TRIGONOMETRY-EQUATION-QUIZ-10

MATHEMATICS TRIGONOMETRY EQUATION QUIZ-10

Dear Readers,

As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background. 

Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced. 

Q1. 

•  11
•  12
•  13
•  14

Solution

Q2.In a ∆ABC if a=13,b=14 and c=15, then reciprocals of r₁,r₂and r₃ are in the ratio

•  6∶7∶8
•  6∶8∶7
•  8∶7∶6
•  None of these

Solution

Q3.  If sin⁡θ+cosecθ=2, the value of sin¹⁰θ+cosec¹⁰ θ is

•  2
•  2¹⁰
•  2⁹
•  10

Solution

Q4. The solution of tan⁡2θtan⁡θ=1 then thye value of θ

•  π/3
•  (6n±1)π/6
•  (4n±1)π/6
•  (2n+π)π/6

Solution

Q5.The sum S=sinθ+ sin⁡2θ+...+sin⁡nθ equals

•  sin⁡1/2 (n+1)θ sin⁡nθ/2/sin⁡θ/2
•  cos⁡1/2(n+1)θ sin⁡nθ/2/sin⁡θ/2
•  sin⁡1/2 (n+1)θ cos⁡nθ/2/sin⁡θ/2
•  cos⁡1/2 (n+1)θ cos⁡nθ/2 /sin⁡θ/2

Solution

Q6. If the equation cos⁡(λ sin⁡θ )=sin⁡(λ cos⁡θ) has a solution in [0,2 π], then the smallest positive value of λ is

•  π/√2
•  √2π
•  π/2
•  π/(2√2)

Solution

Q7.If sin⁡3θ=sin⁡θ , how many solutions exist such that 0 < θ< 2π?

•  8
•  9
•  5
•  7

Solution

Q8.The equation (cos⁡p-1 ) x²+(cos⁡p )x+sin⁡p=0, where x is a variable, has real roots. Then, the interval     of p may be any one of the following:
    1. If cosec x=1+cot⁡x,then x=2nπ+3π/4
    2. General value of θ satisfying tan^2⁡θ+sec⁡2θ=1 is nπ+π/2
    Which of the statements given above is/are correct?

•  (0,2 π)
•  (-π,0)
•  (-π/2,π/2)
•  (0,π)

Solution

Q9.If A=sin²θ+cos⁴θ, then for all real values of θ

•  1≤A≤2
•  3/4≤A≤1
•  13/16≤A≤1
•  3/4≤A≤13/16

Solution

Q10. If cotθ+tan⁡θ=m and sec⁡θ-cos⁡θ=n, then which of the following is correct?

•  m(mn²)^1/3-n(nm²)^1/3=1
•  m(m² n)^1/3-n(mn²)^1/3=1
•  n(mn²)^1/3-m(nm²)^1/3=1
•  n(m²n)^1/3-m(mn² )^1/3=1

Solution