Q76.All x satisfying the inequality (cot−1 x)2 −7 (cot−1 x) + 10 > 0 , lie in the interval : (1) (−∞, cot 5) ∪(cot 4, cot 2) (2) (cot 2, ∞) (3) (−∞, cot 5) ∪(cot 2, ∞) (4) (cot 5, cot 4)
What This Question Tests
This question combines solving a quadratic inequality with the knowledge of the range and monotonic nature of the inverse cotangent function to find the valid interval for x.
Concepts Tested
Formulas Used
Range of cot⁻¹x is (0, π)
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
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.
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
📋 Question Details
- Chapter
- Inverse Trigonometric Functions
- Topic
- Inequalities involving inverse trigonometric functions
- Year
- 2019
- Shift
- 11 Jan Shift 2
- Q Number
- Q76
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 2: Inverse Trigonometric Functions
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