A $$\sqrt{34}$$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ef and Fw are the reaction forces of the floor and the wall, then ratio of $$F_w/F_f$$ will be : (Use g = 10 m/s2.)

Match List-I with List-II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List-I List-II (A) Moment of inertia of solid sphere of radius R about any tangent. (I) {5 \over 3}M{R^2} (B) Moment of inertia of hollow sphere of radius (R) about any tangent. (II) {7 \over 5}M{R^2} (C) Moment of inertia of circular ring of radius (R) about its diameter. (III) {1 \over 4}M{R^2} (D) Moment of inertia of circular disc of radius (R) about any diameter. (IV) {1 \over 2}M{R^2} Choose the correct answer from the options given below :

One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $$\omega$$ about an axis passing through fixed end, then the elongation of the spring will be :

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass m be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in rads$$-$$1).

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

If force $$\overrightarrow{F}=3\hat{i}+4\hat{j}-2\hat{k}$$ acts on a particle position vector $$2\hat{i}+\hat{j}+2\hat{k}$$ then, the torque about the origin will be :

A solid cylinder and a solid sphere, having same mass $$M$$ and radius $$R$$, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be :

The torque of a force $$5\hat{i}+3\hat{j}-7\hat{k}$$ about the origin is $$\tau$$. If the force acts on a particle whose position vector is $$2i+2j+k$$, then the value of $$\tau$$ will be

Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL$$-$$1 and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol$$-$$1 is : (Given : R = 0.082 L atm K$$-$$1 mol$$-$$1)

Two isomers 'A' and 'B' with molecular formula C4H8 give different products on oxidation with KMnO4 in acidic medium. Isomer 'A' on reaction with KMnO4/H+ results in effervescence of a gas and gives ketone. The compound 'A' is

What will be the major product of following sequence of reactions?

Product 'A' of following sequence of reactions is

The major product in the following reaction

The product formed in the following reaction.

Given below are two statements : Statement I : The presence of weaker $$\pi$$-bonds make alkenes less stable than alkanes. Statement II : The strength of the double bond is greater than that of carbon-carbon single bond. In the light of the above statements, choose the correct answer from the options given below :

Which of the following reagents / reactions will convert 'A' to 'B' ?

A compound ‘$$\mathrm{A}$$’ on reaction with ‘$$\mathrm{X}$$’ and ‘$$\mathrm{Y}$$’ produces the same major product but different by product '$$a$$' and '$$b^{\prime }$$. Oxidation of '$$a$$' gives a substance produced by ants. 'X' and 'Y' respectively are

Major product of the following reaction is

$$\stackrel{\bullet }{\mathrm{Cl}}+{\mathrm{CH}}_4\to \mathrm{A}+\mathrm{B}$$ A and B in the above atmospheric reaction step are :