A ball is thrown vertically upwards with a velocity of 20 m/s from the top of a tower of height 25 m. Taking g = 10 m/s², what is the total time taken by the ball to reach the ground?
Physics
Question · Medium
A block of mass 5 kg is placed on a rough horizontal surface with a coefficient of static friction μs = 0.4 and coefficient of kinetic friction μk = 0.3. A horizontal force of 15 N is applied to the block. What is the magnitude of the frictional force acting on the block? (g = 10 m/s²)
Two bodies of masses m₁ = 1 kg and m₂ = 4 kg possess equal kinetic energies. What is the ratio of their linear momenta (p₁ : p₂)?
Question · Easy
An object is placed at a distance of 15 cm in front of a convex lens of focal length 10 cm. What is the position and nature of the image formed?
An electric bulb rated 220 V, 100 W is operated at 110 V. What is the power consumed by the bulb at this lower voltage?
An iron block of mass 2 kg at 100 °C is placed in an insulated container containing 1 kg of water at 20 °C. What is the final equilibrium temperature of the mixture? (Specific heat of iron = 450 J/(kg·K), specific heat of water = 4200 J/(kg·K))
Question · Hard
A sound wave travels in air with a speed of 340 m/s. If the wavelength of the wave is 1.7 cm, what is the frequency of the sound wave, and is it audible to human ears?
A bullet of mass 20 g is fired horizontally from a pistol of mass 2 kg with a velocity of 150 m/s. What is the recoil velocity of the pistol?
If the acceleration due to gravity on the surface of the Earth is g, what will be the acceleration due to gravity at a height equal to the radius of the Earth (R) above the Earth's surface?
An object weighs 10 N in air. When fully immersed in water, it weighs 8 N. What is the relative density of the object?
A stone is dropped from a balloon rising upwards with a velocity of 9.8 m/s. The balloon is at a height of 39.2 m when the stone is dropped. How long does the stone take to reach the ground? (g = 9.8 m/s²)
Three resistors of resistances 3 Ω, 6 Ω, and 9 Ω are connected in parallel. What is the equivalent resistance of the combination?
A convex mirror of focal length f forms an image of a real object. If the object distance is u, which of the following statements about the image is always correct?
A car accelerates from rest at a constant rate of 2 m/s² for 5 seconds, travels at a constant velocity for 10 seconds, and then decelerates to a stop at a constant rate of 1 m/s². What is the total distance covered by the car?
A metal wire of resistance R is stretched to double its original length while keeping its volume constant. What is the new resistance of the stretched wire?
A planet orbits a star in a circular path of radius r with a time period T. If the radius of the orbit is increased to 4r, what will be the new time period of the orbit according to Kepler's third law?
A sound wave of frequency 500 Hz travels from air into water. If the speed of sound in air is 340 m/s and in water is 1500 m/s, what happens to its frequency and wavelength in water?
In a hydraulic lift, the areas of cross-section of the smaller and larger pistons are 5 cm² and 100 cm² respectively. If a force of 50 N is applied to the smaller piston, what is the force exerted on the larger piston?
A spring of force constant k = 200 N/m is compressed by 10 cm. What is the potential energy stored in the spring, and what will be the velocity of a 0.2 kg block released from it (neglecting friction)?
An electron is moving horizontally towards the East. It enters a uniform magnetic field directed vertically downwards. What is the direction of the magnetic force acting on the electron?
A person stands in front of a vertical cliff and claps their hands. They hear the echo after 1.5 seconds. If the speed of sound in air is 340 m/s, what is the distance of the person from the cliff?
A man of mass 60 kg stands on a weighing scale inside a lift. What is the reading on the scale when the lift is accelerating downwards at 2 m/s²? (g = 10 m/s²)
Two point charges Q₁ and Q₂ are separated by a distance r in air. The electrostatic force between them is F. If the distance between them is doubled and the magnitude of each charge is also doubled, what will be the new force between them?
A swimming pool appears to be 3 m deep when viewed from above. If the refractive index of water is 4/3, what is the actual depth of the pool?
Two thin lenses of focal lengths f₁ = +20 cm (convex) and f₂ = -40 cm (concave) are placed in contact. What is the power and effective focal length of the lens combination?
An electric motor of efficiency 80% is used to lift a 100 kg mass vertically through a height of 10 m in 5 seconds. What is the electrical power input to the motor? (g = 10 m/s²)
A magnet is moved rapidly towards a closed coil of wire. What is the nature of the induced current in the coil according to Lenz's law?
A projectile is launched with speed u at an angle θ with the horizontal. If the maximum height attained by the projectile is equal to its horizontal range, what is the value of tan θ?
A car of mass 1000 kg moves at a constant speed of 20 m/s along a circular track of radius 100 m. What is the magnitude of the centripetal force acting on the car?
An electric heater of resistance 50 Ω is connected to a 200 V source. How much heat is generated by the heater in 10 minutes?
The critical angle for a medium-air interface is 30°. What is the refractive index of the medium?
The escape velocity on the surface of the Earth is 11.2 km/s. What will be the escape velocity on a planet whose mass is 8 times and radius is 2 times that of the Earth?
How many water molecules are present in one drop of water weighing 0.06 g? (Given: Avogadro's number Na = 6.022 × 10²³ /mol, molar mass of water = 18 g/mol)
Chemistry
A hydrocarbon contains 80% carbon by mass. What is the empirical formula of the hydrocarbon? (Atomic masses: C = 12, H = 1)
Which of the following electronic configurations represents an element with the highest second ionization energy?
What is the pH of a 1.0 × 10⁻³ M hydrochloric acid (HCl) solution, assuming complete dissociation?
Consider the reaction: MnO₄⁻ + 5Fe²⁺ + 8H⁺ -> Mn²⁺ + 5Fe³⁺ + 4H₂O. Which species acts as the reducing agent in this reaction?
What is the IUPAC name of the compound CH₃-CH(CH₃)-CH₂-CH=CH₂?
Which of the following compounds exhibits tetrahedral molecular geometry?
How many grams of oxygen are required to completely burn 3.0 g of ethane (C₂H₆)? (Atomic masses: C = 12, H = 1, O = 16)
Which of the following compounds contains both ionic and covalent bonds?
Which of the following statements explains why helium has a higher first ionization energy than hydrogen?
What is the concentration of OH⁻ ions in a solution with a pH of 4 at 25 °C?
A gaseous mixture contains equal masses of methane (CH₄) and oxygen (O₂). What is the ratio of their partial pressures in the container?
Which of the following compounds is an isomer of pentane (C₅H₁₂)?
How many sigma (σ) and pi (π) bonds are present in an ethyne (acetylene, C₂H₂) molecule?
Which of the following salts dissolves in water to form an acidic solution?
Which of the following represents a disproportionation reaction?
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