Sets and Relations
Complex Numbers 33
Sequences and Series
Locus and Straight Line
Measures of Dispersion
Bivariate Frequency Distribution and Chi Square Statistic
Permutations and Combinations
- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Concept of Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Concept of Combinations
- Properties of Combinations
Find a and b if the following function is continuous at the point indicated against them.
`f(x) = x^2 + a` , for x ≥ 0
= `2sqrt(x^2 + 1) + b` , for x < 0 and
f(1) = 2 is continuous at x = 0
Discuss the continuity of the following function at the point(s) or in the interval indicated against them.
`f(x) = (3^x + 3^-x - 2)/x^2` for x ≠ 0.
= (log3)2 for x = 0 at x = 0
For what values of a and b is the function
f(x) = ax + 2b + 18 for x ≤ 0
= x2 + 3a − b for 0 < x ≤ 2
= 8x – 2 for x > 2,
continuous for every x ?
If `f(x) = (24^x - 8^x - 3^x + 1)/(12^x - 4^x - 3^x + 1)` for x ≠ 0
= k, for x = 0
is continuous at x = 0, find k.