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Previous year question hub

Limits Continuity And Differentiability - Calculus - Mathematics Previous Year Questions

Practice Limits Continuity And Differentiability - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

172Papers
25Years
278Questions
1Topics

Limits Continuity And Differentiability question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Limits Continuity And Differentiability. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 222 79.9%
Hard 42 15.1%
Easy 14 5%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 216 77.7%
Numerical Answer Type (NAT) 62 22.3%

Subject weightage

Top subjects by unique question coverage.

Mathematics
278 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
278 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Limits Continuity And Differentiability
278 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Main 2026 (Online) 5th April Evening Shift
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JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT
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JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT
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JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT
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JEE Main 2026 (Online) 2nd April Evening Shift
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JEE Main 2026 (Online) 2nd April Morning Shift
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JEE Main 2026 (Online) 4th April Evening Shift
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JEE Main 2026 (Online) 4th April Morning Shift
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JEE Main 2026 (Online) 5th April Morning Shift
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JEE Main 2026 (Online) 6th April Evening Shift
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JEE Main 2026 (Online) 6th April Morning Shift
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JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT
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JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT
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JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT
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JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT
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JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT
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JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT
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JEE Main 2021 (Online) 26th February Evening Shift
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JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT
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JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT
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JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT
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JEE MAIN 2018 OFFLINE
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JEE MAIN 2016 OFFLINE
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JEE MAIN 2015 OFFLINE
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8 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Main 2026 (Online) 2nd April Evening Shift20261View paper
JEE Main 2026 (Online) 2nd April Morning Shift20261View paper
JEE Main 2026 (Online) 4th April Evening Shift20261View paper
JEE Main 2026 (Online) 4th April Morning Shift20261View paper
JEE Main 2026 (Online) 5th April Evening Shift20262View paper
JEE Main 2026 (Online) 5th April Morning Shift20261View paper
JEE Main 2026 (Online) 6th April Evening Shift20261View paper
JEE Main 2026 (Online) 6th April Morning Shift20261View paper
JEE Main 2026 (Online) 8th April Evening Shift20261View paper
JEE MAIN 2026 ONLINE 21ST JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 22ND JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 23RD JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 23RD JANUARY MORNING SHIFT20261View paper
JEE MAIN 2026 ONLINE 24TH JANUARY EVENING SHIFT20262View paper
JEE MAIN 2026 ONLINE 24TH JANUARY MORNING SHIFT20262View paper
JEE MAIN 2026 ONLINE 28TH JANUARY EVENING SHIFT20261View paper
JEE MAIN 2026 ONLINE 28TH JANUARY MORNING SHIFT20261View paper
JEE MAIN 2025 ONLINE 22ND JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 22ND JANUARY MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 23RD JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 24TH JANUARY MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 28TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 28TH JANUARY MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 29TH JANUARY MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 2ND APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 2ND APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 3RD APRIL MORNING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2025 ONLINE 4TH APRIL MORNING SHIFT20253View paper
JEE MAIN 2025 ONLINE 7TH APRIL EVENING SHIFT20252View paper
JEE MAIN 2025 ONLINE 7TH APRIL MORNING SHIFT20252View paper
JEE MAIN 2025 ONLINE 8TH APRIL EVENING SHIFT20251View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 1ST FEBRUARY MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 27TH JANUARY EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 29TH JANUARY EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 30TH JANUARY MORNING SHIFT20241View paper
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JEE MAIN 2024 ONLINE 31ST JANUARY MORNING SHIFT20242View paper
JEE MAIN 2024 ONLINE 4TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 4TH APRIL MORNING SHIFT20242View paper
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JEE MAIN 2024 ONLINE 8TH APRIL EVENING SHIFT20242View paper
JEE MAIN 2024 ONLINE 8TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL EVENING SHIFT20241View paper
JEE MAIN 2024 ONLINE 9TH APRIL MORNING SHIFT20241View paper
JEE MAIN 2023 ONLINE 10TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 11TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 12TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 13TH APRIL EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 15TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 24TH JANUARY MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 25TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 25TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 29TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 30TH JANUARY MORNING SHIFT20231View paper
JEE MAIN 2023 ONLINE 31ST JANUARY EVENING SHIFT20231View paper
JEE MAIN 2023 ONLINE 6TH APRIL MORNING SHIFT20232View paper
JEE MAIN 2023 ONLINE 8TH APRIL EVENING SHIFT20232View paper
JEE MAIN 2023 ONLINE 8TH APRIL MORNING SHIFT20231View paper
JEE MAIN 2022 ONLINE 24TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 24TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 25TH JULY EVENING SHIFT20221View paper
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JEE MAIN 2022 ONLINE 25TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 26TH JULY MORNING SHIFT20224View paper
JEE MAIN 2022 ONLINE 26TH JUNE EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 26TH JUNE MORNING SHIFT20222View paper
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JEE MAIN 2022 ONLINE 27TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 27TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 28TH JULY MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 28TH JUNE EVENING SHIFT20223View paper
JEE MAIN 2022 ONLINE 28TH JUNE MORNING SHIFT20221View paper
JEE MAIN 2022 ONLINE 29TH JULY EVENING SHIFT20222View paper
JEE MAIN 2022 ONLINE 29TH JULY MORNING SHIFT20222View paper
JEE MAIN 2022 ONLINE 29TH JUNE EVENING SHIFT20221View paper
JEE MAIN 2022 ONLINE 30TH JUNE MORNING SHIFT20221View paper
JEE Main 2021 (Online) 24th February Morning Shift20212View paper
JEE Main 2021 (Online) 25th February Evening Shift20212View paper
JEE Main 2021 (Online) 25th February Morning Shift20212View paper
JEE Main 2021 (Online) 26th February Evening Shift20213View paper
JEE Main 2021 (Online) 26th February Morning Shift20211View paper
JEE MAIN 2021 ONLINE 16TH MARCH EVENING SHIFT20213View paper
JEE MAIN 2021 ONLINE 16TH MARCH MORNING SHIFT20213View paper
JEE MAIN 2021 ONLINE 17TH MARCH EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 17TH MARCH MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 18TH MARCH EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 18TH MARCH MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 1ST SEPTEMBER EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 20TH JULY EVENING SHIFT20213View paper
JEE MAIN 2021 ONLINE 20TH JULY MORNING SHIFT20212View paper
JEE MAIN 2021 ONLINE 22TH JULY EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 25TH JULY EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 25TH JULY MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 26TH AUGUST EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 26TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST EVENING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH AUGUST MORNING SHIFT20211View paper
JEE MAIN 2021 ONLINE 27TH JULY EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 27TH JULY MORNING SHIFT20213View paper
JEE MAIN 2021 ONLINE 31ST AUGUST EVENING SHIFT20212View paper
JEE MAIN 2021 ONLINE 31ST AUGUST MORNING SHIFT20213View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 2ND SEPTEMBER MORNING SLOT20202View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 3RD SEPTEMBER MORNING SLOT20202View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 4TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 5TH SEPTEMBER MORNING SLOT20203View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER EVENING SLOT20202View paper
JEE MAIN 2020 ONLINE 6TH SEPTEMBER MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 7TH JANUARY MORNING SLOT20202View paper
JEE MAIN 2020 ONLINE 8TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 8TH JANUARY MORNING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY EVENING SLOT20201View paper
JEE MAIN 2020 ONLINE 9TH JANUARY MORNING SLOT20202View paper
JEE MAIN 2019 ONLINE 10TH APRIL EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH APRIL MORNING SLOT20193View paper
JEE MAIN 2019 ONLINE 10TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 10TH JANUARY MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 11TH JANUARY EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 11TH JANUARY MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 12TH JANUARY EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 12TH JANUARY MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 8TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 8TH APRIL MORNING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH APRIL EVENING SLOT20192View paper
JEE MAIN 2019 ONLINE 9TH APRIL MORNING SLOT20192View paper
JEE MAIN 2019 ONLINE 9TH JANUARY EVENING SLOT20191View paper
JEE MAIN 2019 ONLINE 9TH JANUARY MORNING SLOT20192View paper
JEE MAIN 2018 OFFLINE20182View paper
JEE MAIN 2018 ONLINE 15TH APRIL EVENING SLOT20183View paper
JEE MAIN 2018 ONLINE 15TH APRIL MORNING SLOT20181View paper
JEE MAIN 2018 ONLINE 16TH APRIL MORNING SLOT20182View paper
JEE MAIN 2017 OFFLINE20171View paper
JEE MAIN 2017 ONLINE 8TH APRIL MORNING SLOT20171View paper
JEE MAIN 2017 ONLINE 9TH APRIL MORNING SLOT20171View paper
JEE MAIN 2016 OFFLINE20162View paper
JEE MAIN 2016 ONLINE 10TH APRIL MORNING SLOT20162View paper
JEE MAIN 2016 ONLINE 9TH APRIL MORNING SLOT20162View paper
JEE MAIN 2015 OFFLINE20152View paper
JEE MAIN 2014 OFFLINE20141View paper
JEE MAIN 2013 OFFLINE20131View paper
AIEEE 201220122View paper
AIEEE 201120112View paper
AIEEE 201020101View paper
AIEEE 200920091View paper
AIEEE 200820081View paper
AIEEE 200720072View paper
AIEEE 200620061View paper
AIEEE 200520053View paper
AIEEE 200420042View paper
AIEEE 200320034View paper
AIEEE 200220028View paper

All Limits Continuity And Differentiability previous year questions

Practice every matching question in batches of 20, with every available option.

1
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
If f(x + y) = f(x).f(y) \(\forall\) x, y and f(5) = 2, f'(0) = 3, then
f'(5) is
A
0
B
1
C
6
D
2
Open complete paper
2
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
\(\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - \cos 2x} } \over {\sqrt 2 x}}\) is
A
\(1\)
B
\(-1\)
C
zero
D
does not exist
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3
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
\(f\) is defined in \(\left[ { - 5,5} \right]\) as

\(f\left( x \right) = x\) if \(x\) is rational

\(\,\,\,\,\,\,\,\,\,\,\,\,\,\) \(= - x\) if \(x\) is irrational. Then
A
\(f(x)\) is continuous at every x, except \(x = 0\)
B
\(f(x)\) is discontinuous at every \(x,\) except \(x = 0\)
C
\(f(x)\) is continuous everywhere
D
\(f(x)\) is discontinuous everywhere
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4
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
If \(f\left( 1 \right) = 1,{f'}\left( 1 \right) = 2,\) then
\(\mathop {\lim }\limits_{x \to 1} {{\sqrt {f\left( x \right)} - 1} \over {\sqrt x - 1}}\) is
A
\(2\)
B
\(4\)
C
\(1\)
D
\({1 \over 2}\)
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5
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
$$\mathop {\lim }\limits_{x \to \infty } {\left( {{{{x^2} + 5x + 3} \over {{x^2} + x + 2}}} \right)^x}$$
A
\({e^4}\)
B
\({e^2}\)
C
\({e^3}\)
D
\(1\)
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6
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
f(x) and g(x) are two differentiable functions on [0, 2] such that

f''(x) - g''(x) = 0, f'(1) = 2, g'(1) = 4, f(2) = 3, g(2) = 9

then f(x) - g(x) at x = \({3 \over 2}\) is
A
0
B
2
C
10
D
-5
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7
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
Let \(f(2) = 4\) and \(f'(x) = 4.\)

Then \(\mathop {\lim }\limits_{x \to 2} {{xf\left( 2 \right) - 2f\left( x \right)} \over {x - 2}}\) is given by
A
\(2\)
B
\(- 2\)
C
\(- 4\)
D
\(3\)
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8
2002 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2002
\(\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}\), \(n \in N\), ( [x] denotes the greatest integer less than or equal to x )
A
has value \(-1\)
B
has value \(0\)
C
has value \(1\)
D
does not exist
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9
2003 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2003
If \(f(x) = \left\{ {\matrix{ \[{x{e^{ - \left( {{1 \over {\left| x \right|}} + {1 \over x}} \right)}}} & {,x \ne 0} \cr\] 0 & {,x = 0} \cr } } \right.\)

then \(f(x)\) is
A
discontinuous everywhere
B
continuous as well as differentiable for all x
C
continuous for all x but not differentiable at x = 0
D
neither differentiable nor continuous at x = 0
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10
2003 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2003
If \(\mathop {\lim }\limits_{x \to 0} {{\log \left( {3 + x} \right) - \log \left( {3 - x} \right)} \over x}\) = k, the value of k is
A
\(- {2 \over 3}\)
B
0
C
\(- {1 \over 3}\)
D
\({2 \over 3}\)
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11
2003 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2003
\(\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\left[ {1 - \tan \left( {{x \over 2}} \right)} \right]\left[ {1 - \sin x} \right]} \over {\left[ {1 + \tan \left( {{x \over 2}} \right)} \right]{{\left[ {\pi - 2x} \right]}^3}}}\) is
A
\(\infty\)
B
\({1 \over 8}\)
C
0
D
\({1 \over 32}\)
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12
2003 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2003
Let \(f(a) = g(a) = k\) and their nth derivatives
\({f^n}(a)\), \({g^n}(a)\) exist and are not equal for some n. Further if

$$\mathop {\lim }\limits_{x \to a} {{f(a)g(x) - f(a) - g(a)f(x) + f(a)} \over {g(x) - f(x)}} = 4$$

then the value of k is
A
0
B
4
C
2
D
1
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13
2004 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2004
Let \(f(x) = {{1 - \tan x} \over {4x - \pi }}\), \(x \ne {\pi \over 4}\), \(x \in \left[ {0,{\pi \over 2}} \right]\).

If \(f(x)\) is continuous in \(\left[ {0,{\pi \over 2}} \right]\), then \(f\left( {{\pi \over 4}} \right)\) is
A
\(-1\)
B
\({1 \over 2}\)
C
\(-{1 \over 2}\)
D
\(1\)
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14
2004 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2004
If \(\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}\), then the value of \(a\) and \(b\), are
A
\(a\) = 1 and \(b\) = 2
B
\(a\) = 1 and \(b\) \(\in R\)
C
\(a\) \(\in R\) and \(b\) = 2
D
\(a\) \(\in R\) and \(b\) \(\in R\)
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15
2005 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2005
Suppose \(f(x)\) is differentiable at x = 1 and

\(\mathop {\lim }\limits_{h \to 0} {1 \over h}f\left( {1 + h} \right) = 5\), then \(f'\left( 1 \right)\) equals
A
3
B
4
C
5
D
6
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16
2005 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2005
If \(f\) is a real valued differentiable function satisfying

\(\left| {f\left( x \right) - f\left( y \right)} \right|\) \(\le {\left( {x - y} \right)^2}\), \(x, y\) \(\in R\)
and \(f(0)\) = 0, then \(f(1)\) equals
A
-1
B
0
C
2
D
1
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17
2005 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2005
Let \(\alpha\) and \(\beta\) be the distinct roots of \(a{x^2} + bx + c = 0\), then

\(\mathop {\lim }\limits_{x \to \alpha } {{1 - \cos \left( {a{x^2} + bx + c} \right)} \over {{{\left( {x - \alpha } \right)}^2}}}\) is equal to
A
\({{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}\)
B
0
C
\(- {{{a^2}{{\left( {\alpha - \beta } \right)}^2}} \over 2}\)
D
\({{{{\left( {\alpha - \beta } \right)}^2}} \over 2}\)
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18
2006 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2006
The set of points where \(f\left( x \right) = {x \over {1 + \left| x \right|}}\) is differentiable is
A
\(\left( { - \infty ,0} \right) \cup \left( {0,\infty } \right)\)
B
\(\left( { - \infty ,1} \right) \cup \left( { - 1,\infty } \right)\)
C
\(\left( { - \infty ,\infty } \right)\)
D
\(\left( {0,\infty } \right)\)
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19
2007 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2007
Let \(f:R \to R\) be a function defined by

\(f(x) = \min \left\{ {x + 1,\left| x \right| + 1} \right\}\), then which of the following is true?
A
\(f(x)\) is differentiale everywhere
B
\(f(x)\) is not differentiable at x = 0
C
\(f(x) > 1\) for all \(x \in R\)
D
\(f(x)\) is not differentiable at x = 1
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20
2007 · Mathematics · Calculus · Limits Continuity And Differentiability
AIEEE 2007
The function \(f:R/\left\{ 0 \right\} \to R\) given by

$$f\left( x \right) = {1 \over x} - {2 \over {{e^{2x}} - 1}}$$

can be made continuous at \(x\) = 0 by defining \(f\)(0) as
A
0
B
1
C
2
D
\(-1\)
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