Which of the following graphs is correct for a particle moving in a circle of radius $r$ at a speed of v (where ' $a$ ' is magnitude of acceleration) ?
Electronic configuration of $\mathrm{Na}^{+}$ is $(2,8)$ and that of sodium element is $(2,8,1)$. Choose the correct statements.
What will be the remainder if the number $7^{2015}$ is divided by 25 ?
Light travels from medium $X$ to medium $Y$ as shown in the adjacent figure.
If $A(p, q+r), B(q, r+p)$ and $C(r, p+q)$ are points then area of triangle $A B C$
A particle moves along the $x$-axis according to the equation $x=6 t^{2}$ where $x$ is displacement in meters and $t$ is time in seconds. Therefore
$\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+\ldots+\frac{3}{9700}=$ ?
The "reaction" force does not cancel the "action" force because
What is the sum of all three digit even numbers divisible by seventeen?
A stone is thrown horizontally and follows the XYZ path as shown in the adjacent figure. The direction of the acceleration of the stone at point Y is
The adjacent sides of a parallelogram are 30 cm and 20 cm . The length of one of the diagonal is 40 cm . What is the length of the other diagonal?
The diagram shows total internal reflection. Which of the following statement is not true?
$(41)^{16}-(14)^{16}$ is a multiple of
The centre of gravity of a body coincides with the center of mass
What will be the remainder if the number $(100000)^{3}$ is divided by 143 ?
A body is in equilibrium under the combined action of several forces then
How many four digit numbers divisible by twenty nine have the sum of their digits 29 ?
A photo frame can be hung on the wall with string in three different ways as shown in the adjacent figure below. The tension in the string is
How many triangles are there in this figure?
If a force acting is conservative only when
$8888888 * 8888888$ this fifteen digit number is divisible by 22 . Find the eighth digit in the number.
A lift is moving up at constant speed. Consider the following statements:
In the adjoining figure segment $A D, B E$ and $C F$ are the altitudes of triangle $A B C$. Find $A D \times B C$ if $\mathrm{AB} \times \mathrm{AC}=409.6, \mathrm{BE} \times \mathrm{CF}=202.5$.
Two toy cars ( $a$ and $b$ ) fixed with spring at front, collide as shown in the figure below. ' $a$ ' has a mass of 200 g and is initially moving to the right. Car 'b' has a mass of 300 g and is initially at rest. When the separation between the cars is minimum,
If $\sqrt{338}-\sqrt{288}=\mathrm{m}$ then $\mathrm{m}=$ ?
A concave spherical mirror has a focal length of 12 cm . if an object is placed 6 cm in front of it, the position of the image is
5901 AB 04 is an eight digit number divisible by 792 . Find $\mathrm{A}+\mathrm{B}=$ ?
The current I in the branch shown in the adjacent figure is
A closed circuit shown in the adjacent figure includes a resistor of resistance $20.0 \Omega$ and battery of emf 3.0 V and internal resistance of $1 \Omega$. The internal resistance of the battery can be considered in series with it. The voltage drop across the resistor of resistance $20 \Omega$ is
A circuit which is used for charging a battery is shown in the adjacent figure. The battery ' $B$ ' has emf 6 V and internal resistance of $2 \Omega$. The charging battery ' A ' has an emf of 9 V and internal resistance of $1 \Omega$. The voltage across the points Pand Q
The circuit shown in adjacent figure consists of an external resistance of $10.0 \Omega$ connected across two batteries of emfs 6.0 V and 9.0 V with internal resistance of $1.0 \Omega$ each. Find the power dissipated by the $10.0 \Omega$ resistor.
What is the smallest natural number when multiplied by 15 and divided by 63 gives remainder 21 ?
The sum of first four terms of an A.P is 56. The sum of last four terms of same A.P is 112. The first term of the A.P is 11. Find the number of terms in that A.P.
If $\mathrm{a}: \mathrm{b}=\mathrm{c}: \mathrm{d}$ then how many of the following statements are true?
Select any three distinct digits. Form a three digit number. Form the another number by reversing the digits. Find the difference of these two numbers. What is the G.C.D of all such differences?
The coefficient of linear thermal expansion of steel is $11 \times 10^{-6} /{ }^{0} \mathrm{C}$. The percentage change in the length of the rod when temperature changes by $70^{\circ} \mathrm{C}$.
There are ten numbers in a certain A.P. The sum of first three terms is 321 . The sum of last three numbers is 405 . Find the sum of all the ten numbers.
A cube of side 4 cm made of wood is floating in water of density $1.00 \mathrm{gcc}^{-1}$. When a small steel ball is embedded in the cube it just immerses in water. If density of wood is $0.76 \mathrm{gcc}^{-1}$, then mass of the steel ball is
How many three digit numbers are divisible by 13 and having middle digit 5 ?
A swing playing with small amplitude can be considered as a simple pendulum. Such a swing is set to oscillate with an amplitude $a$ and frequency $f$. When it is at its mean position, a box of same mass as that of the seat of the swing is dropped on it and its starts moving with the swing. Choose the correct statement
Two parallel chords 96 cm and 28 cm long are on the opposite side of the centre of the circle with radius 50 cm . Find the area of the quadrilateral whose vertices are the end points of the chords.
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.