Q65.If x, y, z are positive numbers in A. P. and tan−1 x, tan−1 y and tan−1 z are also in A. P., then which of the following is correct. (1) 6x = 3y = 2z (2) 6x = 4y = 3z (3) x = y = z (4) 2x = 3y = 6z
What This Question Tests
This question combines the properties of arithmetic progression with an identity involving inverse trigonometric functions, requiring careful algebraic manipulation to determine the relationship between x, y, and z.
Concepts Tested
Formulas Used
2b = a+c (for AP)
tan⁻¹x + tan⁻¹z = tan⁻¹((x+z)/(1-xz))
📚 NCERT Sections This Tests
6.11 — Dynamics Of Rotational
Physics Class 11 · Chapter 6
6.11 Dynamics of rotational the motion of extended bodies. motion about a fixed axis A large class of problems with extended bodies can be
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.
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.
📋 Question Details
- Chapter
- Sequences & Series
- Topic
- Arithmetic Progression (AP)
- Year
- 2013
- Shift
- 07 Apr
- Q Number
- Q65
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 9: Sequences and Series
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