Number of solutions in an interval

JEE Main Mathematics · Trigonometric Equations · 13 questions, latest first

• If S={θ ∈[-π, π]: cos θ cos (5 θ)/2= cos 7 θ cos (7 θ)/2}, then n(S) is equal to ____.20265 April, Shift 2 · Q23
• Let S={x ∈[-π, π]: sin x( sin x+ cos x)=a, a ∈ Z}. Then n(S) is equal to:20262 April, Shift 1 · Q12
• Number of solutions of √3 cos 2 θ+8 cos θ+3 √3=0, θ ∈[-3 π, 2 π] is:202623 January, Shift 1 · Q11
• The number of solutions of the equation cos 2 θ cos (θ)/2+ cos (5 θ)/2=2 cos^3 (5 θ)/2 in [-(π)/2, (π)/2] is:20257 April, Shift 2 · Q14
• The number of solutions of the equation (4-√3) sin x-2 √3 cos^2 x=-4/(1+√3), x ∈[-2 π, (5 π)/2] is20253 April, Shift 2 · Q13
• The number of solutions of the equation 2 x+3 tan x=π, x ∈[-2 π, 2 π]-{ ± (π)/2, ± (3 π)/2} is:20253 April, Shift 1 · Q10
• If θ ∈[-(7 π)/6, (4 π)/3], then the number of solutions of √3 cosec^2 θ-2(√3-1) cosec θ-4=0, is equal to:20252 April, Shift 2 · Q13
• If θ ∈[-2 π, 2 π], then the number of solutions of 2 √2 cos^2 θ+(2-√6) cos θ-√3=0, is equal to:20252 April, Shift 1 · Q3
• The number of solutions of sin^2 x+(2+2 x-x^2) sin x-3(x-1)^2=0, where -π ≤ x ≤ π, is ____.20245 April, Shift 2 · Q21
• If 2 sin^3 x+ sin 2 x cos x+4 sin x-4=0 has exactly 3 solutions in the interval [0, (n π)/2], n ∈ N, then the roots of the…202430 January, Shift 1 · Q20
• If 2 tan^2 θ-5 sec θ=1 has exactly 7 solutions in the interval [0, (n π)/2], for the least value of n ε N, then Σ_k=1^n k/(2^k)…202427 January, Shift 2 · Q7
• The number of elements in the set S={θ ∈[0,2 π]: 3 cos^4 θ-5 cos^2 θ-2 sin^6 θ+2=0} is202311 April, Shift 1 · Q16
• If m and n respectively are the numbers of positive and negative values of θ in the interval [-π, π] that satisfy the equation…202325 January, Shift 2 · Q90