Physics: Concepts and Problem Solving

Physics

• A car starting from rest and uniformly accelerating to 180 km/hr in 10s covers 250m in that time.
• When a 12N force is applied to a 3kg block, the block's acceleration becomes 4 m/s².
• The SI unit of work is the Joule.
• Acceleration due to gravity at the center of the Earth is zero.
• A wave with a speed of 960 m/s, where 3600 waves pass in a minute, has a wavelength of 16m.
• The effective resistance between points A and B in the illustrated circuit is 13Ω.
• When a 9Ω wire is broken into two parts with a length ratio of 1:2 and connected in parallel, the net resistance will be 2Ω.
• A concave mirror forms a virtual and magnified image when the object is placed between the principal focus and the pole of the concave mirror.
• An object placed 30 cm from a spherical mirror produces an image half the object's size and has a focal length of -10 cm.
• A magnetic force acts on a proton in the upward direction, determined by the left-hand rule.
• The total work done on a particle always equals the change in its kinetic energy, based on the work-energy theorem.
• A material with a density of 4 g/cm³ in the CGS system will have a density of 40 in a system where the unit of length is 10 cm and the unit of mass is 100 g.
• It is correct to assert that a body can have acceleration even if its velocity is zero momentarily, such as when it reverses direction.
• Pressure exerted by water at the bottom of three vessels (A, B, C) of different shapes is equal if the water height is the same in each.
• The temperature at which the speed of sound in air doubles its value at 0°C (273 K) is 1092 K.
• In a medium, where the refractive index is 3/2, the velocity of light is 2 x 10⁸ m/s.
• The displacement of a person moving along a semicircular path of radius 100m is 200m and the distance traveled by in metres is 314 m.
• The effective resistance between points A and B in the depicted circuit is 2 ohms.
• A wave in air with a velocity of 360 m/s and a frequency of 60 Hz has a wavelength of 6m.
• An object weighing 10kg and moving with a velocity of 4 m/s has a kinetic energy of 80 Joules.
• A 0.2 kg ball thrown upwards with a hand applying force over 0.2 m, and rising 2 m high, experiences a force of 22 N.
• A force F acting on an object varies with distance x, the work done in moving the object from x = 0 to x = 12m is 27 joules
• With two parallel wires carrying current, where one has 10A, the current I in the other wire needed for the magnetic field to be zero at a point is 30 A.
• An object with a height of 2.5 cm placed 1.5f from a concave mirror with focal length f, will have an image length of -5 cm.
• If two identical metal balls having charges of +2Q and -Q exert a force F on each other and are then connected by a wire, the new force will be F/8.

Chemistry

• Silver chloride turning grey in sunlight is an endothermic reaction.
• Adding dilute hydrochloric acid to sodium hydrogen carbonate evolves carbon dioxide gas.
• Cinnabar a compound chemically also called HgS, is chemically an ore of mercury.
• Lemon juice has the lowest pH among the given materials.
• Adding hydrochloric acid in excess to a solution that turned red litmus blue will reverse the color change.
• Trisodium phosphate is not an acidic salt.
• When zinc is added to copper sulphate, zinc sulphate is formed.
• Electrolysis of aqueous NaCl results in Cl₂, H₂, and NaOH.
• Plaster of Paris should be kept in moisture-proof containers because it sets into gypsum when it reacts with water, creating a hard solid.
• A chloride ion (Cl-) has 8 valency electrons.
• Iron (Fe) is an element.
• Oxygen gas reacting with hydrogen gas to produce water is a redox reaction where hydrogen is oxidized and oxygen is reduced.
• Salt can be produced by the reaction between an acid and a metal oxide, a metal, or a mineral oxide.
• Iron corresponds to rust, copper corresponds to Verdigris, potassium corresponds to a soft metal and mercury corresponds to a liquid metal.
• CO₂ and H₂O do not combine on heating to form CH₄ and O₂
• One formula unit of calcium phosphate Ca₃(PO₄)₂ contains 13 atoms.
• Balancing the equation xP₄O₁₀ + yH₂O→zH₃PO₄ indicates that the value of x+y+z is 11.
• A white precipitate forms lime turning it milky, then a water soluble compound forms when carbon dioxide is passed. There are 6 oxygen atoms in total.
• Aluminium and Iron react with steam to form metal oxide and hydrogen.
• Potassium (K) has 1 electron in the N shell.
• Al₂O₃ and ZnO are amphoteric oxides.
• Helium, Neon, and Argon are monoatomic molecules.
• Washing soda (Na₂CO₃.10H₂O) contains Sodium, Hydrogen, Carbon, and Oxygen.

Mathematics

• The greatest power of x is 4 for the polynomial x⁴ – x² + 2.
• If the sum of a two-digit number and its reverse is 187, and the digits differ by 1, the number can be 89 or 98.
• The area of an equilateral triangle with side length 'a' is (√3 / 4)a².
• If a shopkeeper increases his goods by 30% above his cost price and allows 10% discount, he gains 17%.
• If two lines are parallel, one being 2x + 5 and the other 3x - 40. The value of k is 89°.
• A sum of money at simple interest amounts to Rs. 5500 in 1 year and Rs. 6600 in 2 years, then the sum P is Rs. 4400.
• If x + y = 5 and xy + 24 = 0, x³ + y³ = 485.
• If the distance between (2, 2) and (-1, x) is 5, one of the values of x is 2.
• The prime factorization of 96 is 2⁵ × 3.
• The surface area of a sphere with radius r is 4πr².
• sin² 30° + cos² 30° = 1.
• If x² + xy = 9 and xy + y² = 16, then x + y = 5.
• The area of the shaded region among 3 circles is 100π.
• If √3+√2 +2+√3 == (√3-√2), 2+√3 == 2-√3; Sum = 2-√2
• If numerical value of surface area and volume of a cube are equal then the length of largest diagonal of the cube is 6√3
• The smallest number that can be divisible by all the numbers from 1 to 5 is 60.(LCM)
• The arithmetic mean of the observations 9, 12, 16, 22, 37 and 42 is 23.
• The HCF and LCM of the numbers are 168 and 6. Find the other number if one of them is 24, that number is 42
• Three numbers are added to get 54. The largest number is 19.
• If x and y are natural numbers less than 10 and x² = y⁴ then x+y is 6.
• The most balls can be packed in a box with given parameters (dimensions) is 60.
• Sum of the smallest odd prime and the largest even prime is 5
• A square is inscribed in a circle of radius 2 cm then, area of the largest square is 200cm A = d² = 200
• 0.6 x 0.6 x 0.6 - 90 0.012 x 0.2