BITSAT PYQ Continuity and Differentiability - Chapter-wise Questions with Solutions

About Continuity and Differentiability PYQs

Continuity and Differentiability has 18 previous year questions in the Quantrex Academy BITSAT Mathematics bank. The 18 questions in this list come from BITSAT (18), spanning 2010 to 2024. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

2024: 3
2020: 1
2018: 1
2017: 3
2016: 2
2015: 2
2014: 2
2012: 1
2011: 1
2010: 2

BITSAT Continuity and Differentiability PYQs with Solutions

About Continuity and Differentiability PYQs

Questions by year (this list)

Continuity and Differentiability questions with solutions

Let f be the function defined by f(x)=\ array cc (x^2-1)/(x^2-2|x-1|-1), & x ≠ 1 (1)/(2), & x=1 array .

If f(x)=\ array cc (x^2 ( x))/( (1+x)), & x ≠ 0 0, & x=0 array . , then at x=0, f(x) is

f(x)=\ array cc 4 & -∞ < x < - 5 x^2-1 & - 5 ≤ x ≤ 5 4 & 5 ≤ x < ∞ array . If k is the number of points where f(x) is not differentiable then k-2=

Let f be the function defined by f(x)=\ array ll x^ 2 -1 x^ 2 -2|x-1|-1 , & x ≠ 1 1 / 2, & x=1 array .

Let f(x) = \ array ll x^ p sin(1)/(x), x ≠ 0 array cases 0, & x = 0 cases ) then f (x) is continuous but not differentiable at x = 0, if

If f(x) = \ cases e^ x , & x ≤ 0 |1 - x|, & x > 0 cases ), then

The value of f ( 0 ) , so that the function f(x) = 2x - ^ -1 x 2x + ^ -1 x is continuous at each point in its domain, is

Consider the greatest integer function, defined by f ( x ) = [ x ] , 0 ≤ x < 2 . Then

The number of points at which the function f(x)= 1 |x| is discontinuous is:

If f(x)=\ array cl x x (1+x^ 2 ) & , x ≠ 0 0 & , x=0 array . then f(x) is

If a function f(x) is given by f(x)=(x)/(1+x)+(x)/((x+1)(2 x+1))+(x)/((2 x+1)(3 x+1))+…, ∞ , then at x=0, f(x)

Let f: R arrow R be a function such that f(x+y)=f(x)+f(y), ∀ x, y ∈ ℝ If f(x) is differentiable at x=0 , then which one of the following is incorrect?

Let f(x)=\ array c (x-1) (1)/(x-1) if x ≠ 1 0 if x=1 array . Then which one of the following is true?

Let f(x)=\ array l 1- ^ 3 x 3 ^ 2 x , x (π)/(2) array . If f(x) is continuous at x=(π)/(2),(p, q)=

If the function f(x)= cases A x-B, & x ≤ 1 3 x & , 1< x< 2 B x^ 2 -A, & x ≥ 2 cases is continuous at x=2 and 4, then the values of a and b are

The function f(x)=(x-1) |ℓ n x| is at x=1\)

The value of \( | array ccc 1 & 2 & 3 -4 & 3 & 6 2 & -7 & 9 array |\) is

Let \(f(x)= ((e^x-1)^2)/( ((x)/(a)) (1+(x)/(4))) \) for \(x ≠ 0\), and \(f(0)=12\). If \( f \) is continuous at \(x=0\), then the value of \(a\) is equal to

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Continuity and Differentiability in other exams