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Directions: The following question has FOUR choices, out of which ONE or MORE are correct.
The electrostatic potential (Φ_{r}) of a spherical symmetric system, kept at origin, is shown in the adjacent figure, and given as
Which of the following options is/are correct?
Directions: The following question has FOUR choices, out of which ONE or MORE are correct.
A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s immediately after the collision.
Directions: The following question has FOUR choices, out of which ONE or MORE are correct.
A series RC circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The current IR through the resistor and voltage VC across the capacitor are compared in the two cases. Which of the following is/are true?
Directions: The question has four choices, out of which ONE or MORE is correct.
In the given circuit, the AC source has ω = 100 rad/s. Considering the inductor and capacitor to be ideal, the correct choice(s) is/are:
The electron in a hydrogen atom makes a transition n_{1} → n_{2}, where n_{1} and n_{2} are the principal quantum numbers of two states. Assume the Bohr’s model to be valid. The time period of the electron in the initial state is eight times that in the final state. The possible values of n_{1 }and n_{2} are
A resistance R of thermal coefficient of resistivity = α is connected in parallel with a resistance = 3R, having thermal coefficient of resistivity = 2α. Find the value of α_{eff}.
Two cars A and B are approaching each other as shown in figure.
At t = 0, the velocities of A and B are v_{1} and v_{2} and they are at x = 0 and x = x_{0}, respectively. The car A is moving with constant velocity while B is moving with constant acceleration a, whose direction is shown. If X_{rel}, V_{rel} and a_{rel} are displacement, velocity and acceleration of A w.r.t. B respectively, then mark out the correct options.
Suppose the potential energy between electron and proton at a distance r is given by . Application of Bohr's theory to hydrogen atom in this case shows that
For the circuit shown in the figure, find the current (in ampere) through the source.
Suppose the potential energy between an electron and a proton at a distance r is given by Ke^{2} / 3r^{3}. Application of Bohr's theory to hydrogen atom in this case shows that energy in the n^{th} orbit is proportional to n^{x} then x=
A disc of radius R rotating with an angular velocity ω_{0} is placed on a rough horizontal surface. If initial velocity of centre of disc is zero, then velocity of centre of disc when it ceases to slip, comes out to be ω0R/k, value of k is _____.
A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string is set into vibrations using an external vibrator of frequency 100 Hz. Find the separation (in cm) between the successive nodes on the string.
A block is moving on an inclined plane making an angle 45° with the horizontal and the coefficient of friction is μ. The force required to just push it up the inclined plane is 3 times the force required to just prevent it from sliding down. If we define N = 10 μ, then N is
Steel wire of length L' at 40°C is suspended from the ceiling and then a mass 'm' is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length 'L'. The coefficient of linear thermal expansion of the steel is 10^{5}/°C, Young's modulus of steel is 10^{11 }N/m^{2} and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of 'm' in kg is
(Round off up to 2 decimal places)
Answer the following by appropriately matching the lists based on the information given:
One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the PV diagram. List II gives the characteristics involved in the cycle. Match them with each of the processes given in List I.
Answer the following by appropriately matching the lists based on the information given:
List I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as λ_{f} . Match each system with statements given in List II describing the nature and wavelength of the standing waves.
A man is standing on top of a building 100 m high. He throws two balls vertically, one at t = 0 and after a time interval (less than 22 seconds). The later ball is thrown at a velocity of half the first. At t = 2 s, both the balls reach their maximum heights. At this time the vertical gap between first and second ball is +15m.
The speed of the first ball is
A man is standing on top of a building 100 m high. He throws two balls vertically, one at t = 0 and after a time interval (less than 22 seconds). The later ball is thrown at a velocity of half the first. At t = 2 s, both the balls reach their maximum heights. At this time the vertical gap between first and second ball is +15m.
The time interval between the throw of balls is
The given graph represents the variations in compressibility factor (z) = pV/nRT versus p, for three real gases A, B and C.
Which of the following statements is/are correct?
Which of the following statements is/are true about HCOOH?
Which of the following is/are correct statement(s) about [Ni(CO)_{4}]?
Which of the following molecules has as O—O bond ?
Which of the following statements is/are true for P_{4}S_{3} molecule 
If the radius of Na^{+} ion is 95 pm and that of Cl^{−} ion is 181 pm, then
How many gram equivalents are there per mole of H_{2}S in its oxidation to SO_{2}?
How many of the following give pink precipitates with NaOH (Precipitate may or may not dissolve in excess of NaOH )?
In a mixture of HHe^{+} gas (He^{+} is singly ionised He atom), H atoms and He^{+} ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He^{+} ions (by collisions). Assume that the Bohr model of atom is exactly valid.
The quantum number n of the state finally populated in He^{+} ions is
EDTA^{4–} is ethylenediaminetetraacetate ion. What is the total number of N–Co–O bond angles in [Co(EDTA)]^{1–} complex ion?
Directions: Read the paragraph and answer the following question.
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogenous solution. These are called colligative properties. Applications of colligative properties are very useful in day to day life. One of its examples is the use of ethylene glycol and water mixture as antifreezing liquid in the radiator of automobiles.
A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9.
Given: Freezing point depression constant of water (Kwater) = 1.86 K kg mol^{1}
Freezing point depression constant on ethanol (Kethanol) = 2.0 K kg mol^{1}
Boiling point elevation constant of water = 0.52 K kg mol^{1}
Boiling point elevation constant of ethanol = 1.2 K kg mol^{1}
Standard freezing point of water = 273 K
Standard freezing point of ethanol = 155.7K
Standard boiling point of water = 373 K
Standard boiling point of ethanol = 351.5 K
Vapour pressure of pure water = 32.8 mm Hg
Vapour pressure of pure ethanol = 40 mm Hg
Molecular weight of water = 18 g mol^{1}
Molecular weight of ethanol = 46 g mol^{1}
In answering the following question, consider the situations to be ideal dilute solutions and solutes to be nonvolatile and nondissociate.
Arrange the following by appropriately matching the lists based on the information given in the paragraph.
List  1 represents compounds of Xe of group 18 in the modern periodic table.
List  2 represents the corresponding shapes of the compounds given in List  1.
Which of the following options has the correct combination considering List  1 and List  2?
Arrange the following by appropriately matching the lists based on the information given in the paragraph.
List  1 represents coordination compounds.
List  2 represents shapes/geometries and magnetic characters of the coordination compounds given in List  1.
Which of the following options has the correct combination considering List  1 and List  2?
A definite amount of reducing agent is oxidised by 20 mL of 1 M KMnO_{4} in acid medium, then the same amount of reducing agent is oxidised to the same state by how many mL of 1 M KMnO4 in neutral medium itself changing to Mn^{4+} state?
Name the end product in the following series of reaction.
Directions: The following question has four choices, out of which ONE or MORE can be correct.
Let z_{1 }and z_{2} be two distinct complex numbers and let z = (1  t) z_{1} + tz_{2} for some real number t with 0 < t < 1. If Arg(w) denotes the principal argument of a nonzero complex number w, then:
If eccentricity 'e' of conic satisfies the equation , the curve may be
Let l, m and n be three consecutive natural numbers (l > m > n). If the angle A of △ABC be given by and the perimetre of the triangle is 12 units, then the area of the triangle ABC is
Directions: The question has four choices, out of which ONE or MORE may be correct.
Let E and F be two independent events. The probability that exactly one of them occurs is 11/25 and the probability of none of them occurring is 2/25. If P(T) denotes the probability of occurrence of the event T, then
The function f(x) = xe^{x(1−x)} is strictly increasing for every point in
A fair coin is tossed repeatedly between person A and B, they are called alternately for winning a prize of Rs. 30. The person getting Head will be the winner, and game will continue till a person wins. A starts the call. If expectation of A means Rs. 30×Probability of A to win, then the expectation of
If one of the vertices of the triangle of maximum possible area that can be inscribed in the curve z − 2i = 2, is 2 + 2i, then the remaining two vertices are given by
Directions: The question has four choices, out of which ONE or MORE may be correct.
If then
Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2CD.
Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is
The total number of local maxima and local minima of the function
Let A, B, C be three complex numbers as defined below:
A = {z : Im z ≥ 1}
B = {z : z  2  i = 3}
C = {z : Re((1  i)z) = 3√2}
The number of elements in the set A ∩ B ∩ C is
Let (x, y) be such that sin^{1}(ax) + cos^{1}(y) + cos1(bxy) = π/2
Which of the following options correctly matches the statements in Column I with the statements in Column II?
Consider the lines given by:
L_{1} : x + 3y  5 = 0, L2_{ }: 3x  ky  1 = 0, L_{3} : 5x + 2y  12 = 0
Which of the following options correctly matches the statements in Column I with the statements in Column II?
Consider the equation
The number of real values of x for which the equation has solution is
Consider the equation
If x takes the values for which the equation has a solution, then the number of values of a∈[0,100] is
366 docs219 tests

366 docs219 tests
