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![If the domain of the function f (x) = sec−1 is [α, β) ∪ (γ, δ], then
|3α + 10(β + γ) + 21δ| is equal to __________
JEE M 2023](https://image.slidesharecdn.com/functionanditf-240123165619-33cd8eed/75/these-are-the-notes-for-functions-and-itf-for-class-12-jee-5-2048.jpg)
![For x ∈ (−1 , 1], the number of solutions of the equation sin−1 x = 2 tan−1 x
is equal to
JEE M 2023](https://image.slidesharecdn.com/functionanditf-240123165619-33cd8eed/75/these-are-the-notes-for-functions-and-itf-for-class-12-jee-31-2048.jpg)
these are the notes for functions and itf for class 12 jee
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- 5. If the domainof the function f (x) = sec−1 is [α, β) ∪ (γ, δ], then |3α + 10(β + γ) + 21δ| is equal to __________ JEE M 2023
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- 10. (A) (B) (C) (D) Let f :R – {2, 6} → R be real valued function defined as Then range of f is JEE M 2023
- 12. Functional Equations: f(x +y) = f(x) + f(y) ⇒ f(x) = kx f(x + y) = f(x) . f(y) ⇒ f(x) = ax f(xy) = f(x) + f(y) ⇒ f(x) = k lnx or f(x) =0 f(xy) = f(x) . f(y) ⇒ f(x) = xn 1 2 3 4
- 13. (A) (B) (C) (D) 6 8 7 9 Let f(x) bea function such that f(x + y) = f(x)⋅f(y) for all x, y ∈ N , If f(1) = 3 and = 3279, then the value of n is JEE Main 2023
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- 16. Number of Functions CASETotal onto one-one n(A) = n(B) ba a! a! n(A) > n(B) ba Grouping 0 n(A) < n(B) ba 0 n(A) = a and n(B) = b
- 17. Let E ={1, 2, 3,4} and F = {1, 2}. Then the number of onto functions from E to F is A. 14 B. 16 C. 12 D. 8
- 18. Let x denotethe total number of one - one functions from a set A with 3 elements to set B with 5 elements and y denote the total number of one - one functions from the set A to the set A x B. Then : A. B. C. D. y = 273x 2y = 91x y = 91x 2y = 273x JEE Main 2021
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- 31. For x ∈(−1 , 1], the number of solutions of the equation sin−1 x = 2 tan−1 x is equal to JEE M 2023
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- 34. If cot-1(α) =cot-12 + cot-18 + cot-118 + cot-132 +.......upto 100 terms, then α is: 1.01 1 1.02 1.03 A. B. C. D. JEE M 2021
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