PCM Mock Test (31 Dec) - JEE MCQ

A rod of length l, negligible resistance and mass m slides on two horizontal frictionless rails of negligible resistance by hanging a block of mass m₁ by the help of insulating mass less string passing through fixed massless pulley, (as shown). If a constant magnetic field B acts
upward perpendicular to the plane of the figure, find steady state velocity of hanging mass – 

A small circular ring is kept inside a larger loop connected to a switch and a battery as shown. The direction of induced current when the
switch is made (i) ON (ii) OFF after it was ON for a long time is -

A compound A with molecular formula gives a white precipitate on adding silver nitrate solution. A on reacting with alcoholic KOH gives compound B as the main product. B on ozonolysis gives Cannizaro reaction but not aldol condensation. D gives aldol condensation but not Cannizaro reaction. A is:

Which of the below reactions produce carboxylic acids?

(a)

(b)

(c)

(d)

If a₁, b₁, c₁ and a₂, b₂, c₂ are the direction ratios of two lines and θ is the acute angle between the two lines; then

If the coordinates of point A, B, C are (–1, 3, 2), (2, 3, 5) and (3, 5, –2) respectively then angle A is

Find the direction cosines of line joining points (1, –1, –3) and (–1, 2, 3)

Foot of perpendicular from (1, 2, 3) to the line joining points (6, 7, 7) and (9, 9, 5) is-

A line passing through A(1, 2, 3) and having direction ratios (3, 4, 5) meets a plane x + 2y – 3z = 5 at B, then distance AB is equal to-

Angle between the rays with d.r.'s 4, – 3, 5 & 3, 4, 5 is-

The direction cosines of the line joining the points (4, 3, –5) and (–2, 1, –8) are