1
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1

Let $ f $ be the function defined by

$ f(x)=\left\{\begin{array}{cc} \frac{x^{2}-1}{x^{2}-2|x-1|-1}, & x \neq 1 \\ \frac{1}{2}, & x=1 \end{array}\right. $

A
The function is continuous for all values of $ x $
B
The function is continuous only for $ x > 1 $
C
The function is continuous at $ x=1 $
D
The function is not continuous at $ x=1 $.
2
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
If $ x \sqrt{1+y}+y \sqrt{1+x}=0 $, then $ \frac{d y}{d x}= $
A
$ \frac{x+1}{x} $
B
$ \frac{1}{1+x} $
C
$ \frac{-1}{(1+x)^{2}} $
D
$ \frac{x}{1+x} $
3
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
Consider the function $ f(x)=\frac{|x-1|}{x^{2}} $, then $ f(x) $ is
A
increasing in $ (0,1) \cup(2, \infty) $
B
increasing in $ (-\infty, 0) \cup(0,1) $
C
decreasing in $ (-\infty, 0) \cup(2, \infty) $
D
decreasing in $ (0,1) \cup(2, \infty) $
4
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
There are four numbers of which the first three are in GP and the last three are in AP, whose common difference is 6 . If the first and the last numbers are equal, then two other numbers are
A
$ -2,4 $
B
$ -4,2 $
C
2,6
D
None of the above
EXAM MAP