let `f(x)=2+cosx` for all real `x`
Statement 1: For each real `t`, there exists a point `c` in `[t,t+pi]` such that `f'(c)=0` Because
statement 2: `f(t)=f(t+2pi)` for each real `t`
Then
(a) Statement 1 is correct and Statement 2 is also correct; Statement 2 is the correct explanation of statement 1.
(b) Statement 1 is correct and Statement 2 is also correct; Statement 2 is not the correct explanation of statement 1.

let f(x)=2+cosx for all real x Statement 1: For each real t, there exists a pointc in [t,t+pi] such that f'(c)=0 Because statement 2: f(t)=f(t+2pi) for each real t

let f(x)=2+cosx for all real x Statement 1: For each real t, there exists a pointc in [t,t+pi] such that f'(c)=0 Because statement 2: f(t)=f(t+2pi) for each real t

let f(x)=2+cosx for all real x Statement 1: For each real t, there exists a pointc in [t,t+pi] such that f'(c)=0 Because statement 2: f(t)=f(t+2pi) for each real t

let f(x)=2+cosx for all real x. Statement 1: For each real t, there exists a point c in [t,t+pi] such that f '(c)=0 . Statement 2: f(t)=f(t+2pi) for each real t

Statement I For each eal, there exists a pooint c in [t,t+pi] such that f('c) Because Statement II f(t)=f(t+2pi) for each real t .

Let f(x) = {{:(Ax - B,x le -1),(2x^(2) + 3Ax + B,x in (-1, 1]),(4,x gt 1):} Statement I f(x) is continuous at all x if A = (3)/(4), B = - (1)/(4) . Because Statement II Polynomial function is always continuous. (a)Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I (b)Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

Statement I Range of f(x) = x((e^(2x)-e^(-2x))/(e^(2x)+e^(-2x))) + x^(2) + x^(4) is not R. Statement II Range of a continuous evern function cannot be R. (a)Statement I is correct, Statement II is also correct, Statement II is the correct explanation of Statement I (b)Statement I is correct, Statement II is also correct, Statement II is not the correct explanation of Statement I

Statement 1: The greater the decay constant of a radioactive element, the smaller is its half-life. Statement 2: An element, although radioactive, can last longer, if its decay with time is slow. (A) Statement 1 is correct, Statement 2 is correct. But, Statement 2 is not the correct explanation of Statement 1. (B) Statement 1 is correct, Statement 2 is correct. Statement 2 is the correct explanation of Statement 1. (C) Statement 1 is correct, Statement 2 is incorrect. (D) Statement 1 is incorrect, Statement 2 is correct.

Let F(x) be an indefinite integral of sin2x . Statement- 1: The function F(x) satisfies F(x+pi)=F(x) for all real x . Statement- 2: sin2(x+pi)=sin2x for all real x . (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.

Let F(x) be an indefinite integral of sin^(2)x Statement I The function F(x) satisfies F(x+pi)=F(x) for all real x. Because Statement II sin^(2)(x+pi)=sin^(2)x, for all real x. (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.