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In the following, [x] denotes the greate...

In the following, [x] denotes the greatest integer less than or equal to x. Match the functions in Column I with the properties Column II.
`{:(,"Column I",,"Column II"),((A),x|x|,(p),"continuous in (-1, 1)"),((B),sqrt(|x|),(q),"differentiable in (-1, 1)"),((C),x + [x],(r),"strictly increasing (-1, 1)"),((D),|x-1|+|x + 1|,(s),"not differentiable at least at one point in (-1, 1)"):}`

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The correct Answer is:
A, B, C, D
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In the following, [x] denotes the greatest integer less than or equal to x. {:(,"Column I",,"Column II"),(A,x|x|,p,"continuous in (-1, 1)"),(B,sqrt(|x|),q,"differentiable in (-1, 1)"),(C,x + [x],r,"strictly increasing (-1, 1)"),(D,|x-1| + |x + 1|", in"(-1,1),s,"not differentiable atleast at one point in (-1, 1)"):}

In the following, [x] denotes the greatest integer less than or equal to x. {:(,"Column I",,"Column II"),(A.,x|x|,p.,"continuous in (-1, 1)"),(B.,sqrt|x|,q.,"differentiable in (-1, 1) "),(C.,x+[x],r.,"strictly increasing (-1, 1)"),(D.,|x-1|+|x+1| " in (-1,1)",s.,"not differentiable atleast at one point in (-1, 1)"):}

Knowledge Check

  • Let [x] denotes the greatest integer less than or equal to x if x=(sqrt3+1)^5 then [x] is equal to

    A
    50
    B
    76
    C
    51
    D
    152

  • If [ x ] denotes the greatest integer less than or equal to x, then the value of lim_(x to 0) (1-x +[x-1] + [1-x]) is:

    A
    0
    B
    1
    C
    `-1`
    D
    none of these

  • The domain of the function f(x)=cos^(-1)[secx] , where [x] denotes the greatest integer less than or equal to x, is

    A
    `{x:x=(2n+1) pi, n in Z} cup { x : 2 m pi le x lt 2m pi+(pi)/(3), m in Z}`
    B
    `{x:x=2n pi , n in Z} cup { x: 2 m pi lt(x =2n pi) , n in Z} cup { x : 2 m pi lt x lt 2m pi +(pi)/(3), m in Z }`
    C
    `{x:(2n+1) pi, n in Z} cup { x : 2m pi lt x lt 2 m pi +(pi)/(3), m in Z}`
    D
    none of these

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    Let [x] denote the greatest integer less than or equal to x. If x=(sqrt(3)+1)^(5), then [x] is equal to

    If [x] denotes the greatest integer less than or equal to x, then the value of lim_(x rarr1)(1-x+[x-1]+[1-x]) is

    If I=int_(-1)^(1) {[x^(2)]+log((2+x)/(2-x))}dx where [x] denotes the greatest integer less than or equal to x, the I equals

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