1
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R.
Which of the following statements is correct?
A
Both f(x) and g(x) are continuous at x = 0
B
f(x) is continuous at x = 0 but g(x) is not continuous at x = 0
C
g(x) is continuous at x = 0 but f(x) is not continuous at x = 0
D
Both f(x) and g(x) are discontinuous at x = 0
2
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R.
Which one of the following statements is correct?
A
$$\mathop {\lim }\limits_{x \to 0} $$ (fog) (x) exists
B
$$\mathop {\lim }\limits_{x \to 0} $$ (gof) (x) exists
C
$$\mathop {\lim }\limits_{x \to {0^ - }} $$ (fog) (x) = $$\mathop {\lim }\limits_{x \to {0^ - }} $$ (gof) (x)
D
$$\mathop {\lim }\limits_{x \to {0^ + }} $$ (fog) (x) = $$\mathop {\lim }\limits_{x \to {0^ + }} $$ (gof) (x)
3
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let f(x) = [x], where [ . ] is the greatest integer function and g(x) = sin x be two real valued functions over R.
Which of the following statements are correct?

I. (fof) (x) = f(x).

II. (gog) (x) = g(x) only when x = 0.

III. (go(fog)) (x) can taken only three values.

Select the correct answer using the code given below.
A
I and II
B
II and III
C
I and III
D
I, II and III
4
NDA 2016 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
Let $$f(x) = \left\{ {\matrix{ { - 2,} & { - 3 \le x \le 0} \cr {x - 2,} & {0 < x \le 3} \cr } } \right.$$ and $$g(x) = f(|x|) + |f(x)|$$.
Which of the following statements is/are correct?

I. g(x) is differentiable at x = 0

II. g(x) is differentiable at x = 2.

Select the correct answer using the code given below.
A
Only I
B
Only II
C
Both I and II
D
Neither I nor II
EXAM MAP