A student, intending to catch a bus on the bus stand, finds that the bus starts and accelerates away from him/her with uniform acceleration $a=2 m s^{-2}$ when he is 16 m far from the bus. He runs fast enough with a uniform speed so as just to catch the bus. The minimum speed with which the student must run, is
A block of mass 2.0 kg is suspended from the ceiling by a massless string. The string is taut bearing a definite tension when the block is stationary. Suddenly, the string breaks and the block start falling freely. The difference in the tension in string just before and after it breaks is
Having been paddled continuously on a horizontal road, the speed of a bicycle is increasing, the force of friction exerted by the ground on the wheels is
A current $\mathrm{i}=2 \mathrm{amp}$ is established through the long straight conductors which are the arms of a hairpin like structure placed in the plane of paper as shown in the figure. Knowing that a current carrying conductor produces magnetic field represented by the lines of force, analyze the situations described
The correct option is
A certain water pump rated 500 watt lifts water from ground level to a height $h=10$ meter at a rate of $240 \mathrm{ kg} /$ minute . Ignoring the kinetic energy gained by water, the efficiency of water pump is
An electric kettle consists of two filaments $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ of different resistances $R_{1}$ and $R_{2}$ respectively, connected in parallel with separate switches. With a certain fixed amount of water in the kettle pot to prepare the tea, when only $F_{1}$ is switched on, it takes 4 minute to boil the water. When $F_{1}$ and $F_{2}$ both are switched on simultaneously, it takes 3 minute to boil the same amount of water up to the same temperature. The time taken to boil the same amount of water when only $F_{2}$ is switched on (assume that entire heat radiated by filaments is used in boiling the water starting from the same room temperature in each case) is
Two filament bulbs $B_{1}(100 \mathrm{ W}, 220 \mathrm{ V})$ and $B_{2}(60 \mathrm{ W}, 220 \mathrm{ V})$ are connected in series with a 440 V supply voltage source as shown. When switched on, the bulb
The volume of water, spilled out of a completely filled cubic container of side 4 m when the container has been accelerated horizontally with $1.96 \mathrm{ m} / \mathrm{s}^{2}$, is
Two athletes, A and B, run in the ground on an oval track of length L (say) at $8.0 \mathrm{ m} / \mathrm{s}$ and $6.0 \mathrm{ m} / \mathrm{s}$ respectively in the same direction starting from same initial point. How many laps (rounds) will the athlete A complete on the track before overtaking athlete B for the first time?
A wooden solid cylinder (density $0.80 \mathrm{ kg} / \mathrm{m}^{3}$ ), a plastic ball (density $0.90 \mathrm{ kg} / \mathrm{m}^{3}$ ) and a rubber cube (density $0.95 \mathrm{ kg} / \mathrm{m}^{3}$ ) all of equal mass M float partly immersed in a trough containing water (density $1.00 \mathrm{ kg} / \mathrm{m}^{3}$ ) as shown below (ignore any tilt during floatation) You may conclude that
A stone is thrown vertically down into a well, the splash is heard after a time $t_{1}$. If the stone is thrown vertically up with the same speed from the same point, the splash is heard after a time $t_{2}$. The common initial speed ( $u$ ) of the stone in both the cases is given by (the time taken by the splash sound to reach the observer is ignored)
A 80 kg man skating with a speed of $10 \mathrm{ m} / \mathrm{s}$ on a smooth horizontal surface collides with a 20 kg skater at rest, as a result the two cling to each other. What percentage of initial kinetic energy of skaters is lost during the collision? (Ignore any friction)
A beam of light is incident parallel to principal axis on a convex lens (L) of focal length $\mathrm{f}=20 \mathrm{ cm}$. A plane mirror PQ (See figure), inclined at $60^{\circ}$ with the principal axis, is placed a distance ' d ' behind the lens so as to form a real image 1 of the distant object at a distance ' $d$ ' from the optical center of the lens as shown in the figure. The value of ' $d$ ' is
Two cylindrical vessels $V_{1}$ and $V_{2}$ are placed on the same horizontal level. Each vessel contains the same liquid of density $\rho$. Initially the vessels are not connected (valve closed). The height of liquid in vessel $\mathrm{V}_{1}$ is $h_{1}$ and that in vessel $V_{2}$ is $h_{2}$. The diameter of vessels $V_{1}$ and $V_{2}$ are $2 d$ and $d$ respectively. When vessels are interconnected (valve opened) at the bottom, the height h of liquid in each vessel (neglecting the volume of liquid in connecting tube) will be
Two vertical object pins are located on the principal axis of a thin lens at distances of $x_{1}=9.0 \mathrm{ cm}$ and $x_{2}=18.0 \mathrm{ cm}$ from the lens on the two sides of the lens. The images of the two pins formed by the lens are at the same position (overlap). The focal length and the nature of the lens are
A steam boat goes across a lake up to a distance of 1200 meter and comes back. There is a uniform wind blowing with velocity $v$ so as to help the onward journey and to impede the journey back. If the uniform speed of launch of the boat is $5 \mathrm{ ms}^{-1}$ and total time taken by the boat in going and coming back is 500 s , the velocity $v$ of the wind blow is
A trolley of mass 240 kg is initially at rest on the frictionless horizontal straight rails lying in east-west direction. The length of the trolley is 20 meter. A man of mass 60 kg is standing at the eastern end of the trolley. The man starts moving on the trolley from eastern end towards west with velocity $1.0 \mathrm{ m} / \mathrm{s}$ relative to the trolley. Assume the displacement and the velocity in eastward direction to be positive. Choose the correct option.
A homogeneous column of water $\left({ }_{a} \mu_{w}=\frac{4}{3}\right)$ of height 8.0 cm fills the space above a 9.0 cm thick glass $\left({ }_{a} \mu_{g}=\frac{3}{2}\right)$ slab. Observers A and B are in air just outside the top and the bottom whereas the observers C and D are inside just below the top and above the bottom. The total thickness of glass plus water observed by these observers are
In abn experiment performed using a cloud chamber (a device that can show the tracks of subatomic particle) the nature of a particle can be analysed. Under the influence of a strong perpendicular magnetic field $\mathbf{B}$ directed into the plane of the paper, a particle track like the one shown beside as $p q$ was obtained. The track shown may depict
Several resistances of $2 \Omega$ and $3 \Omega$ are used to form a typical electric network as shown in the figure below. A de supply of emf 18 volt and negligible internal resistance has been connected between points $A$ and $B$.
Choose the correct option(s)
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.