Q5. Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x) = sec−1(2[x] + 1) is : (1) (−∞, −1] ∪[0, ∞) (2) (−∞, −1] ∪[1, ∞) (3) (−∞, ∞) (4) (−∞, ∞) −{0}
What This Question Tests
This question requires knowledge of the domain of the inverse secant function and how to apply it when the argument involves the greatest integer function.
Concepts Tested
Formulas Used
Domain of sec⁻¹(y) is |y| ≥ 1
📚 NCERT Sections This Tests
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
5.18 — What Is Crystal Field Splitting Energy? How Does The Magnitude Of Do Decide
Chemistry Class 11 · Chapter 5
5.18 What is crystal field splitting energy? How does the magnitude of Do decide the actual configuration of d orbitals in a coordination entity?
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Sets Relations Functions
- Topic
- Domain of inverse trigonometric functions
- Year
- 2025
- Shift
- 28 Jan Shift 2
- Q Number
- Q5
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions
More from this Chapter
Q86.Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x −y is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not
Q91.Let f : N →Y be a function defined as f(x) = 4x + 3, where Y = {y ∈N : y = 4x + 3 for some x ∈N}. Show that f is invertible and its inverse is (1) g(y) = 3y+43 (2) g(y) = 4 + y+34 (3) g(y) = y+34 (4) g(y) = y−34 1 ), if x ≠1 x−1 . Then which one of the following is true?
Q73.If A, B and C are three sets such that A ∩B = A ∩C and A ∪B = A ∪C , then (1) A = B (2) A = C (3) B = C (4) A ∩B = ϕ
Q77.For real x, let f(x) = x3 + 5x + 1, then (1) f is one-one but not onto R (2) f is onto R but not one-one (3) f is one-one and onto R (4) f is neither one-one nor onto R