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Questions and Answers
What is the value of n in the equation 6 x 10 x 6 = (5 - n) x 9 x 10^-3, which results in n = 1?
What is the value of n in the equation 6 x 10 x 6 = (5 - n) x 9 x 10^-3, which results in n = 1?
1
In the reaction 3CaCO3 + 2H3PO4 -> Ca3(PO4)2 + 3H2O + 3CO2, what is the weight of Ca3(PO4)2 if 50 gm of CaCO3 reacts with 68.6 gm of H3PO4?
In the reaction 3CaCO3 + 2H3PO4 -> Ca3(PO4)2 + 3H2O + 3CO2, what is the weight of Ca3(PO4)2 if 50 gm of CaCO3 reacts with 68.6 gm of H3PO4?
68.6 gm
What is the molarity of H2O2 solution if 0.025 moles of it reacts with KMnO4, given the volume strength is 11.2?
What is the molarity of H2O2 solution if 0.025 moles of it reacts with KMnO4, given the volume strength is 11.2?
0.025 mol/L
In the equation 2x^2 + x = 3, the equation can be rewritten as __.
In the equation 2x^2 + x = 3, the equation can be rewritten as __.
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The solutions of the equation x^2 - 1 = 1 are x = 0 and x = 1.
The solutions of the equation x^2 - 1 = 1 are x = 0 and x = 1.
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A point charge (+q) of mass m is released from a distance d from the centre of a solid sphere of radius R and charge Q. What is the speed of the point charge when it reaches a distance R from the surface of the sphere?
A point charge (+q) of mass m is released from a distance d from the centre of a solid sphere of radius R and charge Q. What is the speed of the point charge when it reaches a distance R from the surface of the sphere?
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A uniformly charged ring of charge Q and radius R is folded from its diameter such that two halves make an angle 60° with each other. What is the net electric field at the centre of the ring?
A uniformly charged ring of charge Q and radius R is folded from its diameter such that two halves make an angle 60° with each other. What is the net electric field at the centre of the ring?
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What thickness H is needed for a flat disc Earth with the same gravitational acceleration on its surface as a spherical Earth?
What thickness H is needed for a flat disc Earth with the same gravitational acceleration on its surface as a spherical Earth?
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Six stars of equal mass moving about the centre of mass of the system in a regular hexagon. What is their common time period of revolution around the centre?
Six stars of equal mass moving about the centre of mass of the system in a regular hexagon. What is their common time period of revolution around the centre?
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If three forces can form a triangle with sides a, b, and c and a + b = c, are these forces concurrent and satisfy equilibrium conditions?
If three forces can form a triangle with sides a, b, and c and a + b = c, are these forces concurrent and satisfy equilibrium conditions?
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Which of the following equations is dimensionally incorrect? (Where t = time, h = height, s = surface tension, θ = angle, ρ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done)
Which of the following equations is dimensionally incorrect? (Where t = time, h = height, s = surface tension, θ = angle, ρ = density, a, r = radius, g = acceleration due to gravity, v = volume, p = pressure, W = work done)
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Study Notes
Part 1: Physics
Section I
- A point charge (+q) is released from a distance from the center of a solid sphere of radius R and charge Q. The speed of the point charge when it reaches a distance R from the surface of the sphere is to be found.
- A uniformly charged ring of charge Q and radius R is folded from its diameter, and the net electric field at the center of the ring (O) is to be found.
- The thickness of a flat disc (H) is needed to experience the same gravitational acceleration as on the surface of a spherical Earth.
- Six stars of equal mass m move about the center of mass of the system, and their common time period of revolution around the center is to be found.
- Statement 1: If three forces are represented by three sides of a triangle, they are concurrent forces and satisfy the condition for equilibrium. Statement 2: A triangle made up of three forces as its sides taken in the same order satisfies the condition for translatory equilibrium.
Section II
- A particle of mass m and charge q is projected towards a non-conducting fixed sphere having the same charge uniformly distributed throughout the volume of the sphere.
- A small dipole is placed at a distance R from the surface of a charged solid conducting sphere, and the options are:
- Charge distribution on the surface of the sphere will be non-uniform.
- Electric field due to charges on the sphere at point C (center of the sphere) will be zero.
- Potential at point C will be zero.
- Potential at point D due to the charges on the sphere will be zero.
- A narrow smooth tunnel of L-shape is made into the Earth up to the center, and a small ball is released from 'A'. The collision of the ball is perfectly inelastic.
- A planet of mass m revolves around the Sun in an elliptical orbit of eccentricity e, and its speed at apogee and perigee is to be found.
Section III
- The distance of a point from the Earth's center where the resultant gravitational field due to the Earth and the Moon is zero is to be found.
- The vector is given, and its magnitude and derivative at t = 1s are to be found.
Part 2: Chemistry
Section I
- NaN3 is decomposed into Na and N2, and the number of moles of N2 produced is to be found.
- CaC2 reacts with H2O to produce CaO and C2H2, and the number of moles of C2H4 produced is to be found.
Section II
- The reaction between K2Cr2O7 and FeSO4 is to be balanced, and the number of moles of Fe2+(aq) produced is to be found.
- The oxidation of MnO2 by alkaline oxidative fusion is to be balanced.
- The molarity of a solution of H2O2 is to be found.
Part 3: Mathematics
Section I
- The function f(x) = x^100 is to be found, and its value at x = 1 is to be found.
- The polynomial P(x) = (x-1)(x-2)(x-3)(x-4)(x-5) + x^2 is to be evaluated at x = 6.
- The equation (x^2-1)^3 - (2x-1)^3 = x^3(x-2)^3 is to be solved.
Section II
- The equation x^2-2x+2 = x is to be solved, and the number of solutions is to be found.
- The equation x^2-1 = x-1 is to be solved, and the number of solutions is to be found.
Section III
- The equation |x^2-1| + |x-1| = 3 is to be solved, and the number of solutions is to be found.
- The equation (2)^(2/x) - 3(2)^(1/x) + 8 = 0 is to be solved, and the number of solutions is to be found.
- The equation (5x+7)(13y+1) = 156x is to be solved, and the value of x and y is to be found.
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Solve a problem involving a point charge and a uniformly charged solid sphere, calculating the speed of the point charge. Practice your physics skills!
