# 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.… Read More
Question 9. Fill in the blanks: (i) ∛(125 × 27) = 3 × … (ii) ∛(8 × …) = 8 (iii) ∛1728 = 4 ×… 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 … 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)… 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) = x3… 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:    Total… 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)… 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: Total… 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) Ways… 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 the… Read More
Question 1. In how many ways can the letters of the word ‘FAILURE’ be arranged so that the consonants may occupy only odd positions? Solution:… 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 =… Read More
Question 1. ∫sin4x cos3x dx Solution:  Let I = ∫ sin4x cos3x dx          -(i) Let sinx = t On differentiating with respect… 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: Question… 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 number… Read More