In a series LCR circuit, R = 200 Ω and the voltage and frequency of the main supply are 220 V and 50 Hz, respectively. On taking out the capacitance from the circuit, the current lags behind the voltage by 30°. On taking out the inductor from the circuit, the current leads the voltage by 30°. The power dissipated in the LCR circuit is

Shown in the figure below is a meter bridge set up with null deflection in the galvanometer. The value of the unknown resistance R is

In this question, two statements are given, numbered 1 and 2. Read both the statements carefully and choose the correct option accordingly.

Statement-1: The temperature dependence of resistance is usually given as R = R₀(1 + α Δt). The resistance of a wire changes from 100 Ω to 150 Ω when its temperature is increased from 27°C to 227°C. This implies that α = 2.7 × 10^-3/°C.
Statement-2: R = R₀(1 + α Δt)is valid only when the change in the temperature ΔT is small and ΔR = (R - R₀) << R₀.

Electric field intensity due to a semi-infinite wire at point P (as shown in the figure) is

Two equally charged identical metal spheres A and B repel each other with a force of 2.0 × 10^–5 N. Another identical uncharged sphere C is made to touch A and then placed at the midpoint between A and B. What is the net force on C?

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

What is the use of ball bearings between hubs and the axle of ceiling fans and bicycles?

Three forces start acting simultaneously on a particle moving with velocity These forces are represented in magnitude and direction by the three sides of a triangle ABC (as shown). The particle will now move with velocity

A particle of mass 0.3 kg is subjected to a force F = -kx, with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

A charged particle of specific charge (charge/mass) α is released from the origin at time t = 0 with velocity  in a uniform magnetic field . The coordinates of the particle at time t =  are

A projectile is fired at an angle 60° with some velocity u. If the angle is changed infinitesimally, let the corresponding fractional changes in the range and the time of flight be x and y, respectively, then find the value of y.

Consider a rubber ball falling freely from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then, velocity as a function of time, and height as a function of time will be represented as

The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

The sequence of decays of a radioactive nucleus is:

If the mass number and the atomic number of D₂ respectively are 176 and 71, the corresponding values of D will be

A giant telescope in an observatory has an objective of focal length 19 m and an eye-piece of focal length 1.0 cm. In normal adjustment, the telescope is used to view the moon. What is the diameter of the image of the moon formed by the objective? (The diameter of the moon is 3.5 × 10⁶ m and the radius of the lunar orbit around the Earth is 3.8 × 10⁸ m)

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m², the number of rotations made by the pulley before its direction of motion is reversed is

Carbon, silicon and germanium have four valence electrons each. At room temperature, which of the following statements is the most appropriate?

A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumferences of the discs touch each other. The centre of mass of the new disc is αR away from the centre of the bigger disc. The value of α is

A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is 2.0 × 10^-6 per °C and the coefficient of cubical expansion of the liquid is 6.0 × 10^-6 per °C. On heating the vessel,

In Young's double slit experiment, one of the slits is wider than the other, so that the amplitude of the light from one slit is double that from the other slit. If I_m be the maximum intensity, then the resultant intensity I when they interfere at phase difference φ is given by

Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to each other. How long (in number of days) will it be before the gravitational attraction brings them 1 cm closer together? (Answer up to two decimal places)

In the given figure, if a battery is connected between points A and B, and e.m.f. E = 18 V, then the current (in A) flowing through the battery is

An object O is placed at a distance of 20 cm from a thin plano-convex lens of focal length 15 cm. The plane surface of the lens is silvered as shown in the figure below:

The image is formed at a distance of ___ cm to the left of the lens. Fill in the blank with appropriate integer.

The surface of a metal is illuminated with light of wavelength 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal (in eV) is
(hc = 1240 eV-nm) (Answer up to two decimal places)

Water is drawn from a well into a 5 kg drum of capacity 55 litres, by two ropes connected to the top of the drum. The linear mass density of each rope is 0.5 kg m^-1. The work done in lifting water to the ground from the surface of water in the well 20 m below is c × 10⁴ J. The value of c, up to one decimal place, is [g = 10 ms^-2]

The radioactive isotope , which is used in the treatment of cancer, can be made by (n, p) reaction. What is the target nucleus for this reaction?

The van der Waals equation for a real gas is given by the formula (V - nb) = nRT; P, V, T and n are the pressure, volume, temperature, and number of moles of the gas, respectively. Which of the following is the correct interpretation for the parameter 'a'?

The bond lengths and bond angles in the molecules of methane, ammonia and water are given below:

This variation in bond angle is a result of
(i) the increasing repulsion between hydrogen atoms as the bond length decreases
(ii) the number of non-bonding electron pairs in the molecule
(iii) a non-bonding electron pair having a greater repulsive force than a bonding electron pair

The following question has four choices, out of which ONLY ONE is correct.

100 ml of a 0.1 M solution of a reducing agent whose equivalent weight is equal to its molecular weight in both acidic and alkaline media requires 75 ml of a KMnO₄ solution in acidic medium for complete oxidation. What is the molar concentration of the KMnO₄ solution if the titration is carried out in alkaline medium?

For a first order reaction A → P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = -(2000)1/T + 6.0.
The pre-exponential factor A and the activation energy E_a respectively are

The volume of a colloidal particle, V_c, as compared to the volume of a solute particle in a true solution, V_s, could be

The following question has four choices, out of which ONLY ONE is correct.

Wavelengths of X-ray lines of Mg and Cr are 0.987 nm and 0.229 nm, respectively. The values of the constants 'a' and 'b' for this series should respecively be

Which one of the following species is not a pseudohalide?

Identify the incorrect statement.

The oxidation state of chromium in the final product formed by the reaction between KI and acidified potassium dichromate solution is

Which of the following is aromatic?

What would be the product formed when 1-bromo-3-chlorocyclobutane reacts with two equivalents of metallic sodium in ether?

Consider the following reaction:

Identify the structure of the major product X.

Consider the following sequence of reactions:

The end product Q is

What is A?

Identify product 'Z' in the following reaction scheme:

Which of the following characteristics is/are not correct for enzymes?

a. Enzymes show maximum activity when pH is either very low or very high.
b. Enzymes are normally heterogeneous catalysts that are very specific in action.
c. Enzymes are specific biological catalysts that possess well-defined active sites.
d. Chemically, all enzymes are globular proteins.

The compound is used as

The enthalpies of formation of OH(g), H(g) and O(g) are 42, 218 and 248 kJ mol^-1. The value of bond enthalpy O-H (in kJ mol^-1) is

A 0.004 M solution of Na₂SO₄ is isotonic with a 0.010 M solution of glucose at the temperature. The apparent percentage of degree of dissociation of Na₂SO₄ is

0.6 g urea is added to 360 g water. Calculate lowering in vapor pressure (in mm of Hg, rounded upto 3 decimal places) for this solution.
(Given: Vapour pressure of H₂O is 35 mm of Hg)

The volume strength (in L) of 1.5 N H₂O₂ solution is

On mixing 400 ml of 0.1 M solution of H₂SO₄ with and equal volume of NaOH solution of the same molarity, the pH (value rounded to 1 decimal place is) of the resultant mixture is