Skip to main content
Back to INCREASING & DECREASING

Your Progress

0 / 200 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • INCREASING & DECREASING

Increasing & decreasing practice · Mixed difficulty

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 1-30 of 200 questions
1 Medium
1 of 200
Analyzing +4 | -1
If the function f(x)=Ksin⁡x+2cos⁡xsin⁡x+cos⁡xf\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}} is increasing for all values of xx, then
View answer and explanation
Correct option: D
K>2K > 2
Option D (K>2K > 2) is correct because for the function to be increasing, its derivative must be greater than 0, leading to the condition K > 2.
2 Hard
2 of 200
Application +4 | -1
The set of values of a for which the function f(x)=x2+ax+1f\left( x \right) = {x^2} + ax + 1 is an increasing function on [1,2] is
View answer and explanation
Correct option: A
(−2,  ∞)\left( { - 2,\;\infty } \right)
Option A ((-2, ∞)) is correct because the function is increasing when its derivative is greater than 0 on the given interval.
3 Easy
3 of 200
Application +4 | -1
The value of aa in order that f(x)=f(x)= sin⁡x−cos⁡x−ax+b\sin x-\cos x-a x+b decreases for all real values is given by
View answer and explanation
Correct option: A
a≥2a \geq \sqrt{2}
Option A (a≥2a \geq \sqrt{2}) is correct because it ensures that the derivative of the function is always negative, indicating that the function is decreasing for all real values.
4 Easy
4 of 200
Analyzing +4 | -1
The function f(x)=xex(1−x),x∈Rf(x)=x e^{x(1-x)}, x \in R, is
View answer and explanation
Correct option: A
increasing in (−12,1)\left(-\frac{1}{2}, 1\right)
Option A (increasing in (-1/2, 1)) is correct because the derivative of the function is positive in this interval, indicating that the function is increasing.
5 Easy
5 of 200
Analyzing +4 | -1
If ff and gg are two increasing functions such that fogfog is defined, then
View answer and explanation
Correct option: A
gofgof is an increasing function
Option A (gofgof is an increasing function) is correct because the composition of two increasing functions is also an increasing function.
6 Medium
6 of 200
Analyzing +4 | -1
If f(x)=x3+bx2+cx+df\left( x \right) = {x^3} + b{x^2} + cx + d and 0<b2<c0 < {b^2} < c, then in (−∞,  ∞)\left( { - \infty ,\;\infty } \right)
View answer and explanation
Correct option: A
f(x)f\left( x \right) is strictly increasing function
Option A (f(x)f(x) is strictly increasing function) is correct because the derivative of the function is always positive, indicating that the function is strictly increasing.
7 Easy
7 of 200
Analyzing +4 | -1
Let g: (0,∞)→Rg:\,(0,\infty ) \to R be a differentiable function such that
∫(x(cos⁡x−sin⁡x)ex+1+g(x)(ex+1−xex)(ex+1)2)dx=xg(x)ex+1+c\int {\left( {\frac{{x(\cos x - \sin x)}}{{{e^x} + 1}} + \frac{{g(x)\left( {{e^x} + 1 - x{e^x}} \right)}}{{{{\left( {{e^x} + 1} \right)}^2}}}} \right)} dx = \frac{{xg(x)}}{{{e^x} + 1}} + c, for all x>0,x > 0, where cc is an arbitrary constant. Then:
View answer and explanation
Correct option: D
g−g′g - g' is increasing in (0,π2)\left( {0,\frac{\pi }{2}} \right)
Option D (g−g′g - g' is increasing in (0,π2)\left( {0,\frac{\pi }{2}} \right)) is correct because by differentiating the given integral equation and analyzing the sign of J′(x)=g′(x)−g′′(x)J'(x) = g'(x) - g''(x), it can be shown that g−g′g - g' is increasing in the specified interval.
8 Medium
8 of 200
Analyzing +4 | -1
f(x)=(e2x−1e2x+1)f\left( x \right) = \left( {\frac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}}} \right) is
View answer and explanation
Correct option: A
An increasing
Option A (An increasing) is correct because the derivative of the function is positive for all x in R, indicating an increasing function.
9 Medium
9 of 200
Analyzing +4 | -1
The function f(x)=cos⁡(π/x)f\left( x \right) = \cos \left( {\pi /x} \right) is increasing in the interval
View answer and explanation
Correct option: D
None of these
None of the provided options are correct. The function is increasing in the interval (12n+1,12n)(\frac{1}{2n+1}, \frac{1}{2n}) for n∈Nn \in N.
10 Medium
10 of 200
Analyzing +4 | -1
If x2f(4a)+y2f(a2−5)\frac{{{x^2}}}{{f\left( {4a} \right)}} + \frac{{{y^2}}}{{f\left( {{a^2} - 5} \right)}} represents an ellipse with major axis as yy-axis and ff is a decreasing function, then
View answer and explanation
Correct option: D
a∈(−1,5)a \in \left( { - 1,5} \right)
Option D (a∈(−1,5)a \in (-1,5)) is correct because it satisfies the condition for the given equation to represent an ellipse with the major axis as the y-axis, considering that f is a decreasing function.
11 Medium
11 of 200
Analyzing +4 | -1
If f:[1,10]→[1,10]f:[1,10] \rightarrow[1,10] is a non-decreasing function and g:[1,10]→[1,10]g:[1,10] \rightarrow[1,10] is a non-increasing function. Let h(x)=f(g(x))h(x)=f(g(x)) with h(1)=1h(1)=1. Then, h(2)h(2)
View answer and explanation
Correct option: C
is equal to one
Option C (is equal to one) is correct because since f is non-decreasing and g is non-increasing, h(x) = f(g(x)) is non-increasing and h(1) = 1, implying h(x) is a constant function equal to 1.
12 Easy
12 of 200
Analyzing +4 | -1
The function f(x)=sin⁡4x+cos⁡4xf(x)=\sin ^4 x+\cos ^4 x increasing, if
View answer and explanation
Correct option: B
π/4<x<3π/8\pi /4 < x < 3\pi /8
Option B (π/4<x<3π/8\pi /4 < x < 3\pi /8) is correct because the derivative of the function is positive in this interval, indicating an increasing function.
13 Medium
13 of 200
Analyzing +4 | -1
The values of 'xx' for which the function (a+2)x3−3  a  x2+9ax−1\left( {a + 2} \right){x^3} - 3\;a\;{x^2} + 9ax - 1 decreases monotonically throughout for all real xx are
View answer and explanation
Correct option: D
−∞<a≤−3- \infty < a \le - 3
Option D (−∞<a≤−3- \infty < a \le - 3) is correct because it ensures that the derivative of the given function is always non-positive, making the function monotonically decreasing.
14 Easy
14 of 200
Analyzing +4 | -1
If a<0,f(x)=eax+e−axa < 0, f(x)=e^{a x}+e^{-a x} and S={x:f(x)S=\{x: f(x) is monotonically increasing}\}, then SS equals
View answer and explanation
Correct option: A
{x:x>0}\{x: x > 0\}
The correct answer is A ({x: x > 0}) because the condition for f(x)f(x) to be monotonically increasing, given a<0a < 0, leads to x>0x > 0.
15 Easy
15 of 200
Understanding +4 | -1
For the every value of xx the function f(x)=15xf(x)=\frac{1}{5^x} is
View answer and explanation
Correct option: A
Decreasing
Option A (Decreasing) is correct because the derivative of the function is negative for all values of x, indicating a decreasing function.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
16 Easy
16 of 200
Analyzing +4 | -1
The function y=x3−3  x2+6  x−17y = {x^3} - 3\;{x^2} + 6\;x - 17
View answer and explanation
Correct option: A
Increases everywhere
Option A (Increases everywhere) is correct because the derivative of the function is always positive, indicating an increasing function.
17 Medium
17 of 200
Analyzing +4 | -1
Let f(x)=2sin⁡3x−3sin⁡2x+12sin⁡x+5f(x)=2 \sin ^3 x-3 \sin ^2 x+12 \sin x+5, 0≤x≤π20 \leq x \leq \frac{\pi}{2}. Then, f(x)f(x), is
View answer and explanation
Correct option: B
Increasing on [0,π/2][0, \pi / 2]
Option B (Increasing on [0,π/2][0, \pi / 2]) is correct because the derivative of f(x)f(x) is positive on the interval [0,π/2][0, \pi / 2], indicating that the function is increasing.
18 Easy
18 of 200
Application +4 | -1
Let y=x2e−x,y = {x^2}{e^{ - x}}, then the interval in which y increases with respect to xx is
View answer and explanation
Correct option: D
(0,  2)\left( {0,\;2} \right)
Option D ((0, 2)) is correct because it represents the interval where the derivative of the function is positive, indicating that the function is increasing.
19 Medium
19 of 200
Analyzing +4 | -1
Let f(x)f(x) be a function given by f(x)=x2+1[x]f(x)=\frac{x^2+1}{[x]} for all x∈[1,4),x \in[1,4), where [.] denotes the greatest integer function. Then, f(x)f(x) is monotonically
View answer and explanation
Correct option: C
Increasing on [1,2)[1,2)
Option C (Increasing on [1,2)[1,2)) is correct because the derivative of f(x)f(x) is positive on this interval, indicating that f(x)f(x) is increasing.
20 Easy
20 of 200
Application +4 | -1
The value of bb for which the function f(x)=sin⁡x−bx+cf\left( x \right) = \sin x - bx + c is decreasing in the interval (−∞,  ∞)\left( { - \infty ,\;\infty } \right) is given by
View answer and explanation
Correct option: C
b>1b > 1
Option C (b>1b > 1) is correct because for the function to be decreasing, its derivative must be negative for all x, implying b>cos⁡xb > \cos x for all x, hence b>1b > 1.
21 Easy
21 of 200
Analyzing +4 | -1
Let f(x)=sin⁡4x+cos⁡4xf(x)=\sin ^4 x+\cos ^4 x. Then ff is increasing function in the interval
View answer and explanation
Correct option: A
(π4,π2)\left(\frac{\pi}{4}, \frac{\pi}{2}\right)
Option A ((π4,π2)\left(\frac{\pi}{4}, \frac{\pi}{2}\right)) is correct because the derivative of the function is positive in this interval, indicating an increasing function.
22 Easy
22 of 200
Analyzing +4 | -1
If f(x)=sin⁡x,x∈[−π/2,π/2],f(x)=\sin x, x \in[-\pi / 2, \pi / 2], then which one of the following is not correct?
View answer and explanation
Correct option: C
fof(x)fof(x) is decreasing on [−π/2,0][-\pi / 2,0] and is increasing on [0,π/2][0, \pi / 2]
The correct answer is C because fof(x)fof(x) is increasing on the entire interval [−π/2,π/2][-\pi / 2, \pi / 2], not decreasing on [−π/2,0][-\pi / 2,0] and increasing on [0,π/2][0, \pi / 2].
23 Medium
23 of 200
Analyzing +4 | -1
Consider the following two propositions P1P_1 and P2P_2. P1\mathbf{P}_1 : If ff and gg are increasing functions on [a,b][a, b], then f+gf+g is also increasing on [a,b][a, b].
P2\mathbf{P}_2 : If f(x)=xf(x)=x and g(x)=1−xg(x)=1-x are defined on [0,1][0,1], then the product fgf g is increasing on [0,1][0,1].
Then
View answer and explanation
Correct option: B
P1\mathrm{P}_1 is true, but P2\mathrm{P}_2 is false
Option B is correct because P1 is true (sum of increasing functions is increasing), while P2 is false (product fg is not increasing on [0,1]).
24 Easy
24 of 200
Analyzing +4 | -1
The function f(x)=sin⁡xxf(x)=\frac{\sin x}{x} is decreasing in the interval
View answer and explanation
Correct option: B
(0,π/2)(0, \pi / 2)
Option B ((0,π/2)(0, \pi / 2)) is correct because the derivative of the function is negative in this interval, indicating a decreasing function.
25 Medium
25 of 200
Analyzing +4 | -1
The function f(x)=1−x3−x5f\left( x \right) = 1 - {x^3} - {x^5} is decreasing for
View answer and explanation
Correct option: D
All values of xx
Option D (All values of xx) is correct because the derivative of the function is always negative, indicating that the function is always decreasing.
26 Easy
26 of 200
Analyzing +4 | -1
Let the function g:(−∞,∞)→(−π/2,π/2)g:(-\infty, \infty) \rightarrow(-\pi / 2, \pi / 2) be given by g(u)=2tan⁡−1(eu)−π2g(u)=2 \tan ^{-1}\left(e^{u }\right)-\frac{\pi}{2}. Then, gg is
View answer and explanation
Correct option: C
Odd and is strictly increasing in (−∞,∞)(-\infty, \infty)
The correct answer is C (Odd and is strictly increasing in (−∞,∞)(-\infty, \infty)) because the derivative g′(u)g'(u) is always positive, indicating that g(u)g(u) is strictly increasing, and g(−u)=−g(u)g(-u) = -g(u), showing that g(u)g(u) is odd.
27 Easy
27 of 200
Application +4 | -1
The value of xx for which the polynomial 2x3−9x2+12x+42{x^3} - 9{x^2} + 12x + 4 is a decreasing function of xx, is
View answer and explanation
Correct option: D
1<x<21 < x < 2
Option D (1<x<21 < x < 2) is correct because the function is decreasing when its derivative is negative, which occurs in the interval 1<x<21 < x < 2.
28 Easy
28 of 200
Understanding +4 | -1
Which of the following function is decreasing on (0,π2)\left(0, \frac{\pi}{2}\right) ?
View answer and explanation
Correct option: C
cos⁡x\cos x
Option C (cos x) is correct because its derivative, -sin x, is negative in the interval (0, π/2), indicating a decreasing function.
29 Easy
29 of 200
Analyzing +4 | -1
If f(x)=asin⁡x+bcos⁡xcsin⁡x+dcos⁡xf\left( x \right) = \frac{{a\sin x + b\cos x}}{{c\sin x + d\cos x}} is decreasing for all xx, then
View answer and explanation
Correct option: B
ad−bc<0ad - bc < 0
Option B (ad−bc<0ad - bc < 0) is correct because for the function to be decreasing, its derivative must be negative, leading to this condition on the coefficients.
30 Easy
30 of 200
Analyzing +4 | -1
If the function f(x)=cos⁡∣x∣−2  ax+bf\left( x \right) = \cos \left| x \right| - 2\;ax + b increases along the entire number scale, the range of a is given by
View answer and explanation
Correct option: C
a<−12a < - \frac{1}{2}
Option C (a<−12a < - \frac{1}{2}) is correct because it ensures that the derivative of the function f(x)f(x) is always positive, making the function increasing along the entire number scale.
Revision notes and key takeaways

Review INCREASING & DECREASING in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

  • ✓ This set contains 200 single-correct-answer MCQs on INCREASING & DECREASING.
  • ✓ Try each question before opening its answer. Read the explanation where one is available.
  • ✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.
Showing 1-30 of 200 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - INCREASING & DECREASING MCQs (Easy) 101 MCQs → ENGINEERING MATHEMATICS - INCREASING & DECREASING MCQs (Hard) 7 MCQs → ENGINEERING MATHEMATICS - INCREASING & DECREASING MCQs (Medium) 92 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs
📚 Switch Set (ALL)
Chapter Sets
ALL 200 MCQs EASY 101 MCQs HARD 7 MCQs MEDIUM 92 MCQs
0 /200
0✓ 0✗
0% Accuracy
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →