Class 11th

A ball of mass 10kg, moving with a velocity 10√3 m/s along, the x-axis, hits another ball of mass 20kg which is at rest. After the collision, first ball comes to rest while second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of 10 m/s. The second piece starts moving at an angle of 30° with respect to the x-axis. The velocity of the ball moving at 30° with x-axis is x m/s. The configuration of pieces after collision is shown in the figure below. The value of x to the nearest integer is---------

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is 10m/s and slows down with uniform deceleration, then magnitude effective retarding force on the bullet is 'x' N. The value of 'x' to the nearest integer is----------.

In the ground state of atomic Fe(Z = 26), the spin- only magnetic moment is ___*10?¹ BM.
(Round off to the nearest integer).
[Given √3 = 1.73, √2 = 1.41]

The minimum distance between any two points P₁ and P₂ while considering point P₁ on one circle and point P₂ on the other circle for the given circles' equations x² + y² - 10x - 10y + 41 = 0, x² + y² - 24x - 10y + 160 = 0 is.

The reaction 2A + B₂ → 2AB is an elementary reaction.
For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of reaction increases by a factor of ______.

If (2021)³⁷⁶² is divided by 17, then the remainder is .

The sum of possible values of x for tan^-1(x + 1) + cot^-1(1/(x - 1)) = tan^-1(8/31) is:

The line 2x - y + 1 = 0 is a tangent to the circle at the point (2, 5) and the centre of the circle lies on x - 2y = 4. Then, the radius of the circle is:

The value of 4 + 1 / (5 + 1 / (4 + 1 / (5 + 1 / (4 + .∞)))) is:

If the fourth term in the expansion of (x + xˡᵒᵍ²ˣ)⁷ is 4480, then the value of x where x ∈ N is equal to: