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The volumes of containers A and B, connected by a tube and a closed valve are V and 4 V, respectively. Both the containers A and B have the same ideal gas at pressures (temperatures) 5.0 ×10^{5} Pa(300 K) and 1.0 ×10^{5}Pa (400 K), respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.
A block of mass 10 kg is suspended through two light spring balances as shown in figure
If E = 100 sin (100t) volt and are the instantaneous values of voltage and current, then the R.M.S values of voltage and current are respectively.
Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
The length of a given cylindrical wire is increased by 100%. Due to the consequent decrease in diameter the change in the resistance of the wire will be
Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1 s
If E_{I}, E_{II} and E_{III}_{ }are the percentage errors in g, i.e.,
for students I, II and III, respectively, then
Write down the expression for capacitance of a spherical capacitor whose conductors radii are R_{1 }and R_{2}(R_{2}>R1),when inner sphere is grounded.
A mass of M kg is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of 45° with the initial vertical direction is
Acceleration of each block is given as g/5√2. Find the magnitude and direction of force exerted by string on pulley. (μ = 0.4)
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
Three identical spheres, each of mass 1 kg are kept as shown in the figure below, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is
A resistor R and 2μF capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed (log_{10} 2.5 = 0.4)
A α−particle passes through a potential difference of 2×10^{6}V and then it becomes incident on a silver foil. The charge number of silver is 47. The energy of incident particles will be: (in joule)
Direction: Question is based on the following paragraph.
A wire of length L, mass m and carrying a current is suspended from point O as shown. An infinitely long wire carrying the same current I is at a distance L below the lower end of the wire. Given, I = 2A, L= 1m and m = 0.1 kg (ln 2 = 0.693)
What is angular acceleration of the wire just after it is released from the position shown?
The figure shows three circuits with identical batteries, inductors and resistances. Rank the circuits according to the currents through the battery just after the switch is closed, greatest first
A bullet when fired into a fixed target loses half of its velocity after penetrating 20 cm.How much further it will penetrate before coming to rest?
Directions: Question are Assertion  Reaction type each of these contains two statements: Statement I (Assertion), Statement II (Reason) Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I : The isothermal curves intersect each other at a certain point
Statement II: The isothermal changes takes place slowly, so the isothermal curves have very little slope.
A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of dielectric constant 5, the percentage increase in the capacitance will be
A ball is dropped from a bridge at a height of 176.4 m over a river. After 2s, a second ball is thrown straight downwards. What should be the initial velocity of the second ball so that both hit the water simultaneously? (Take g=10m/s^{2})
Directions: The answer to this question is a singledigit integer, ranging from 0 to 9. Enter the correct digit in the box given below.
Q. A 40 cm diameter pipe branches into two pipes of diameters 10 cm and 20 cm each. If the average velocities of water that flows through 10 cm and 20 cm pipes are 6 m/s and 2 m/s, respectively, then the speed of the water that flows through the 40 cm pipe (in m/s) is
(Answer up to nearest integer)
Directions: The answer to this question is a singledigit integer, ranging from 0 to 9. Enter the correct digit in the box given below.
Q. Two point objects A and B are 40 cm apart. A convex lens L of focal length 15 cm should be placed in between them such that the images due to the two point objects coincide. If the least distance between L and A is x, then the value of x – 1 is
Directions: The answer to this question is a singledigit integer, ranging from 0 to 9. Enter the correct digit in the box given below.
Q. An airfilled parallel plate capacitor having circular plates has a capacitance of 10 pF. When the radii of the plates are increased two times, the distance between them is halved and if a medium of dielectric constant k is introduced, the capacitance increases 16 times. The value of k is
Directions: The answer to this question is a singledigit integer, ranging from 0 to 9. Enter the correct digit in the box given below.
Q. Two parallel identical plates carry equal and opposite charges having a uniform charge of 88.9 C. Positive plate is fixed on the ceiling of a box and the negative plate has to be suspended. If the area of the plates is 6.35 sq. m and 'm' is the mass of the negative plate, then the value of [m] in kg, where [ ] stands for maximum integer value, is
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
A radioactive sample S_{1} having an activity of 5 μ Ci and half life of 20 years has twice the number of nuclei as another sample S_{2}, which has an activity of 10 μCi. The half lives (in years) of S_{2} is
Directions: Questions are based on the following paragraph.
When ammonium vanadate is heated with oxalic add solution, a compound Z is formed. A sample of Z was titrated with KMnO_{4} solution in hot acidic solution. The resulting liquid was reduced with SO_{2}, the excess SO_{2 }boiled off, and the liquid again titrated with KMnO_{4}. The ratio of the volumes of KMnO_{4} used in the two titrations was 5 : 1. KMnO_{4} oxidises all oxidation state of vanadium to Vanadium (+V) and SO_{2} reduces vanadium (+V) to vanadium (+IV). Read the above experiment and answer the following questions. If vanadium exists as , reduced species by SO_{2} would be
In a cubic dosed packed structure of mixed oxides, the lattice is made up of oxide ions, one eighth of tetrahedral/voids are occupied by divalent ions (A^{2}+), while one half of the octahedral voids are occupied by trivalent ions(B^{3+})What is the formula of the oxide ?
Which of the following sequence of reaction is the best means to furnish the conversion RCH_{2}OH→RCH_{2}NH_{2}
The standard heat of combustion of carbon(s), sulphur (s) and carbon disulphide (l) are 393.3, 293.72 and  1108.76 kJ/mol respectively. The standard heat of formation of carbon disulphide(l) is
The volume of 0.1 M oxalic acid that can be completely oxidised by 20 mL of 0.025 M KMnO_{4} solution is
Match List I with List II and select the correct answer using the codes given below the lists:
Which one of the following is the structure of polyacrylonitrile?
In the hydrocarbon
The state of hybrization of carbons 1,3 and 5 are in the following sequence :
If for then the value of k_{eq} for the reaction will be
For the elementary reaction M → N, the rate of disappearance of M increases by factor of 8 upon doubling the concentration of M. The order of the reaction with respect to M is
In which of the following case, increase in concentration of ion cause increase in E_{cell}?
Directions: Questions are based on the following paragraph.
When ammonium vanadate is heated with oxalic add solution, a compound Z is formed. A sample of Z was titrated with KMnO_{4} solution in hot acidic solution. The resulting liquid was reduced with SO_{2}, the excess SO_{2 }boiled off, and the liquid again titrated with KMnO_{4}. The ratio of the volumes of KMnO_{4 }used in the two titrations was 5 : 1. KMnO_{4} oxidises all oxidation state of vanadium to Vanadium (+V) and SO_{2} reduces vanadium (+V) to vanadium (+IV). Read the above experiment and answer the following questions.
Q. What is the oxidation state of vanadium in the compound Z?
Direction: Question is assertion reason type. These question contains two statements Statement I (Assertion), Statement II (Reason). These question also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes (a), (b), (c) and (d) given below:
Statement I : Detection of chlorine in 2, 4, 6 trinitrochlorobenzene can be done directly by addition of aq. AgNO_{3} solution.
Statement II: CCl bond is weakened by electron withdrawing  NO_{2} group
Silver (atomic weight = 108 g mol^{1} ) has a density of 10.5 g cm^{3}. The number of silver atoms on a surface of area 10^{12} m^{2 }can be expressed in scientific notation as y * 10^{x} . The value of x is
Names of some compounds are given. Which one is not correct in IUPAC system?
The structure of isobutyl group in an organic compound is :
consider the follwing reaction,
the value of x, y and z in the reaction respectively are
The correct statement about the following disaccharide is
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. X x 10^{2} moles of NaCl need to be added to precipitate out PbCl_{2} from 1 L solution of Pb(NO_{3})_{2} having concentration 0.01M. If K_{sp} of PbCl_{2} at 298K is 1.6 x 10^{5}, then the value of X will be
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. For a diatomic molecule having bond distance , the dipole moment is 1.2 D. What is the integral value obtained as a product of the fraction of charge separated and 16?
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. On complete combustion of a 9 L mixture of ethane and propane, 21 L of CO_{2} at STP is produced. The molar ratio of ethane and propane in the mixture is
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. How many open chain structures are possible for NMethyl butanamine (including it) that are referred to as metamers.
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. 100gm of is reduced to 3.125 g in 25 days. Half life of bismuth 210 (in days) is
A bag contains a white and b black balls. Two players A and B alternately draw a ball from the bag replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, then the ratio a : b is
If Z is the set of integers. Then, the relation R= {(a, b) :1+ ab > 0} on Z is
Direction: Question is AssertionReason type question. These question contains two statements: Statement I (Assertion) and Statement II (Reason). These question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the cedes (a), (b), (c) and (d) in the given below:
Statement I:
Staement II: x is non differential at x = 0
For any two real numbers θ and ϕ, we define θRϕ , if and only if sec^{2} θ  tan^{2}ϕ =1. The relation R is
Direction: Question is AssertionReason type question. These question contains two statements: Statement I (Assertion) and Statement II (Reason). These question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the cedes (a), (b), (c) and (d) in the given below:
if n≥ 2 is an integer and I is the identity matrix of order 3. then
The number of real solutions of the equation 2^{x/2}+(√2+1)^{x}=(5+2√2)^{x/2 }is
If m_{1}, m_{2}, m_{3} and m_{4} are, respectively the magnitudes of the vectors
then the corect order of m_{1}, m_{2}, m_{3} and m_{4} is
The area bounded by y = xsin x and X  axis between x = 0, x = 2π is
If θ is the angle between the tangents from (1, 0) to the circle x^{2} + y^{2}  5x + 4y  2 = 0, then θ is equal to
Let S_{k} be the sum of an infinite GP series whose first term k is k and common ratio is k/(k + 1) (k> 0). Then, the value of is equal to
Let z_{1} ≠ z_{2} and z_{1} = z_{2}. If z_{1} has positive real part and z_{2} has negative imaginary part. Then,
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. if , then the number of solutions of
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Q. The points (1, 3) and (5, 1) are two opposites vertices of a rectangle and the other two vertices lie on the line y – 2x + C = 0. Then the value of C is
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
Given that α and γ are the roots of the equation Ax^{2} – 4x + 1 = 0, and β and δ are the roots of the equation Bx^{2} – 6x + 1 = 0. Find the value of B  A, such that α, β, γ, δ are in H.P.
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
if the greatest value of is
Directions: The answer to the following question is a single digit integer ranging from 0 to 9. Enter the correct digit in the box given below.
if range of the function f(x) = sin^{–1} x + 2 tan^{–1} x + x^{2} + 4x + 1 is [a, b], then the value of a + b is
357 docs148 tests

357 docs148 tests
