The value of \(\frac{999 \times 999 \times 999}{(999+999) \times 111 \times 111}\), when simplified, is
When \(4 \frac{1}{2}\) is divided by \(3 \frac{1}{4}\), the result is x. When \(3 \frac{3}{4}\) is divided by \(2 \frac{1}{8}\), the result is y. Then the numerical value of \(13 x+17 y\) is
There are 5 cards numbered as shown. In the figure. The number of ways in which one can choose 3 or less cards which contain only odd numbers is.
ABC is a triangle. The bisector of \(\angle \mathrm{C}\) meets AB at D. The bisectors of \(\angle \mathrm{A}\) and \(\angle \mathrm{BDC}\) meet at E. Then the measure of \(\angle A E D\) is.
Samrud secures 20% of the marks but fails by 30 marks. Saket gets 32% marks which is 42 marks more than the minimum pass marks. The maximum marks in the test would be
The greatest number that divides 25, 73 and 97 to leave the same remainder is
If \(\frac{19}{7}=a+\frac{2}{a+\frac{b}{c}}\) where \(a b c\), are natural numbers, then the numerical value of \((a+b+c)\) is
In the adjoining figure, two equilateral triangles ABP, CDP are placed such that AB is parallel to CD. If \(\mathrm{AB}=3 \mathrm{ cm}, \mathrm{CD}=1 \mathrm{ cm}\), the area (in \(\mathrm{cm}^{2}\) ) of trapezium ABCD is.
Siva found the average of 5 numbers. He got an answer 40 which is wrong because, while listing, instead of writing the number 43 he wrote 48. The correct average must be
In the adjoining figure, ABCD is a square. Also \(\mathrm{BE}=\mathrm{BF}\). Then the value of 2x (in degrees) is
If the numerator and denominator of a fraction are increased by 20% and 30% respectively, then the fraction becomes \(\frac{9}{13}\). If the original fraction is \(\frac{p}{q}\), where \(p\) and \(q\) have no common factors, then \(p+q\) is
Gita divided 360 into 4 parts such that twice the first part, thrice the second part, five times the third part and six times the fourth part are all equal. Then the difference between the third and fourth parts is
In the adjoining figure, the degree measure of \(\angle \mathrm{FAB}\) is.
Consider the following sequence: 1, 3, 5, 7, 9, 7, 5, 3, 1, 3, 5, 7, 9, 7, 5, 3, 1, 3, 5, 7, 9, 7, 5, 3, 1, \(\) The digit in the \(2023{ }^{\text {rd }}\) place is
In the two figures, there is a pattern of numbers which are same. Then the number in the head of the second figure,
Fill in the blanks
There are two cars \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\). The speed of \(\mathrm{C}_{1}\) is 20% less than that of \(\mathrm{C}_{2}\). They travel a certain equal distance. The percentage of time does \(\mathrm{C}_{1}\) need to travel than \(\mathrm{C}_{2}\) is x%. Then x is = (____)
Six equal unit squares are arranged in different shapes as shown in the diagram below:
[] In diagram (1), the perimeter is \(A B C D\), which equals 10 . Similarly the perimeters of the other shapes also are found out. Let the perimeters be denoted by \(P_{1}, P_{2}, P_{3}\) and \(P_{4}\). Then the value of \(\left(P_{1}+P_{4}\right)-\left(P_{2}+P_{3}\right)\) is_.
In a two digit number, the digit in the tens place is twice the digit in the units place. If we swap the places of these two digits, a new two-digit number is formed. The sum of these two numbers is 132. The original number is. (____)
An ant starts from A and wants to go to D. It isallowed to go along the lines and pass a line and a point only once. The number of different routes that it can take to go from A to D is (____).
Three consecutive natural numbers are taken from 1 to 6 . With these three numbers, three digit numbers are formed. The total number of such 3-digit numbers is (____)
In the adjoining figure, \(\angle B A C=20^{\circ}, \angle B C A=10^{\circ}, \angle A C D=90^{\circ}\) and \(\angle C D B=55^{\circ}\). If \(\angle A B D=x^{\mathrm{o}}\), then \(x=\) (____)
The number of 5-digit numbers of the form \(34 a 5 b\) (where \(a, b\) are digits), each of which is divisible by 36 is (____)
The units digit of the sum of all 2-digit numbers is (____)
A natural number is taken. One sixth of this number is subtracted from it. From the resulting number, half of the number is taken and from this number one fifth is taken. If the resulting number is 3 , then the original number taken is (____).
The least number that is added to 2716321 to make it exactly divisible by 3456 is (____)
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
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 […]