The number of integral values of k for which the equation 7 cosx + 5 sinx = 2k + 1 has a solution is

A
4
B
8
C
12
D
10

Solution:

The range of $7 \cos x + 5 \sin x$ is

$\begin{array}{l} [- \sqrt{7^{2} + 5^{2}}, \sqrt{7^{2} + 5^{2}}] = [- \sqrt{74}, \sqrt{74}] \\ ∴ - \sqrt{74} \leq 2 k + 1 \leq \sqrt{74} \\ k = 0, 1, 2, 3, - 1, - 2, - 3, - 4 \end{array}$

Related content

JEE Main 2023 Question Papers with Solutions

JEE Main 2024 Syllabus

Best Books for JEE Main 2024

JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria

JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria

JEE 2024: Exam Date, Syllabus, Eligibility Criteria

NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3

JEE Crash Course – JEE Crash Course 2023

NEET Crash Course – NEET Crash Course 2023

JEE Advanced Crash Course – JEE Advanced Crash Course 2023