Finding Unknowns When the Limit Is Given

JEE Main Mathematics · Limits · 10 questions, latest first

• The product of all possible values of α, for which lim_x → 0((1- cos (α x) cos ((α+1) x) cos ((α+2) x))/(sin^2((α+1) x)))=2, is:20265 April, Shift 1 · Q17
• If lim_x → 2 (sin (x^3-5 x^2+a x+b))/((√(x-1)-1) log_e(x-1))=m, then a+b+m is equal to:20262 April, Shift 1 · Q16
• If lim_x → 0 (e^(a-1) x+2 cos b x+(c-2) e^-x)/(x cos x- log_e(1+x))=2, then a^2+b^2+c^2 is equal to:202622 January, Shift 2 · Q17
• If lim_x → 1^+ ((x-1)(6+λ cos (x-1))+μ sin (1-x))/((x-1)^3)=-1, where λ, μ ∈ R, then λ+μ is equal to20254 April, Shift 1 · Q17
• If lim_x → 0 (cos (2 x)+a cos (4 x)-b)/x^4 is finite, then (a+b) is equal to:20252 April, Shift 2 · Q17
• For α, β, γ ∈ R, if lim_x → 0 (x^2 sin α x+(γ-1) e^x^2)/(sin 2 x-β x)=3, then β+γ-α is equal to:20252 April, Shift 1 · Q7
• If the function f(x)=(sin 3 x+α sin x-β cos 3 x)/x^3, x ∈ R, is continuous at x=0, then f(0) is equal to:20245 April, Shift 1 · Q7
• If lim_x → 0 (a x^2 e^x-b log_e(1+x)+c x e^-x)/(x^2 sin x)=1, then 16(a^2+b^2+c^2) is equal to ____.202431 January, Shift 2 · Q25
• If lim_x → 0 (3+α sin x+β cos x+ log_e(1-x))/(3 tan^2 x)=1/3, then 2 α-β is equal to:202427 January, Shift 2 · Q8
• If lim_x → 0 (e^a x- cos (b x)-(c x e^-c x)/2)/(1- cos (2 x))=17, then 5 a^2+b^2 is equal to202313 April, Shift 2 · Q9