Two wave pulses I and II have the same wavelength. They are travelling in the directions as shown by the single headed arrows. The resultant sketch of the two wave pulses at some instant of time when $P$ coincides with $R$ is ____ .
The equivalent resistance of two resistances in series is ' $S$ '. These resistances are now joined in parallel. The parallel equivalent resistance is ' $P$ '. If $S =n P$. Then the minimum possible value of $n$ is
A copper disc of radius $a_{0}$ has a hole of radius $b_{0}$ at the centre, at $0^{\circ} \mathrm{C}$. The disc is now heated and maintained at $200^{\circ} \mathrm{C}$. The new radii of disc and hole are $a_{t}$ and $b_{t}$ respectively. For the heated disc it can be concluded that
A liquid, whose density doesn't change during the motion, is flowing steadily through a pipe of varying cross sectional area as shown in the given figure. If $a_{1}, a_{2}$ are the cross sectional areas, $v_{1}, v_{2}$ are the values of velocities (or speeds) at $L$ and $H$ respectively, then the correct relation between $a_{1}, a_{2}$ and $v_{1}, v_{2}$ is
A common hydrometer has a uniform scale and its stem is graduated downwards from 0 to 20 . While floating in water, it reads 0 and while floating in a liquid of density $1.40 \mathrm{ g} / \mathrm{cm}^{3}$, it reads 20 . Then the density of the liquid in which it will read 10 is ____ .
A boy throws a steel ball straight up. Consider the motion of the ball only after it has left the boy's hand but before it touches the ground and assume that forces exerted by the air are negligible. For these conditions, the force(s) acting on the ball is (are)
In bringing a $\alpha$-particle towards another $\alpha$-particle, the electrostatic potential energy of the system ____ .
An empty office chair is at rest on a floor. Consider the following forces
I. A downward force of gravity
II. An upward force exerted by the floor,
III. A net downward force exerted by the air
Then, which of the force(s) is (are) acting on the office chair?
If $x, v$ and $t$ represent displacement (m), velocity (m/s) and time (s) respectively for a certain particle then which pair of the following figures can be best correlated to each other?
In rural areas, an indigenous way of keeping kitchen materials cool is to put them in a box and wrap the box with wet blanket; the blanket is kept wet as tap is allowed to drip in to its corner Choose the correct statement:
An electron and $\alpha$-particle enter a region of uniform magnetic field (of induction $B$ ) with equal velocities. The direction of $B$ is perpendicular and into the plane of the paper. Then qualitatively identify the direction of paths of electron and the $\alpha$-particle.
A concave mirror of radius of curvature 1 m is placed at the bottom of a water tank. The mirror forms an image of the sun when it is directly overhead. If the depth of water in the tank is 80 cm , then the distance of the image formed is ____ . (refractive index of water is 1.33 )
As shown in adjacent figure, two plane mirrors $M_{1}$ and $M_{2}$ are inclined to each other at an angle $70^{\circ}$ (angle $M_{1} O M_{2}$ ). Incident ray $A B$ makes an angle of incidence $\theta$ on $M_{1}$. This ray after reflection at $B$ on $M_{1}$ and further at $C$ on $M_{2}$ travels along the direction $C D$, such that path $C D$ is parallel to $M_{1}$. Then angle $\theta$ is ____ -
For the same angle of incidence, the angle of refraction in three different media $A, B, C$ are $15^{\circ}$, $25^{\circ}$ and $35^{\circ}$ respectively. Then which statement is correct? $\left(\mu_{A}\right.$ is refractive index of $\left.A\right)$
A large truck collides head-on with a small compact car. During the collision
A magnet is placed between two coils $A B$ and $C D$ as shown. It is being moved in the direction as shown by the arrow, then which of the following statements is correct?
The ability of eye to focus both near and distant objects, by adjusting its focal length, is called
The take-off speed of Airbus A340 is $288 \mathrm{ km} / \mathrm{hr}$. From the taxi track it comes to the main runway and waits for a while for the final clearance from Air Traffic Control. The aircraft then achieves this speed within 50 seconds, Neglecting the effect of the wind direction and friction, what should be the minimum length of main runway decided by civil engineers for this aircraft for a take-off?
In the adjacent circuit what is the current flowing from $N$ to $K$ ?
The positions of two blocks at successive 0.20 second time intervals are represented by the numbered squares in the figure below. The blocks are moving towards right.
The accelerations of the blocks are related as follows :
If $x^{2}-3 x+2$ is a factor of $x^{4}-p x^{2}+q$, then $p, q$ are
If the roots of the equation $\frac{x^{2}-b x}{a x-c}=\frac{m-1}{m+1}$ are equal and of opposite signs, then the value of $m$ is -.
If $p+q+r=2, p^{2}+q^{2}+r^{2}=30$ and $p q r=10$, the value of $(1-p)(1-q)(1-r)$ will be
What is the radius of the circumcircle of a triangle whose sides are $30 \mathrm{ cm}, 36 \mathrm{ cm}$ and 30 cm ?
If $A B C D$ is a cyclic quadrilateral, $A B=204, B C=$ 104, $C D=195, D A=85$ and $B D=221$, then $A C=$
By which smallest number we should divide 198396198 to get a perfect square?
If $(a+b+c+d)=4$, then $\frac{1}{(1-a)(1-b)(1-c)}+\frac{1}{(1-b)(1-c)(1-d)}+$ $\frac{1}{(1-c)(1-d)(1-a)}+\frac{1}{(1-d)(1-a)(1-b)}=$ ____
In triangle $A B C$, segment $A D$, segment $B E$ and segment $C F$ are altitudes. If $A B \times A C=172.8 \mathrm{ cm}^{2}$ and $B E \times C F=108.3 \mathrm{ cm}^{2}$ then $A D \times B C=$ ____
$1 \frac{1}{2}+1 \frac{1}{6}+1 \frac{1}{12}+1 \frac{1}{20}+1 \frac{1}{30}+\ldots \ldots .+1 \frac{1}{380}=$ ____
If $x=(\sqrt{21}-\sqrt{20})$ and $y=(\sqrt{18}-\sqrt{17})$, then
If $\left(x+\frac{1}{x}\right)=5$, then $\left(x^{3}+\frac{1}{x^{3}}\right)-5\left(x^{2}+\frac{1}{x^{2}}\right)+ \left(x+\frac{1}{x}\right)=$ ____ .
The mean of the following frequency distribution is ____ .
| __TABULAR__:W1siQ2xhc3MiXSxbImludGVydmFsIl1d | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Frequency | 4 | 6 | 8 | 10 | 12 |
On seventy first 'Independence Day' there was Tuesday. After how many years there will be Tuesday on 'Independence Day'?
If $x^{2}+x y+x z=135, y^{2}+y z+x y=351$ and $x^{2}+x z+y z=243$, then $x^{2}+y^{2}+z^{2}=$ ____
What will be the remainder if the number $(7)^{2017}$ is divided by 25 ?
The sum of two numbers is 13 and the sum of their cubes is 1066 . Find the product of those two numbers.
Diagonals of a quadrilateral bisect each other. Therefore the quadrilateral must be a ____
A train is running at a speed of $54 \mathrm{ km} / \mathrm{hr}$. It is not stopping at a certain station. It crosses the person showing green flag in 20 seconds and crosses the platform in 36 seconds. What is the length of the train?
What is the sum of all odd numbers between 500 and 600 ?
How many four digit numbers are there such that when they are divided by 101, they have 99 as remainder?
An open vessel contains air at $27^{\circ} \mathrm{C}$. The vessel is heated till two-fifth of the air in it has been expelled. Assuming the volume of the vessel remains constant, find the temperature to which the vessel has to be heated?
Rajiv, Nikhil, Shubha and Nilima wanted to establish a relationship between loss in weight of a solid with weight of water displaced by immersing it in tap water and sea water. After performing their experiment, they noted their observations for the same solid as follows: Rajiv : Loss of weight of solid is more in tap water. Nikhil : Loss of weight of solid is more in sea water. Shubha : Loss of weight of solid is equal in the tap water and the sea water. Nilima : Loss of weight of solid may be more in tap water or sea water, depending upon how deeply it is immersed. Identify the correct observation.
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.