Class 11th

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms⁻¹ :

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is :

For the equilibrium A ? B, the variation of the rate of the forward (a) and reverse (B) reaction with time is given by:

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + β)v, this angle changes to 45°. The value of β is close to:

Particle A of mass m₁ moving with velocity (√3î + ĵ)ms⁻¹ collides with another particle B of mass m₂ which is at rest initially. Let V₁ and V₂ be the velocities of particles A and B after collision respectively. If m₁ = 2m₂ and after collision V₁ = (î + √3ĵ)ms⁻¹, the angle between V₁ and V₂ is:

A particle moving in the xy plane experiences a velocity dependent force F = k(vᵧî + vₓĵ), where vₓ and vᵧ are the x and y components of its velocity v. If a is the acceleration of the particle, then which of the following statements is true for the particle?

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is:

Two planets have masses M and 16M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firings speed needed is:

A quantity X is given by (IFv²MLL⁴) in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of: