Irrational Numbers
) It is not possible to find the exact value of an irrational number. (iii) All rational and irrational numbers can be marked on the number line. Write two possible irrational numbers between 2 and 3..
) It is not possible to find the exact value of an irrational number. (iii) All rational and irrational numbers can be marked on the number line. Write two possible irrational numbers between 2 and 3..Suggested answer:
In (3 + 2x) 9 , we have ..
In (3 + 2x) 9 , we have ..Matrices and Determinants
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determ..
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determ..Step 3:
Simplify the inequality and find the greatest possible value of r satisfy this inequalit..
Simplify the inequality and find the greatest possible value of r satisfy this inequalit..Question 4
Question: Express the following sets in set builder form. (i) Set A consists of the letters p, q, r, s and t (ii) Set C = {1,3,5,7,....} (iii) Set D = {8} Answer: ..
Question: Express the following sets in set builder form. (i) Set A consists of the letters p, q, r, s and t (ii) Set C = {1,3,5,7,....} (iii) Set D = {8} Answer: ..Question 2
Question: For the given sequence, suggest possible next three terms and find the general term. -3, 1, 5,---- Answer: First term = -3, Common difference = 1-(-3) = 4 = 5 - 1 Next three terms are 5 + 4 = 9, ..
Factorisation of Polynomials
You know that any polynomial of the form p(a) can also be written as If the remainder is zero, then p(a) = g(a) x h(a). That is, the polynomial p(a) is a product of two other polynomials g(a) and h(a). For example, 3a + 6a 2 = 3a x (1 + 2a). It may ..
You know that any polynomial of the form p(a) can also be written as If the remainder is zero, then p(a) = g(a) x h(a). That is, the polynomial p(a) is a product of two other polynomials g(a) and h(a). For example, 3a + 6a 2 = 3a x (1 + 2a). It may ..Greatest Terms for Positive Integral Index
Working rules for finding the greatest term: Step 1: In (a + b) n , the constants a and b must be positive. Step 2: Write T r+1 and T r and find the value of T r+1 /T r . Step 3: Simplif..
Examples:
(1) " January has 31 days” is a statement. (2) "Null set is a subset of every set” is a statement. (3) "All girls are studious” is not a statement. (4) "Apoorva is honest” is not a statement. Some sen..
(1) " January has 31 days” is a statement. (2) "Null set is a subset of every set” is a statement. (3) "All girls are studious” is not a statement. (4) "Apoorva is honest” is not a statement. Some sen..Approximation
We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (h..
We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (h.. Result
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