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JEE 2020: Weekly Quiz -1 (15.06.2019)

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Question 1

The period of oscillation of simple pendulum is . Measured value of L is 20.0 cm known to
1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is

Question 2

Which of the following units denotes the dimensions ML2 / Q2, where Q denotes the electric charge ?

Question 3

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current an the voltage difference are 3% each, then error in the value of resistance of the wire is

Question 4

A beaker contains a fluid of density , specific heat and viscosity . The beaker is filled up to height h. To estimate the rate of heat transfer per unit area by convection when beaker is put on a hot plate, a student proposes that it should depend on and when (in °C) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for is:

Question 5

Identify the pair whose dimensions are equal:

Question 6

Let there be a spherically symmetric charge distribution with charge density varying as upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r ( r < R) from the origin is given by?

Question 7

In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

Question 8

A wire, of length , is bent into a semi-circular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges[ Coulomb where is the permittivity (in SI units) of free space] the net electric field at the centre O of the semi-circular arc would be:

Question 9

A thin semi–circular ring of radius r has a positive charge q distributed uniformly over it. The net field at the center O is

Question 10

A charged ball B hangs from a silk thread S which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density of the sheet is proportional to

Question 11

The radius of the second Bohr orbit for hydrogen atom is:

mass of electron
charge of electron
permittivity of vacuum

Question 12

According to Bohr’s theory, the angular momentum of electron in 5th orbit is what times of 

Question 13

At temperature T, the average kinetic energy of any particle is . The de Broglie wavelength follows the order:

Question 14

Energy of an electron is given by . Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be
(h = 6.62 × 1034 Js and c = 3.0 × 108 ms1)

Question 15

Ionization energy of He+ is 19.6 × 10–18 J atom–1. The energy of the first stationary state (n = 1) of Li2+ is

Question 16

If we consider that 1/6, in place of 1/12; mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Question 17

Experimentally it was found that a metal oxide has formula M0.98O. Metal M, is present as M2+ and M3+ in its oxide. Fraction of the metal which exists as M3+ would be

Question 18

Excess of NaOH (aq) was added to 100 mL of FeCl3 (aq) resulting into 2.14 g of Fe(OH)3. The molarity of FeCl3 (aq) is:
(Given molar mass of Fe=56 g mol-1 and molar mass of Cl=35.5 g mol-1)

Question 19

29.5 mg of an organic compound containing nitrogen was digested according to Kjeldahl’s method and the evolved ammonia was absorbed in 20 mL of 0.1 M HCl solution. The excess of the acid required 15 mL of 0.1 M NaOH solution for complete neutralization. The percentage of nitrogen in the compound is

Question 20

If 10–4 dm3 of water is introduced into a 1.0 dm3 flask at 300 K, how many moles of water are in the vapour phase when equilibrium is established?
(Given : Vapour pressure of H2O at 300 K is 3170 Pa; R = 8.314 J K–1 mol–1)

Question 21

Let be regions in the xy-plane defined by

Then

Question 22

Let A and B be two sets containing 4 and 2 elements respectively. Then the number of elements in the subsets of A x B having 3 or more elements is?

Question 23

{x : xand -1 < x < 1 } is which type of set?

Question 24

{x : x W and -2 < x < 1}

Question 25

If
 

                                                                          is continuous at x 0 then K is

Question 26

If then

Question 27

If , then

Question 28

Let where are natural numbers. Given that , the value of is

Question 29

Let S be the set of all points in (–π, π) at which the function, f(x) = min {sinx, cosx} is not differentiable. Then S is a subset of which of the following?

Question 30

All x satisfying the inequality
(cot–1 x)2 – 7 (cot–1x) + 10 > 0, lie in the interval:
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Feb 1JEE & BITSAT