In the figure shown the acceleration of A is, , then the acceleration of B is : (A remains in contact with B)
The speed of sound in hydrogen gas at N.T.P. is 1,328 ms^{1}. What will be its value in air at N.T.P., if density of hydrogen is 1/16th that of air?
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A balloon that is initially flat, is inflated by filling it from a tank of compressed air. The final volume of the balloon is 5m^{3}. The barometer reads 95 kPa. The work done in this process is
Two bodies of same mass tied with an inelastic string of length together on a horizontal surface. One a horizontal surface of them is projected vertically upwards with velocity Find the maximum height up to which the centre of mass of system of the two masses rises.
The electric potential at a point (x, y, z) is given by V = x^{2}y  xz^{3} + 4 The electric field at that point is
Binding energy per nucleon versus mass number curve for nuclei is shown in figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is
A wire of length 1.0 m and radius 10^{3} m is carrying a heavy current and is assumed to radiate as a black body. At equilibrium, its temperature is 900 K while that of the surroundings is 300 K. The resistivity of the material of the wire at 300 K is π^{2} × 10^{8} ohmm and its temperature coefficient of resistance is 7.8× 10^{−3} C^{o}. Find the current in the wire. [Given Stefan's constant = 5.68 × 10^{8} W/m^{2}K^{4}]
50 V battery is supplying a steady current of 10 amp when connected to an external resistor. If the efficiency of the battery at this current is 25%, then internal resistance of battery is:
A capacitor of capacitance C is charged to a potential difference V from a cell and then disconnected from it. A charge +Q is now given to its positive plate. Now, the potential difference across the capacitor is.
Energy from the sun falls on the earth at a rate of 1353 W/m^{2}, which is known as solar constant, i.e., the power incident per unit area per second at the top of atmosphere. Find the r.m.s values of the electric and magnetic fields in the sunlight reaching the top of the atmosphere.
The size of the image of an object, which is at infinity, is formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image
A network of Four capacitors of capacity equal to C_{1} = C, C_{2} = 2C, C_{3} = 3C and C_{4} = 4C, are connected to a battery as shown in the figure. The ratio of the charges on C_{2} and C_{4} is
A rod AD, consisting of three segments AB, BC and CD joined together, is hanging vertically from a fixed support at A. The lengths of the segments are respectively 0.1 m, 0.2 m and 0.15 m. The cross  section of the rod is uniform 10^{4 }m^{2}. A weight of 10 kg is hung from D. Calculate the displacements of point D if Y_{AB} = 2.5 x 10^{10} N/m^{2}, Y_{BC} = 4 x 10^{10 }N/m^{2} and Y_{CD} = 1 x 10^{10} N/m^{2}. (Neglect the weight of the rod.)
A block of mass m & charge q is released on a long smooth inclined plane. Magnetic field B is constant, uniform, horizontal and out of the plane of paper as shown. Find the time from start when block loses contact with the surface.
A battery of internal resistance 4Ω is connected to the network of resistances as shown in figure. In order that the maximum power can be delivered to the network, the value of R in $$ should be
In the circuit shown in diagram, the equivalent resistance between point A and B is
Two trains, which are moving along different tracks in opposite directions, are put on the same track due to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when they are 300 m apart. Graphs given below show their velocities as a function of time as they slow down. The separation between the trains, when both have stopped, is:
A tuning fork sends out waves of wavelength 68.75 cm and 3 m in air and hydrogen gas respectively. If the velocity of sound in air is 330 ms^{1}, find the velocity of sound in hydrogen. Also, find the frequency of the tuning fork
A particle executes S.H.M. given by x = 0 · 24 cos (400 t  0.5) in SI units. Find amplitude
A lens (μ = 1.5) is coated with a thin film of refractive index 1.2 in order to reduce the reflection from its surface at λ = 4800 Å. Find the minimum thickness of the film which will minimise the intensity of the reflected light. (Assume near normal incidence)
A ray of light from a liquid (μ = √3) is incident on a system of two right angled prism of refractive indices √3 and √2 as shown in the figure. The light suffers zero net deviation when it emerges into air from surface CD. If the angle of incidence (in degrees) is 5n. Find n ?
A drop water of mass m = 4.0 g is placed between two clean glass plates, the distance between the plates is 0.01cm. Find the force (10^{3}N) required to pull the plates away. Surface tension of water = 0.08 N/m and density of water is 1000 kg/m^{3}
A car is accelerating horizontally with constant acceleration a=10m/s^{2}. One end of a light string is attached to the roof of the ceiling and there is a small bob at other end of string. The bob is given an initial velocity such that it continues to move in uniform circular motion with respect to an observer inside the car. The bob moves such the maximum vertical separation between two points of its path is h=1m. The length of the string is and acceleration due to gravity g=10m/s^{2}. If the angular speed of the bob in rad/s is √x .find the value of x.
Find the current (in A) through the battery after the switch S is closed if L/R = RC = 1 ms.
Assuming that the law of gravitation is of the form and attractive. A body of mass m revolves in a circular path of radius r around a fixed body of mass M. Find on what power of r will the square of time period depend.
Place the following alcohols in decreasing order of rate of dehydration with concentrated H_{2}SO_{4} :
1. CH_{3}CH_{2}CH(OH)CH_{2}CH_{2}CH_{3}
2. (CH_{3})_{2}C(OH)CH_{2}CH_{2}CH_{3}
3. (CH_{3})_{2}C(OH)CH(CH_{3})_{2}
4. CH_{3}CH_{2}CH(OH)CH(CH_{3})_{2}
5. CH_{3}CH_{2}CH_{2}CH_{2}CH_{2}CH_{2}OH
1.2 g of a salt with its empirical formula K_{x}H_{y}(C_{2}O_{4})_{z} was dissolved in 50 mL of water and its 10 mL portion required 11 mL of a 0.1 M HCl solution to reach the equivalence point. In a separate titration, 15 mL of the stock solution required 20 mL 0.2475 M KOH to reach the equivalence point. Identify the correct option.
In nitroprusside ion the iron and NO exist as Fe II and NO^{+ }rather than Fe III and NO. These forms can be differentiated by
Among the following pair of oxides, which pair cannot be reduced by carbon to give the respective metals ?
Two liquids A and B are mixed. The partial vapour pressures of A and B in pure state are 100 and 200 mm respectively. If they are mixed in 1 : 4 mole ratio, assuming that mixture obeys Raoult's law, the mole fractions of A and B present in gaseous state in equilibrium of above solution are :
Identify the final product (Z) in the following sequence of reactions :
In a face centred cubic lattice, atom A occupies the corner positions and atom B occupies the face centre positions. If one atom of B is missing from one of the face centred points, the formula of the compound is
The standard e.m.f. of a cell, involving one electron change is found to be 0.591 V at 25. The equilibrium constant of the reaction is
(F = 96500 C mol^{1} ,R = 8.314 JK^{1} mol^{1}
For the indicator HIn the ratio [In_{}]/[HIn] is 7.0 at pH of 4.3. K_{eq} for the indicator is [Given log 7 = 0.845 and Antilogo (0.545) = 3.5
Match the hybrid bond orbitals of list I with the species of the list II and pick out the correct ?
The electrochemical cell shown below is a concentration cell.
MM^{2+} (saturated solution of a sparingly soluble salt, MX_{2}) M^{2+} (0.001 mol dm^{ }^{3})  M
The emf of the cell depends on the difference in concentrations of M^{2}^{+} ions at the two electrodes. The emf of the cell at 298 K is 0.059 V.
The value of Δ G (kJ mol^{1}) for the given cell is (Take 1 F = 96500 C mol^{1})
First and second ionization energies of Magnesium are 7.646 and 15.035 eV respectively. The amount of energy in KJ needed to convert all the atoms of Magnesium into Mg^{2}^{+} ions present in 12 mg of Magnesium vapours is :
[Given : 1 eV = 96.5 kJ mol^{1}]
The enthalpy change of the reaction is 57.3 kJ mol^{1}. If the enthalpies of Formation of are zero and 285.84 kJ mol^{1} respectively, then the enthalpy of formation of
Amongst the halides
(1) BCl_{3}
(2) AlCl_{3}
(3) GaCl_{3}
(4) InCl_{3}
The order of decreasing Lewis acid character is
A cationic colloidal electrolyte forms micelle at 10^{4} M concentration in water. If 1 mm^{3} solution contains 10^{12} micelle structure, then the no. of cations involved in one micelle are NA = 6 × 10^{23}.
The halflife of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be
When H_{2}O_{2} is added to ice cold solution of acidified potassium dichromate in ether and the contents are shaken and allowed to stand
Identify the compounds in given set which can form enol.
A reaction takes place at 300K. When catalyst is added, rate of reaction increases. How much temperature should be increased (in ^{∘}C) which can create same affect as produced by catalyst. (Experimentally it is known that catalyst change the activation energy by20%).
The vapour pressure of a certain liquid is given by the equation Where P is vapour pressure in mmHg and T is temperature in K. Calculate latent heat of vaporisation (in cal mol^{−1}) at 75 .
K(R=2calmol^{−1}K^{−1})
How many of total isomers are possible for the complex [Co(NH_{3})_{4}(NO_{2})_{2}]NO_{3}?
How many atoms will have positive charge due to delocalization in given structure. Give answer including carbon on which charge is shown.
If the area bounded by y = ax^{2} and x = ay^{2}, a > 0, is 1, then a is equal to
A single letter is selected at random from the word 'PROBABILITY'. The probability that it is a vowel, is :
Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number.
A point R with xcoordinate 4 lies on the line segment joining the points P (2,  3, 4) and Q (8, 0,10). Find the coordinates of the point R.
A ray of light coming from the point (1, 2) is reflected at a point A on the xaxis and then passes through the point (5, 3). The coordinates of the point A are
The points A, B and C represent the complex numbers z_{1}, z_{2}, (1−i)z_{1}+iz_{2} (where ) respectively on the complex plane. The triangle ABC is :
In the expansion of the term containing same powers of a and b is 
All the spades are taken out from a pack of cards. From these cards, cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is
Fifteen coupons are numbered 1, 2, 3, ....., 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupons is at most 9, is :
Find the value(s) of the parameter 'a'(a>0) for each of which the area of the figure bounded by the straight line, the parabola is the greatest
The parameter on which the value of the determinant
does not depend upon, is
If n is even positive integer, then the condition that the greatest term in the expansion of (1 + x)^{n} may have the greatest coefficient also is
The equation of the common tangent to the curves y^{2} = 8 x and xy = 1 is
If ABC be a triangle with and AB = x such that (AB) (AC) = 1. If x varies, then the longest possible length of the angle bisector AD is
The locus of the midpoint of the portion of the line x cos α + y sin α = p intercepted between the axes is
Find the derivative with respect to x of the function :
A lady wants to select one cotton saree and one polyester saree from a textile shop. If there are 10 cotton varieties and 12 polyester varieties, in how many ways can she choose the two sarees ?
A man will take 3 steps forward or 3 steps backward he will fall in the well. Given the probability of steps forward is 1/2 and steps backward is 1/2. If probability that he fells in well in the 5^{th} steps is p/2q when p and q are coprime, then find the value of q+p.
The sum of the areas of n squares in n^{2}. If the areas of the squares can be put in A.P. What is the length of the side of the 25^{th} square?
If where p and q are coprime, then find the value of p+q.
If A is a square matrix of order n such that then find the possible value of n.
357 docs148 tests

357 docs148 tests
