# Category Archives: School Learning

Theorem Statement: There is one and only one circle passing through three given non-collinear points. Required Diagram: Given: Three non-collinear points P, Q, and R.â€¦ Read More
Question 9. Fill in the blanks: (i) âˆ›(125 Ã— 27) = 3 Ã— â€¦ (ii) âˆ›(8 Ã— â€¦) = 8 (iii) âˆ›1728 = 4 Ã—â€¦ Read More
Question 1. Find the cube roots of each of the following integers: (i) -125  (ii) -5832 (iii) -2744000  (iv) -753571 (v) -32768 Solution: (i) -125 â€¦ Read More
Question 1. Find the shortest distance between the lines  and . Solution:  Let us consider According to the equations line P1 passes through the point P(2, 5, 0)â€¦ Read More
Question 1. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) p(x) = x3â€¦ Read More
Question 15.  There are three copies each of 4 different books. In how many ways can they be arranged in a shelf? Solution:    Totalâ€¦ Read More
Question 1. Find the number of words formed by permuting all the letters of the following words : (i) INDEPENDENCE (ii) INTERMEDIATE (iii) ARRANGE (iv)â€¦ Read More
Question 33. How many four digit natural numbers not exceeding 4321 can be formed with the digits 1,2,3,4, if the digits can repeat? Solution: Totalâ€¦ Read More
Question 17. How many three-digit numbers are there? Solution: Ways of selecting 100th place = 9P1 = 9 (Selecting from all digits except 0) Waysâ€¦ Read More
Question 1.  In a class, there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent theâ€¦ Read More
Question 1. In how many ways can the letters of the word â€˜FAILUREâ€™ be arranged so that the consonants may occupy only odd positions? Solution:â€¦ Read More
Question 1.  Find the volume of a cylinder whose (i) r = 3.5 cm, h = 40 cm (ii) r = 2.8 m, h =â€¦ Read More
Question 1. âˆ«sin4x cos3x dx Solution:  Let I = âˆ« sin4x cos3x dx          -(i) Let sinx = t On differentiating with respectâ€¦ Read More
Question 1. Evaluate  Solution: Question 2. Evaluate  Solution: Question 3. Evaluate  Solution: Question 4. Evaluate  Solution:  Question 5. Evaluate  Solution: Question 6. Evaluate  Solution: Questionâ€¦ Read More
Question 1: What is the least number of planes that can enclose a solid? What is the name of the solid? Solution: The least numberâ€¦ Read More