Home
Class 12
MATHS
If f(x)={(([x]-1)/(x-1), x ne 1),(0, x=1...

If f(x)=`{(([x]-1)/(x-1), x ne 1),(0, x=1):}` then f(x) is

A

continuous as well as differentiable at x=1

B

differentiable but not continuous at x= 1

C

continuous but not differentiableat x= 1

D

neither continuous nor differentiable at x=1

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 4

    KVPY PREVIOUS YEAR|Exercise EXERCISE|25 Videos

  • MOCK TEST 6

    KVPY PREVIOUS YEAR|Exercise EXERCISE|23 Videos

Similar Questions

Explore conceptually related problems

Examine the continuity of f(x) = {(|x-1|/(x-1), x ne 1),(0, x =1):} at x = 1

If f(x) = {{:(1/(1+e^(1//x)), x ne 0),(0,x=0):} then f(x) is

If f(x)={((tanx)/(sinx)",", x ne 0),(1",", x =0):} then f(x) is

If f(x)={{:(,(e^(x[x])-1)/(x+[x]),x ne 0),(,1,x=0):} then

If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

If f(x)={((1)/(1+e^(1//x))"," ,x ne 0),(0",", x =0):} then f(x) is :

If f(x)=(x+1)/(x-1) , x ne 1 , then f^(-1)(x) is

If f(x)={{:(,(x-a)^(n)cos ((1)/(x-a)), x ne a),(,0,x=a):} then at x=a, f(x) is

KVPY PREVIOUS YEAR-MOCK TEST 5-EXERCISE
  1. The solution set of the inequality |9^x-3^(x+1) + 15| < 2.9^x - 3^x i...

    Text Solution

    |

  2. Let R be the relation in the set Z of all integers defined by R= {(x,y...

    Text Solution

    |

  3. If the integers m and n are chosen at random between 1 and 100, then t...

    Text Solution

    |

  4. If the circumcenter of an acute-angled triangle lies at the origin ...

    Text Solution

    |

  5. If f(x) = cospi(| x|+[x]), then choose the incorrect option.

    Text Solution

    |

  6. the set of equations lambdax-y+(cos 0) z=0,3x+y+2z=0 (cos 0) x+y+2z...

    Text Solution

    |

  7. The probability that the graph of y=16x^2 +8(a +5)x-7a-5=0, is strictl...

    Text Solution

    |

  8. Let f:R->R and g:R->R be two one-one and onto functions such that they...

    Text Solution

    |

  9. The value of a for which a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1...

    Text Solution

    |

  10. if the equation x^(4)-4x^(3)+ax^(2)+bx+1=0 has four positive roots, th...

    Text Solution

    |

  11. If f(x)={(([x]-1)/(x-1), x ne 1),(0, x=1):} then f(x) is

    Text Solution

    |

  12. Calculate the area bounded by the curve y=x(3-x)^2 the x-axis and the ...

    Text Solution

    |

  13. If x , y, z in R, x + y + z= 4 and x^(2) + y^(2) + z^(2) = 6, then the...

    Text Solution

    |

  14. the minimum value of 3tan^2theta+12cot^2theta is (A) 6 (B) 15 (C) 24 (...

    Text Solution

    |

  15. If the range of the function f(x)=(x-1)/(p-x^2+1) does not contain any...

    Text Solution

    |

  16. The int(tan^-1 alpha)^(cot^-1 alpha) (tanx)/(tanx+cotx)dx alpha in R c...

    Text Solution

    |

  17. Let f(x) =[x]+|1-x|,-1lex< 3,(here [.] denotes greatest integer functi...

    Text Solution

    |

  18. The greatest of the numbers 2^(1/2), 3^(1/3), 4^(1/4), 5^(1/5), 6^(1/6...

    Text Solution

    |

  19. If |vec a + vecb| = |vec a - vecb| , then which one of the following i...

    Text Solution

    |

  20. ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked...

    Text Solution

    |