JEE 2020 : Weekly Quiz 27 (14.09.2019) for JEE & BITSAT Exams

Question 1

The equations of tangents to the ellipse 9x² + 16y² = 144 which pass through the point (2, 3) is -

Question 2

An ellipse is described by using an endless string which is passed over two pins. If the axes are 6 cm and 4 cm, the necessary length of the string and the distance between the pins respectively in cms, are-

Question 3

The equation of the ellipse with its centre at (1, 2), one focus at (6, 2) and passing through the point (4, 6) is -

Question 4

The eccentricity, foci and the length of the latus rectum of the ellipse x² + 4y² + 8y – 2x + 1 = 0 is

Question 5

The eccentricity of the ellipse which meets the straight line

+

= 1 on the axis of x and the straight line

–

= 1 on the axis of y and whose axis lie along the axes of coordinates, is

Question 6

The radius of the circle passing through the foci of the ellipse

+

= 1, and having its centre (0, 3) is-

Question 7

An arc of a bridge is semi-elliptical with major axis horizontal. The length of the base is 9 meter and the highest part of the bridge is 3 meter from the horizontal. The best approximation of the Pillar 2 meter from the centre of the base is -

Question 8

Find the equation of the parabola having vertex

passing through

and axis along X-axis.

Question 9

The tangent at (1,7) to curve x²=y-6 touches the circle x²+y²+16x+12Y+c=0 at

Question 10

The condition so that the line lx+my+n=0 may touch the parabola y²=8x

Question 11

Of the following, which is the product formed when cyclohexanone undergoes aldol condensation followed by heating?

Question 12

Clemmensen reduction of a ketone is carried out in the presence of which of the following?

Question 13

Which of the following acid\s does not exhibit optical isomerism?

Question 14

and

can be distinguished chemically byn

Question 15

Predict the products in the given reactions,

Question 16

Propionic acid with Br₂—P yields a dibromo product. Its structure would be

Question 17

Consider the following reaction,

the product, Z, is

Question 18

Propanoyl chloride is isomeric with

Question 19

Which of the following product is formed when Adipic Acid is heated with P₂O₅?

Question 20

Question 21

An inductor of 1 H is connected across a 220 V, 50 Hz supply. The peak value of the current is approximately.

Question 22

A coil of inductance 8.4 mH and resistance 6

is connected to 12V battery. The current in the coil is 1 A at approximately the time

Question 23

Two concentric coils of 10 turns each are placed in the same plane. Their radii are 20cm and 40 cm and carry 0.2 A and 0.3 A current respectively in opposite directions. The magnetic induction (in Tesla) at the centre is

Question 24

A triangular wire frame (each side = 2m) is placed in a region of time variant magnetic field having

. The magnetic field is perpendicular to the plane of the triangle. The base of the triangle AB has a resistance 1Ω while the other two sides have resistance 2 Ω each. The magnitude of potential difference between the points A and B will be

Question 25

A uniform magnetic field of induction B is confined to a cylindrical region of radius R. The magnetic field is increasing at a constant rate of

(tesla/second). An electron of charge q, placed at the point P on the periphery of the field experiences an acceleration

Question 26

The magnetic flux through a stationary loop with resistance R varies during interval of time T as ϕ = at (T - t). The heat generated during this time neglecting the inductance of loop will be

Question 27

A circular conducting ring of radius 2 m rotates with constant angular velocity

about its diameter placed along the x-axis. A uniform magnetic field 50 T is applied along the y-axis. If at time t=0 the ring is entirely in the xy-plane, so the emf induced in the ring at

Question 28

A conducting loop (as shown) has total resistance R. A uniform magnetic field B = γt is applied perpendicular to plane of the loop where γ is a constant and t is time. The induced current flowing through loop is:

Question 29

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A square frame of side 10 cm and a long straight wire carrying current 1 Amp are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of

(see figure). The e.m.f induced at the time the left arm of the frame is at x = 10 cm from the wire is :

Question 30

A long straight wire carrying current and a π-shaped conductor with sliding connector are placed in the same plane as shown in the figure. The connector of length and resistance R slides to the right with constant velocity. Neglecting resistance of π shaped conductor and the self-inductance of the loop. Find the current induced in the loop as a function of separation r between the connector and the straight wire.