Class 11th

For a suitably chosen real constant a, let a function, f: R − {−a} → R be defined by f(x) = (a-x)/(a+x). Further suppose that for any real number x ≠ −a and f(x) ≠ −a, (f ? f)(x) = x. Then f(-1/3) is equal to:

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies:

The common difference of the A.P. b?, b?, ., b? is 2 more than the common difference of A.P. a?, a?, ., a?. If a? = –159, a? = –399 and b? = a?, then b? is equal to:

A force F = (î + 2ĵ + 3k)N acts at a point (4î + 3ĵ – k)m. Then the magnitude of torque about the point (î + 2ĵ + k)m will be √xN m. The value of x is

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [ g is the acceleration due to gravity]:

Assume that the displacement (s) of air is proportional to the pressure difference (Ap) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ( ρ ) and the frequency (f). If Ap ~ 10 Pa, v ~ 300 m/s, p ~ π11g/m³ and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

Number of molecules in a volume of 4 cm³ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 * 10⁻¹⁴erg, g = 980 cm/s², density of mercury = 13.6 g/cm³ )

The value of the acceleration due to gravity is g₁ at a height h = R/2 (R = radius of the earth) from the surface of the earth. It is again equal to g₁ at a depth d below the surface of the earth. The ratio (d/R) equals:

A bullet of mass 5 g, traveling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030cal/(g- °C)(1cal = 4.2 * 10⁷ergs) close to:

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is: