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Two radioactive substances A and B have decay constants 5λ and λ, respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become (1/e)^{2 }will be:
The magnetic field and number of turns of the coil of an electric generator is doubled then the magnetic flux of the coil will:
If λ_{1} and λ_{2} are the wavelengths of the first members of Lyman and Paschen series, respectively, then λ_{1} : λ_{2 }is:
Three rods of Copper, Brass and Steel are welded together to from a Y –shaped structure. Area of cross – section of each rod = 4 cm^{2}. End of copper rod is maintained at 100°C where as ends of brass and steel are kept at 0°C. Lengths of the copper, brass and steel rods are 46, 13 and 12 cms respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are 0.92, 0.26 and 0.12 CGS units respectively. Rate of heat flow through copper rod is
In an experiment for determination of refractive index of glass of a prism by i – δ plot, it was found that a ray incident at an angle of 35° suffers a deviation of 40° and that it emerges at an angle of 79°. In that case, which of the following is closest to the maximum possible value of the refractive index?
In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10^{12 }m, the minimum electron energy required is close to:
Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of emergent light is reduced to I/3. The angle between polarizers A and C is θ. Then,
Assume that an electric field exists in space. Then the potential difference V_{A} – V_{O}, where V_{O} is the potential at the origin and V_{A} the potential at x = 2 m is:
In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60 μA/division. In the absence of shunt resistance, the galvanometer produces a deflection of θ = 9 divisions, when current flows in the circuit. The value of the shunt resistance that can cause the deflection of θ/2 is closest to:
A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 × 10^{2} m. The magnetic field at the centroid of the triangle will be:
A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero ? Mass of the sun = 2 × 10^{30} kg, mass of the earth 6 × 10^{24} kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10^{11} m).
A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?
The figure shows a 2.0 V potentiometer used for the determination of the internal resistance of a 1.5 V cell. The balance point of the cell in the open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm of the potentiometer wire. Determine the internal resistance of the cell.
What speed should a galaxy move with respect to us so that the sodium line at 589.0 nm is observed at 589.6 nm?
Light from a point source in the air falls on a spherical glass surface (μ=1.5 and radius of curvature 20cm). The distance of the light source from the glass surface is 100cm. The position where the image is formed is:
One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle ( directed towards the centre ) is:
A metal block of area 0.10 m^{2} is connected to a 0.01 kg mass via a string that passes over a massless and frictionless 0.01 kg pulley as shown in the figure. A liquid with a film thickness of 0.3 mm is placed between the block and the table. When released the block moves to the right with a constant speed of 0.085 ms^{1}. The coefficient of viscosity of the liquid is: (Take g = 10 ms^{2})
Assume that the light of wavelength is 6000Å coming from a star. What is the time resolution of a telescope whose objective has a diameter of 100 inch?
The magnetic field in a plane electromagnetic wave is given by By = (2 x 10^{7}) T Sin (0.5 x 10^{3}x + 1.5 x 10^{11}t). This electromagnetic wave is:
A pure inductor of 25.0 mH is connected to a source of 220 V. Find the inductive reactance and rms current in the circuit if the frequency of the source is 50 Hz.
Ice at 20°C is added to 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount of ice (in nearest integer) added to the water was _____g.
(Specific heat of water = 4.2 J/g/°C
Specific heat of Ice = 2.1 J/g/°C
Heat of fusion of water at 0°C = 334 J/g)
Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an ntype semiconductor, the density of electrons is 10^{19} m^{3} and their mobility is 1.6 m^{2}/(V.s) then the resistivity of the semiconductor (since it is an ntype semiconductor contribution of holes is ignored) is close to k × 10^{1}Ωm. Find the value of k.
The resistance of the meter bridge AB in given figure is 4Ω. With a cell of emf ε = 0.5V and rheostat resistance R_{h} = 2 ohm, the null point is obtained at some point J. When the cell is replaced by another one of emf ε = ε_{2} the same null point J is found for R_{h} = 6Ω. The emf ε_{2 }is k × 10^{1 }V.
(Answer up to the nearest integer)
When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to:
Calculate the Coulomb force between 2 alpha particles separated by 3.2 x 10^{15}m.
In KO_{2}, the nature of oxygen species and the oxidation state of oxygen atom are (respectively)
Consider separate solutions of 0.500 M C_{2}H_{5}OH (aq), 0.100 M Mg_{3}(PO_{4})_{2 }(aq), 0.250 M KBr (aq) and 0.125 M Na_{3}PO_{4 }(aq) at 25^{o}C. Which statement is true about these solutions, assuming all salts to be strong electrolytes?
The concentrations of fluoride, lead, nitrate and iron in a water sample from an underground lake were found to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of
The correct structure of product 'P' in the following reaction is:
When 2butyne is treated with H_{2}/Lindlar's catalyst, compound X is produced as the major product, and when treated with Na/liq. NH_{3}, it produces y as the major product. Which of the following statements is correct?
In graphite and diamond, the percentage of pcharacters of the hybrid orbital in hybridisation is respectively:
Which of the following conversions involves change in both shape and hybridisation?
Which of the following lines correctly show the temperature dependence of equilibrium constant K for an exothermic reaction?
An aqueous solution contains 0.10 M H_{2}S and 0.20 M HCI. If the equilibrium constant for the formation of HS^{} from H_{2}S is 1 .0 x 10^{7} and that of S^{2} from HS^{} ions is 1.2 x 10^{13}, then the concentration of S^{2} ions in aqueous solution is
Which of the following is not a property of physical adsorption?
Peroxyacetyl nitrate (PAN), an eye irritant is produced by:
Which of the following atoms has the highest first ionisation energy?
Which of the following compounds is metallic and ferromagnetic?
Which one of the following is not a common component of Photochemical Smog?
The mole fraction of glucose (C_{6}H_{12}O_{6}) in an aqueous binary solution is 0.1. The mass percentage of water in it, is ________. (Nearest integer)
For the estimation of nitrogen, 1.4 g of an organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of M/10 sulphuric acid. The unreacted acid required 20 ml of M/10 sodium hydroxide for complete neutralisation. The percentage of nitrogen in the compound is (Nearest integer)
An element with molar mass 2.7 × 10^{2} kg mol^{1} forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 10^{3} kg m^{3}, the radius of the element is approximately _______ × 10^{12} m (Nearest integer).
Given:
(i) 2Fe_{2}O_{3}(s) → 4Fe(s) + 3O_{2}(g); G° = +1487.0 kJ mol^{1}
(ii) 2CO(g) + O_{2}(g) → 2CO_{2}(q): Δ_{r}G° = 514.4 kJ mol^{1}
Free energy change, Δ_{f}G° for the following reaction will be _____ KJ mol^{1}. (Nearest integer)
2Fe_{2}O_{3}(s) + 6CO(g) → 4Fe(s) + 6CO_{2}(g)
If the standard deviation of x_{1}, x_{2}, …, x_{n} is 3.5, then the standard deviation of – 2x_{1} – 3, – 2x_{2} – 3, …, – 2x_{n} – 3 is:
Consider three observations a, b and c such that b = a + c. If the standard deviation of a + 2, b + 2, c + 2 is d, then which of the following is true?
In how many different ways can the letters of the word 'GEOGRAPHY' be arranged such that the vowels must always come together?
The equations ax + 9y = 1 and 9y  x  1 = 0 represent the same line if a =
Let R be a relation defined on the set of N natural numbers as R = {(x, y): y is a factor of x, x, y∈ N} then,
If y = y(x) is the solution of the differential equation e^{y } such that y(0) = 0, then y(1) is equal to:
The mean and variance of a binomial distribution are 4 and 2, respectively. What is the probability of two successes?
If a plane bisects the line segment joining the points (1, 2, 3) and (3, 4, 5) at right angles, then this plane also passes through the point
The value of k for which the points A (1, 0, 3), B (– 1, 3, 4), C (1, 2, 1) and D (k, 2, 5) are coplanar, is
A unit tangent vector at t = 2 on the curve x = t^{2} + 2, y = 4t^{3 }– 5, z = 2t^{2} – 6t is
For each t ∈ R, let [t] be the greatest integer less than or equal to t. Then,
Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, each of whose sides contains exactly 2 balls less than the number of balls that each side of the triangle contains. Then, the number of balls used to form the equilateral triangle is:
Consider the following three statements:
P : 5 is a prime number.
Q : 7 is a factor of 192
R : L.C.M. of 5 and 7 is 35.
Then the truth value of which one of the following statements is true?
The differential equation of the family of curves x^{2} = 4b(y + b), b ∈ R is
If m is the minimum value of k for which the function f(x) = x is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to
A line with positive direction cosines passes through the point P(2,  1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ is equal to
The curve amongst the family of curves, represented by the differential equation. (x^{2}  y^{2})dx + 2xy dy = 0 which passes through (1, 1) is:
Let A = R and A^{4} = [a_{ij}]. If a_{11} = 109, then a_{22} is equal to _______.
If the third term in the binomial expansion of (1 + x ^{log2x})^{5} equals 2560, and the fractional possible value of x is k/4. Find the value of k.
where x and y are real numbers, then y  x is equal to _____.
The value of the integral (where [x] denotes the greatest integer less than or equal to x) is ___.
357 docs148 tests

JEE Main Mock Test  5 Test  75 ques 
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357 docs148 tests

JEE Main Mock Test  5 Test  75 ques 
JEE Main Mock Test  6 Test  75 ques 
JEE Main Mock Test  7 Test  75 ques 
JEE Main Mock Test  8 Test  75 ques 
JEE Main Mock Test  9 Test  75 ques 