Continuity of Special Functions

JEE Main Mathematics · Continuity and Differentiability · 12 questions, latest first

• The number of points in the interval [2,4], at which the function f(x)=[x^2-x-1/2], where [•] denotes the greatest integer…20262 April, Shift 2 · Q25
• Let [·] denote the greatest integer function, and let f(x)= min {√2 x, x^2}. Let S={x ∈(-2,2).: the function g(x)=|x|[x^2] is…202622 January, Shift 2 · Q16
• The number of points of discontinuity of the function f(x)=[x^2/2]-[√x], x ∈[0,4], where [·] denotes the greatest integer…20257 April, Shift 1 · Q25
• Let f(x)= {3 x, x<0; min {1+x+[x], x+2[x]}, 0 ≤ x ≤ 2; 5, x>2,} where [.] denotes greatest integer function. If α and β are the…202528 January, Shift 1 · Q25
• Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function…202524 January, Shift 2 · Q17
• Let [t] denote the greatest integer less than or equal to t. Let f:[0, ∞) → R be a function defined by f(x)=[x/2+3]-[√x]. Let S…20246 April, Shift 2 · Q24
• Let f:[-1,2] → R be given by f(x)=2 x^2+x+[x^2]-[x], where [t] denotes the greatest integer less than or equal to t. The number…20245 April, Shift 2 · Q10
• Let [x] denote the greatest integer function and f(x)= max {1+x+[x], 2+x, x+2[x]}, 0 ≤ x ≤ 2. Let m be the number of points in…202315 April, Shift 1 · Q9
• Let [x] be the greatest integer ≤ x. Then the number of points in the interval (-2,1), where the function f(x)=|[x]|+√(x-[x]) is…202312 April, Shift 1 · Q25
• Let f(x)=[x^2-x]+|-x+[x]|, where x ∈ R and [t] denotes the greatest integer less than or equal to t. Then, f is202311 April, Shift 1 · Q7
• Let f:(-2,2) → R be defined by f(x)= {x[x],-2<x<0; (x-1)[x], 0 ≤ x<2} where [x] denotes the greatest integer function. If m and n…202310 April, Shift 1 · Q27
• Let a ∈ Z and [t] be the greatest integer ≤ t. Then the number of points, where the function f(x)=[a+13 sin x], x ∈(0, π) is not…20236 April, Shift 1 · Q25