Which of the following sets are equal ?
`A={x:x inN,xlt4},B=(1,1,2,3,3},C={1,3},D={x:x` is an odd natural number `lt5} E={1,2,3},F={1,1,3}`

Which o the following sets are equal? A={x : x in N ,\ x<3},\ B={1,2},\ C={3, 11} D={x : x in N ,\ xi s\ od d ,\ x<5},\ E={1,2,1,1},\ F={1,1,3}

Which of the following pairs of sets are disjoint(i) {1, 2, 3, 4} and {x : x is a natural number and 4 lt=xlt= 6 }(ii) {a , e , i , o, u } and { c , d , e , f} (iii) {x : x is an even integer } and {x : x is an odd integer}

Which of the following statements is true for the function f(x)={sqrt(x),xgeq1x^3,0lt=xlt=1(x^3)/3-4x ,x 0

The number of solutions of x_1 + x_2 + x_3 = 51 (X1, X2, X3 being odd natural numbers) is

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

The value of b for which the function f(x)={5x-4,0xlt=1 , 4x^2+3b x ,1< x <2 and continuous at x=1

Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f\'\'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] If the function e^(-x)f(x) assumes its minimum in the interval [0,1] at x=1/4 , which of the following is true? (A) f\'(x) lt f(x), 1/4 lt x lt 3/4 (B) f\'(x) gt f(x), 0 lt x lt 1/4 (C) f\'(x) lt f(x), 0 lt x lt 1/4 (D) f\'(x) lt f(x), 3/4 lt x lt 1

Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies f'(x)-2f\'(x)+f(x) ge e^x, x in [0,1] If the function e^(-x)f(x) assumes its minimum in the interval [0,1] at x=1/4 , which of the following is true? (A) f\'(x) lt f(x), 1/4 lt x lt 3/4 (B) f\'(x) gt f(x), 0 lt x lt 1/4 (C) f\'(x) lt f(x), 0 lt x lt 1/4 (D) f\'(x) lt f(x), 3/4 lt x lt 1

Find the complete set of values of alpha for which the function f(x) = {(x+1,xlt1 alpha , x =1 , is strictly increasing x=1 x^(2)-x+3,xlt1

The range of the function f(x)=|x-1|+|x-2|,-1lt=xlt=3, is [1,3] (b) [1,5] (c) [3,5] (d) none of these