 4.14 × 10^{15} eVs)
Velocity of a point on the equator of a rotating spherical planet is v. The angular velocity of the planet is such that the apparent value of acceleration due to gravity ‘g’ at the equator is half of that at the poles. The escape velocity of a particle from the surface of the planet is
A positive charge q is projected from origin with a velocity along positive xaxis in a region having uniform magnetic field directed towards negative yaxis. If T is the time period of circular motion then the velocity vector of charge q at some instant t where
Four charges q_{1}, q_{2}, q_{3} and q_{4} are placed at the positions as shown in the figure, given q_{1} +q_{2}+ q_{3} + q_{4} = 0 . The electric field on zaxis
For the circuit as shown in the figure q_{1} and q_{2} be the charges on 3μF and 6μF capacitors respectively, then
A ball is released from position A and drops 10 m before striking a smooth incline. The coefficient of . If the time taken by the ball to strike the incline again is t then find the value of t^{2} [in (second)^{2}]. (g = 10 m/s^{2})
Two identical beads P and Q of mass 1 kg each are connected by an inextensible massless string and they can slide along the two arms AB and BC of a rigid smooth wire frame in vertical plane. If the system is released from rest and vQ is the speed of bead Q when they have both moved by a distance of 0.1 m then find the value of (in m/s). (g = 10 m/s^{2})
A solid uniform sphere rotating about its axis with kinetic energy E_{o} is gently placed on a rough horizontal plane. The coefficient of friction on the plane varies from point to point. After some time, the sphere begins pure rolling with total kinetic energy equal to E. Then find the value of
A variable voltage V = 2t is applied across an inductor of inductance L = 2H as shown in figure. Then find the rate at which magnetic potential energy stored in the inductor is increasing at t = 1 s (in J/s). Take the current through the inductor at t = 0 as zero.
A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t_{2}. A block of ice of mass m and temperature t_{3} < 0^{o}C is gently dropped into the calorimeter. Let C_{1}, C_{2} and C_{3} be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.
Q.
The whole mixture in the calorimeter becomes ice if
A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t_{2}. A block of ice of mass m and temperature t_{3} < 0^{o}C is gently dropped into the calorimeter. Let C_{1}, C_{2} and C_{3} be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.
Q.
The whole mixture in the calorimeter becomes water if
A calorimeter of mass m contains an equal mass of water in it. The temperature of water and calorimeter is t_{2}. A block of ice of mass m and temperature t_{3} < 0^{o}C is gently dropped into the calorimeter. Let C_{1}, C_{2} and C_{3} be the specific heats of calorimeter, water and ice respectively and L be the latent heat of fusion of ice.
Q.
Water equivalent of calorimeter is
A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d_{1}. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d_{2} at equilibrium. The mass of lower plate is ‘m’ and crosssectional area of each plate is A.
Q.
The spring constant k is
A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d_{1}. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d_{2} at equilibrium. The mass of lower plate is ‘m’ and crosssectional area of each plate is A.
Q.
The maximum voltage V_{m} for a given k for which an equilibrium exists is
A parallel plate capacitor has its plate horizontal with air occupying the space between the plates. The upper plate is fixed with a rigid support and the lower one is connected to a spring as shown. The distance between the plates is d_{1}. Now the capacitor is connected with an electric source having voltage V. The separation between the plates changes to d_{2} at equilibrium. The mass of lower plate is ‘m’ and crosssectional area of each plate is A.
Q.
When lower plate is slightly displaced about equilibrium position, time period T of small oscillations is
Two thin symmetrical lenses of different nature have equal radii of curvature R = 20 cm. The lenses are placed in contact and then immersed in water. The focal length of the system is found to be 24 cm. If the refractive indices of the two lenses are μ_{1} and μ_{2} respectively, then find the magnitude of 9(μ_{1}  μ_{2}). Refractive index of water is 4/3.
A certain weak acid has a dissociation constant 1.0 x 10^{4}. The equilibrium constant for its reaction with strong base is
The major product formed in the following reaction is
Identify the major product of the following reaction:
The oxidation state of molybdenum in [(η^{7}tropylium)Mo(CO)_{3}]^{+} is
In metalolefin interaction, the extent of increase in metal ⎯→ olefin πbackdonation would
The highest oxidation state of an element in the following compound that behaves as an acid in H_{2}SO_{4} is
AcOH, HNO_{2}, HNO_{3}, H_{2}O, HClO, HClO_{4}
How many unpaired electrons are present in O_{2} molecule?
One mole of Pb_{3}O_{4} is separately reacted with excess of HCl and HNO_{3}. The difference in moles of HCl and HNO_{3} is
How many moles of phenyl hydrazine are used in the formation of osazone from glucose?
If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.
Q.
for an indefinitely dilute boundary then dμ_{1} is
If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.
Q.
Which of the following solution has highest osmotic pressure?
If a concentrated solution of copper sulphate is placed at the bottom of a beaker of water or that of a dilute solution of copper sulphate is carefully poured over it there will be a two distinct layer visible. However, after some time the boundaries will disappear. This property is called diffusion. If we now consider a solution which is separated from the pure solvent by a semipermeable membrane then the solvent particles move from the pure solvent region through the SPM to the solution region. This phenomenon is called osmosis.
Q.
Which of the following is correct?
Thionyl chloride can be synthesized by chlorinating SO_{2} using PCl_{5}. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2dimethoxypropane.
Q.
Consider the following reaction
The compound X is
Thionyl chloride can be synthesized by chlorinating SO_{2} using PCl_{5}. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2dimethoxypropane.
Q.
In the preparation of anhydrous FeCl_{3} from hexahydrated salt, SOCl_{2} acts as
Thionyl chloride can be synthesized by chlorinating SO_{2} using PCl_{5}. Thionyl chloride is used to prepare anhydrous ferric chloride starting from its hexahydrated salt. Alternatively, the anhydrous ferric chloride can also be prepared from hexahydrated salt by treating with 2,2dimethoxypropane.
Q.
In the following reaction
FeCl_{3}.6H_{2}O + 6MeC(OH)(OH)Me ⎯⎯→FeCl_{3} + Y + Z
Each question has four statements (A, B, C and D) given in Columns I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II.
Each question has four statements (A, B, C and D) given in Columns I and five statements (p, q, r, s and t) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II.
How many lone pair of electrons at Xe atom are present in XeOF_{4}?
Matrices of order 3 × 3 are formed by using the elements of the set A = {−3, −2, −1, 0, 1, 2, 3}, then probability that matrix is either symmetric or skew symmetric is
Through any point (x, y) of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of
is neither an even function nor an odd function. {0}, where [.] is greatest integer function.
S_{3}: f(x) = sgn (x) and g(x) = sgn(sgn(x)) is not a pair of identical function.
S_{4}: The sum of two non periodic function is always a non periodic function.
If the number of subsets X of {1, 2, 3, …. 10} such that X contains at least two elements and no two elements of X differ by 1 is K, then sum of digits of K is equal to
A rectangle, HOMF is constructed with sides HO = 11 and OM = 5. The triangle ABC has orthocenter H, circumcentre O, M is the mid point of BC and F is foot of altitude from A. If length of BC = l , then l/7 is equal to
If the smallest integer with exactly 24 divisors is N, then N/40 is equal to
In a certain town, the probability that, all the outgoing telephone lines are jammed, in the telephone exchange is 1/4. The probability that the customer will attempt to telephone is 3/20. If a customer telephones and it fails to get connected, the probability that he would replace his telephone by a cell phone is 3/4. If P is the probability that the customer replaces the telephone by a cell phone, when the outgoing lines of the exchange are jammed then is equal to
(where [ ] denotes the greatest integer function)
The terms of are all integers (where a, x > 0). If K is the least composite odd integral value of ‘a’, then K/5 is equal to
Let z_{1} and z_{2} be complex numbers such that and the roots α and β of x^{2} + z_{1}x + z^{2} + m = 0 for some complex number m satisfies
Q.
The locus of the complex number m is a curve
Let z_{1} and z_{2} be complex numbers such that and the roots α and β of x^{2} + z_{1}x + z^{2} + m = 0 for some complex number m satisfies
Q.
The maximum value of m is
Let z_{1} and z_{2} be complex numbers such that and the roots α and β of x^{2} + z_{1}x + z^{2} + m = 0 for some complex number m satisfies
Q.
The minimum value of m is
If functions f(x) and g(x) are continuous on the interval [a, b] and g(x) retain the same sign on [a, b] then there is c ∈ (a , b) such that . This is known as MeanValue Theorem. This result can be used to estimate some definite integrals. Other results which can be used for estimation are
(i) If f increases and has a concave graph in the interval [a, b] then
(ii) If f increases and has a convex graph in the interval [a, b] then
Q.
Using MeanValue Theorem, the best upper bound of
If functions f(x) and g(x) are continuous on the interval [a, b] and g(x) retain the same sign on [a, b] then there is c ∈ (a , b) such that . This is known as MeanValue Theorem. This result can be used to estimate some definite integrals. Other results which can be used for estimation are
(i) If f increases and has a concave graph in the interval [a, b] then
(ii) If f increases and has a convex graph in the interval [a, b] then
Q.
Using (i) or (ii) (above), the best upper bound of
If functions f(x) and g(x) are continuous on the interval [a, b] and g(x) retain the same sign on [a, b] then there is c ∈ (a , b) such that . This is known as MeanValue Theorem. This result can be used to estimate some definite integrals. Other results which can be used for estimation are
(i) If f increases and has a concave graph in the interval [a, b] then
(ii) If f increases and has a convex graph in the interval [a, b] then
Q.
Using (iii) (above), the best upper bound of
In a Δ A BC, A ≡ (α, β ) , B ≡ (1, 2), C ≡ (2, 3) and point A lies on the line y = 2x + 1 where α,β∈ integer. Area of triangle ABC is Δ such that [Δ] = 2, where [.] denotes greatest integer function. Find number of all possible coordinates of A.
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1 videos356 docs217 tests
