JEE Advanced Mi...

A solid cube is placed on a horizontal surface. The coefficient of friction between them is μ, where μ < 1/2 . A variable horizontal force is applied on the cube’s upper face, perpendicular to one edge and passing through the mid-point of that edge. The maximum acceleration with which it can move without toppling is

A spherical body of mass m, radius r and moment of inertia I about its centre moves along the x-axis. Its centre of mass moves with velocity = v₀ and it rotates about its centre of mass with angular velocity ω₀.L_O = lω₀ + mv_or . The angular momentum of the body about the origin O is

The base of a hollow right cone of semi vertical angle 30^o is fixed to a horizontal plane. Two particle each of mass m are connected by a light inextensible string which passes through a small hole in the vertex of the cone. One particle A hangs at rest inside the cone. The other particle B moves on the outer smooth surface of the cone at a distance ℓ from vertex in a horizontal circle with centre at A. Neglecting friction, now answer the following.

The tention in the string is

The base of a hollow right cone of semi vertical angle 30^o is fixed to a horizontal plane. Two particle each of mass m are connected by a light inextensible string which passes through a small hole in the vertex of the cone. One particle A hangs at rest inside the cone. The other particle B moves on the outer smooth surface of the cone at a distance ℓ from vertex in a horizontal circle with centre at A. Neglecting friction, now answer the following.

The angular velocity of B is

Where X is a compound that forms azodye with benzene diazonium chloride in faintly basic medium.

Hence the products P, X and Y are respectively.

A white compound (A) on strong heating decomposes to produce two products (B) and (C). (B) on reaction with white phosphorus produces (D), which is a strong dehydrating agent. (D) on reaction with perchloric acid converts it to its anhydride.

The compound (A) is

A white compound (A) on strong heating decomposes to produce two products (B) and (C). (B) on reaction with white phosphorus produces (D), which is a strong dehydrating agent. (D) on reaction with perchloric acid converts it to its anhydride.

The product/s obtained on hydrolysis of (D) is

PQ is the double ordinate of the parabola y2 = 4x which passes through the focus S. ΔPQA is an isosceles right angle triangle, where A is on the axis of the parabola. Line PA meets the parabola at C and QA meets the parabola at B.

The area of trapezium PBCQ is

PQ is the double ordinate of the parabola y2 = 4x which passes through the focus S. ΔPQA is an isosceles right angle triangle, where A is on the axis of the parabola. Line PA meets the parabola at C and QA meets the parabola at B.

The circumradius of trapezium PBCQ is

Let z be a complex number satisfying z² + 2αz + 1 = 0 where α is a parameter which can take any real value.

The roots of this equation lie on a certain circle if