Class XI Revision Quiz Week 3 Day 1 for JEE & BITSAT Exams

Question 1

The shortest distance between the parabola y² = 4x and the circle x² + y² + 6x − 12y + 20 = 0 is

Question 2

The condition for a line y = mx + C to be normal to a parabola is?(consider the equation to be

Question 3

Normals drawn from the point P to the parabola

have slopes m₁, m₂, m₃. If the locus of P is such that m₁m₂=α is a part of parabola itself, then find α.

Question 4

For the parabola

Question 5

The curve with parametric equations x = 1 + 4 cos θ, y = 2 + 3 sin θ is

Question 6

A thick walled cylinder tube with inner radius r and outer radius 3r with open ends and mass m starts rolling down an inclined plane of inclination

. Friction is enough to prevent slipping. The speed of its centre of mass is

. Find the value of a.

Question 7

A particle falls freely near the surface of the earth. Consider a fixed point O (not vertically below the particle) on the ground. Then pick up the incorrect alternative

Question 8

A ball of mass m moving with constant velocity u collides with a smooth horizontal surface at O as shown. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact O and x-axis is horizontal as shown. About which point will the angular momentum of ball be conserved.

Question 9

A canon shell moving along a straight line bursts into parts. Just after the burst, one part moves with momentum 20 N-s making an angle 30 ° with the original line of motion. The minimum momentum of the other part shell just after the burst is:

Question 10

A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same Kinetic Energy E₀, energy of explosion will be:

Question 11

At what time the reaction reaches equilibrium?

Question 12

The reaction between acetic acid and ethyl alcohol attains a state of equilibrium in an open vessel but decomposition of CaCO₃ does not because:

Question 13

At 783 K at the reaction H₂(g) + I₂ (g)

2HI (g), the molar concentrations (mol l^–1) of H₂, I₂ and HI at some instant of time are 0.1, 0.2 and 0.4 respectively. If the equilibrium constant is 46 at the same temperature, then as the reaction proceeds.

Question 14

Two solid compounds ‘X’ and ‘Y’ dissociates at certain temperature as follows :
X(s)

A(g) + 2B(g) Kp1 = 9 x 10^–3 atm³
Y(s)

2B(g) + C(g) Kp2 = 4.5 x 10^–3 atm³
The total pressure(in atm) of gases over a mixture of ‘X’ and ‘Y’ is

Question 15

What % of CO₂ in air (by volume) would be sufficient to prevent any loss in weight when Ag₂CO₃ is dried at 120°C?