JEE 2020 : Weekly Quiz 30 (22.09.2019) for JEE & BITSAT Exams

Question 1

If arg

= arg(z₂), then

Question 2

If a > 0, a ∈ R, z = a + 2i and z|z| - az + 1 = 0 then

Question 3

If α is the angle which each side of a regular polygon of n sides subtends at its centre, then 1 + cosα + cos2α + cos3α … + cos(n-1)α is equal to

Question 4

If z =

Question 5

If z is a complex number such that |z| = 4 and arg(z)

Then z is equal to

Question 6

The sum of the first n terms of the series 1²+2.2²+3²+2.4²+5²+2.6²+ . . . is

, when n is even. When n is odd, the sum is

Question 7

Given p A.P’s, each of which consists of n terms. If their first terms are 1, 2, 3,……, p and common differences are 1, 3, 5, ….., 2p – 1 respectively , then sum of the terms of all the progressions is

Question 8

If ar > 0, r ∈ N and a₁, a₂, a₃, ……, a_2n are in A.P, then

is equal to

Question 9

a, b, c, d, e are five numbers in which the first three are in A.P and the last three are in H.P. If the three numbers in the middle are in G.P then the numbers at the odd places are in

Question 10

If the sides of a right-angled triangle form an A.P. then the sines of the acute angle is

Question 11

Clemmensen reduction will convert acetone into

Question 12

The oxime of which of the following species will exist is syn and anti geometrical forms?

Question 13

Which of the following intermediate form when an alcohol reacts with concentrated H₂SO₄?

Question 14

The reaction of Glycerol with bismuth nitrate yields:

Question 15

Oxalic acid when reduced with zinc and

gives

Question 16

The bond dissociation enthalpy C—X in CH₃X (where X is halogen) follows the order

Question 17

Chlorination of toluene with excess of chlorine under the condition of light and heat produces

Question 18

Consider the following compounds

C₆H₅CH₂Br (I), C₆H₅—CH(C₆H₅)Br (II), C₆H₅CH(CH₃) Br (III) and

C₆H₅C(CH₃)(C₆H₅) Br (IV)

The order of reactivity of these towards nucleophilic substitution by S_N1 mechanism is

Question 19

The major product when 2-bromobutane is treated with ethanolic KOH is

Question 20

The shown compound is treated with sodium and methyl iodide in the presence of ether. Identify the final product.

Question 21

A thin convex lens of focal length 10 cm and refractive index 1.5 is cut vertically into two equal pieces. They are placed with a liquid of refractive index 3 between them. What is the focal length of the combination?

Question 22

An object is placed at 2x cm from the pole in front of a concave mirror giving 5 times magnified real image. If it is moved to a distance of (x+10) cm, magnification becomes 4. What is the focal length of the mirror?

Question 23

A body is placed in front of two lenses 1 and 2 which have focal lengths as 20 cm and 8 cm respectively and lens separation of 20 cm. The object is 5 cm from lens 1. What is position of the image produced by the system of two lenses?

Question 24

An observer is looking at a body in water with refractive index 4/3 through a converging lens with focal length of 60 cms. The lens is made to fall from 70 cm height along its vertical axis. The body moves up with constant velocity 50 cm/s, initially at the depth of 30 cm. What is the velocity with which the body appears to move to the observer at t=0.7 s?

Question 25

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen:

Question 26

A focal length of a lens is 10 cm. What is power of a lens in dioptre?

Question 27

If ε₀ and μ₀ are the permittivity and permeability of free space and ε and μ are the corresponding quantities for a medium, then refractive index of the medium is

Question 28

A planoconvex lens has a maximum thickness of 6 cm. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottom most point of the lens is found to be 4 cm. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the center of the plane face is found to be $Description: E:\KCET-1-Feb\KARNATAKA-CET-2011_files\image093.png$ cm. The radius of curvature of the lens is

Question 29

Two thin lenses have a combined power of +9(d) When they are separated by a distance of 20 cm, their equivalent power becomes + $Description: E:\KCET-1-Feb\KARNATAKA-CET-2011_files\image105.png$ (d) Their individual powers (in dioptres) are

Question 30

The speed of light in media M₁ and M₂ are 1.5 × 10⁸ ms^-1 and 2 × 10⁸ ms^-1 respectively. A ray traels from medium M₁ to the medium M₂ with an angle of incidence θ is