Class 11th

If the Boolean [removed]p ⇒ q) ⇔ (q * (~p)) is a tautology, then the Boolean expression p * (~q) is equivalent to:

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that boy can exert on the rope so that the piece of wood does not move from its place is _____ N. (Round off to the Nearest Integer) [Take g = 10 ms?²]

The time period of a simple pendulum is given by T = 2π√(l/g). The measured value of the length of pendulum is 10cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is,

If cot⁻¹(α) = cot⁻¹2 + cot⁻¹8 + cot⁻¹18 + cot⁻¹32 + . upto 100 terms, then α is:

The disc of mass M with uniform surface mass density σ is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position (xa/3π, xa/3π) where x is---------. (Round off to the Nearest integer) [a is an area as shown in the figure]

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction 1/√3. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ______. (Round off to Nearest Integer) [Take g = 10 ms?²]

The inverse of y = 5^logx is:

Two particles A and B of equal masses are suspended from two massless springs of spring constants K₁ and K₂ respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is

Team 'A' consists of 7 boys and n girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to:

A block of mass 1 kg attached to a spring is made to oscillate with initial amplitude of 12cm. After 2 minutes the amplitude decreases to 6cm. Determine the value of the damping constant for this motion. (take ln 2 = 0.693)