Statement 1: `int(sinxdx)/x ,(x >0),` cannot be evaluated. Statement 2: Only differentiable functions can be integrated.

Statement -1 : lim_( x to 0) (sin x)/x exists ,. Statement -2 : |x| is differentiable at x=0 Statement -3 : If lim_(x to 0) (tan kx)/(sin 5x) = 3 , then k = 15

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. if both the statements are true and statement 2 is the correct explanation of statement 1. If both the statements are true but statement 2 is not the correct explanation of statement 1. If statement is True and statement2 is false. If statement1 is false and statement2 is true. Statement 1: f(x)=(log)_ex cannot be expressed as the sum of odd and even function. Statement 2 : f(x)=(log)_e x in neither odd nor even function.

Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a

Statement-1 f(x)=(sin x)/(x) lt 1 for 0 lt x lt pi/2 Statement -2 f(x)=(sin x)/(x) is decreasing function on (0,pi//2)

Let a solution y=y(x) of the differential equation (dy)/(dx)cosx+y sin x=1 satisfy y(0)=1 Statement-1: y(x)=sin((pi)/(4)+x) Statement-2: The integrating factor of the given differential equation is sec x.

Statement-1: If ad-bc ne 0 , then f(x)=(ax+b)/(cx+d) cannot attain the value {(a)/(c )} . Statement-2: The domain of the function g(x)=(b-dx)/(cx-a) is R-{(a)/( c)}

Consider the function f(x)=|x-2|+|x-5|,x in R . Statement 1: f'(4)=0 Statement 2: f is continuous in [2, 5] , differentiable in (2, 5) and f(2) = f(5) . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

Statement 1: If e^(xy)+ln(xy)+cos(xy)+5=0, then (dy)/(dx)=-y/x . Statement 2: d/(dx)(xy)=0,y is a function of x implies(dy)/(dx)=-y/x .

Statement 1: Minimum number of points of discontinuity of the function f(x)=(g(x)[2x-1]AAx in (-3,-1) , where [.] denotes the greatest integer function and g(x)=a x^3=x^2+1 is zero. Statement 2: f(x) can be continuous at a point of discontinuity, say x=c_1of[2x-1]ifg(c_1)=0. Statement 1 is True, Statement 2 is True, Statement 2 isa correct explanation for Statement 1. Statement 1 is True, Statement 2 is True, Statement 2 is NOT a correct explanation for statement 1. Statement 1 is True, Statement 2 is False Statement 1 is False, Statement 2 is True.

Statement -1 : y = [x] , ([.] denotes greatest integer function) is not a continuous function . Statement -2 : {x} ({.} denotes fractional fractional function) is discontinuous at integral points. Statement -3 : y = 7^(x) is continuous in its domain.