This document contains a multiple choice questions (MCQs) quiz on topics related to limits, functions, differentiation, and integration in mathematics. There are 52 questions testing concepts like limits, domains of functions, inverse functions, asymptotes of graphs, and properties of trigonometric, exponential and logarithmic functions. The questions cover topics typically found in a first calculus course on functions, limits, and introductory calculus concepts.

1. MATHS
PRESENTATION
MCQS of Topics: Functions, Limits, differentiation, and
Integration
CHAPTER#1
LIMITS AND FUNCTIONS
1.
𝑥 →0
𝐿𝑖𝑚𝑖𝑡 √49+𝑥−7
𝑥
=?
(a)0 (b) 1
14
(c)-6 (d)∞
2. The domain of the function h(x)=√𝑥2 − 4 is:
(a)Real no’s (b)Real no’s-{2}
(c){x/x 𝛜 R ^-2<x<2} (d)R-(-2,2)

2. 3. 𝐿𝑖𝑚𝑖𝑡
𝑥→0
𝑒𝑥
−1
4
=?
(a)∞ (b)0
(c) -1 (d)1
4. The domain of the inverse of the function f(x)=
2+√𝑥 − 1 is _______:
(a)[1,∞) (b)[2,∞)
(c)(1,∞) (d)(2,∞)
5.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 𝑥𝑝−𝑒𝑛
𝑥−𝑒
(a)0 (b)1
(c)𝑝𝑥𝑛−1 (d)𝑝𝑒𝑝−1
6.
𝑥→0
𝐿𝑖𝑚𝑖𝑡
4𝑥−8
𝑥+2
(a)-6 (b)20
(c)-20 (d)4
5
7. Given f(x)=𝑥2+3 then f(a+b)=?
(a)𝑎2
+ 𝑏2
+ 2𝑎𝑏 + 3 (b) 𝑎2
+ 𝑏2
− 2𝑎𝑏 − 3
(c) 𝑎2
+ 𝑏2
− 3𝑎𝑏 (d) 𝑥2
+ 3
8.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 5𝑥4+3𝑥3+9
7𝑥4+5𝑥2+17
=?
(a) 5
7
(b) 3
5
(c) 9
17
(d) 0
9. Let the Variable Z take in succession the values
6,62
1
, 63
2
, 65
4
, … then z→?
(a)0 (b)7

3. (c)5 (d)6
10. Give f(x)=4x+5, g(x)=3x+7 then f(g(x))=?
(a)12x+28 (b)12x+33
(c)4x-31 (d)25x+34
11.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 𝑥5+3𝑥3+9𝑥2+7𝑥+8
2𝑥6+17𝑥4+3𝑥2+5
=?
(a)0 (b)8
5
(c)1
2
(d)∞
12.
𝑧 →0
𝐿𝑖𝑚𝑖𝑡
sin 𝑝𝑧
𝑚𝑧
(a)0 (b)∞
(c)1
𝑚
(d)𝑝
𝑚
13. Which one is true?
(𝐼) 𝑥 →∞
𝐿𝑖𝑚𝑖𝑡
𝑒𝑥
= ∞ (𝐼𝐼) 𝑥 →∞
𝐿𝑖𝑚𝑖𝑡
𝑒𝑥
= 0 (𝐼𝐼𝐼) 𝑥 →∞
𝐿𝑖𝑚𝑖𝑡
𝑎𝑥
= 𝑎
(a)𝐼 𝑎𝑛𝑑 𝐼𝐼 𝑜𝑛𝑙𝑦 (b)𝐼𝐼 𝑎𝑛𝑑 𝐼𝐼𝐼 𝑜𝑛𝑙𝑦
(c) 𝐼 𝑜𝑛𝑙𝑦 (d)𝑎𝑙𝑙
14. Let |𝑥| denotes the number of elements in X, then
|𝑋 ∗ 𝑌| =?
(a)|𝑥| + |𝑦| (b)|𝑥| − |𝑦|
(c)|𝑥| ∗ |𝑦| (d)none of these
15. Let A={3,5,7,-9}, B={0,1,-3} and R={(3,0),(7,-3),(-9,0)}
then domain of R=?
(a){0,1,-3,0} (b){0,1,-3}
(c){3,5,7,-9} (d){3,5} (e) none.

4. 16. 𝑥 →0
𝐿𝑖𝑚𝑖𝑡 1−𝑐𝑜𝑠2𝑥
𝑥2 =?
(a)0 (b)1
(c)-1 (d)2
17. 𝑥 →3
𝐿𝑖𝑚𝑖𝑡 𝑥3−27
𝑥2−9
=?
(a)0 (b)∞
(c)1 (d)9
2
18. 𝜃→0
𝐿𝑖𝑚𝑖𝑡 1−𝑐𝑜𝑠𝑝𝜃
1−𝑐𝑜𝑠𝑞𝜃
=?
(a) 𝑝2
𝑞2
(b) 𝑞2
𝑝2
(c)0 (d)∞
19. 𝑥 →𝑎
𝐿𝑖𝑚𝑖𝑡 𝑓(𝑥)−𝑓(𝑎)
𝑥−𝑎
=?
(a) ℎ →0
𝐿𝑖𝑚𝑖𝑡 𝑓(𝑎+𝐻)+𝑓(𝑎)
𝐻
(b) ℎ →0
𝐿𝑖𝑚𝑖𝑡 𝑓(𝑎+𝐻)−𝑓(𝑎)
𝐻
(c)𝑙𝑛𝑎 (d)𝑒
20. Inverse function of y= 𝑥
𝑥+5
is
(a) 𝑥
𝑥+5
(b) 𝑥
𝑥−5
(c) 1𝑥
1−𝑥
(d) 15𝑥
1−𝑥
21. ℎ →0
𝐿𝑖𝑚𝑖𝑡
𝑐𝑜𝑠𝑒𝑐(𝜋 + 𝕙) =?
(a)0 (b)1
(c)-1 (d)∞
22. The graph of function y-logx has an asymptote
at______.
(a)𝑦 = 0 (b)𝑥 = 0
(c)𝑥 = 10 (d)𝑦 = 10

5. 23.
𝑥 →∞
𝐿𝑖𝑚𝑖𝑡
(
𝑥
1+𝑥
) 𝑥
=?
(a)𝑒 (b)𝑒1
(c)𝑒2 (d) 1
𝑒2
24. The graph of the parametric equations 𝑥 = 𝑟2
and 𝑦 = 𝑡
(a)circle (b)parabola
(c)ellipse (d)straight line
25. If A={1,2,……..n}, how many distinct relations
can be defined on A?
(a)𝑛2 (b)2𝑛
(c)2𝑛2
(d)0
26.
𝑥 →0
𝐿𝑖𝑚𝑖𝑡 𝑒
−1
𝑥2
1+𝑒
−1
𝑥2
(a)0 (b)1
(c)-1 (d)∞
27.
𝑥 →0
𝐿𝑖𝑚𝑖𝑡(1 − 4𝑥)
1
𝑥 =?
(a)𝑒4 (b) 1
𝑒4
(c)𝑒 (d)𝑒−4𝑥
28.
𝑥 →
𝜋
2
𝐿𝑖𝑚𝑖𝑡
tan (
𝜃
2
) =?
(a)1 (b)0
(c)∞ (d)-1

6. 29. The values of b and c for which f(x+1)-f(x)=8x+3
hold true, where f(x)=b𝑥2
+ 𝑐𝑥 + 𝑑 are
(a)b=2, c=-1 (b)b=4,c=-1
(c)b=-1, c=4 (d)none
30. If f(x)=𝑥2
−
1
𝑥2 𝑡ℎ𝑒𝑛 𝑓(𝑥) =?
(a)−𝑓(
1
𝑥
) (b)𝑓(
1
𝑥
)
(c)𝑓(𝑥) (d)𝑓(𝑥2
)
31. The range of a function f(x)=[x] is
(a)N (b)Z
(c)R (d)none
32.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 (1−𝑐𝑜𝑠2𝑥)𝑠𝑖𝑛5𝑥
𝑥2𝑠𝑖𝑛3𝑥
(a)10
3
(b) 3
10
(c)6
5
(d)5
6
33.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 𝑥2−3𝑥+2
2𝑥2+𝑥−3
(a)2 (b)1
2
(c)0 (d)does not exist
34.
𝑥→∞
𝐿𝑖𝑚𝑖𝑡 𝑠𝑖𝑛𝑥
𝑥
(a)0 (b)undefined
(c)1 (d)∞

7. 35.
𝑥→∞
𝐿𝑖𝑚𝑖𝑡
(
𝑥
𝑥+2
) 𝑦
(a)𝑒 (b)𝑒−1
(c) 1
𝑒2
(d)𝑒5
36. 𝑒𝑥+𝑒−𝑥
𝑒𝑥−𝑒−𝑥
(a)tanhx (b)cothx
(c)𝑐𝑜𝑡ℎ−1
𝑥 (d)cosechx
37. 𝐶𝑜𝑠ℎ−1
𝑥 = _____?
(a)1
2
ln(1 + 𝑥) (b)1
2
ln(1 − 𝑥)
(c)1
2
ln(𝑥 + 𝑥√𝑥2 − 1) (d) ln(𝑥 + 𝑥√𝑥2 − 1)
38. Which of the following is an implicit function?
(a)y=x-1 (b)y-1=𝑥2
(c)𝑥2
+ 𝑦 + 2 = 0 (d) 𝑥2
+ 𝑥𝑦 + 𝑦2
= 9
39. If 𝑓(𝑥) = 4𝑥2
+ 𝑥𝑦 + 𝑦2
− 7 then f(x) is
(an)_____function
(a)Even (b)Odd
(c)Both even and odd (d)Neither even nor odd
40. 𝑓(𝑥) =
3𝑥+1
2𝑥−1
𝑡ℎ𝑒𝑛 𝑓(𝑓−1(2)) =?
(a)x (b)1
2
⁄
(c)2 (d)7
41. 𝐿𝑒𝑡 𝑝 𝑏𝑒 𝑎 + 𝑣𝑒 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑓 𝑥𝑝
𝑖𝑠
𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑡ℎ𝑒𝑛: 𝑥→∞
𝐿𝑖𝑚𝑖𝑡 𝑎
𝑥𝑝 =?

8. (a)1 (b)p
(c)0 (d)x
42. If 𝑓(𝑥) −
<
𝑔(𝑥) −
<
ℎ(𝑥)𝑎𝑛𝑑 𝑥→𝑐
𝐿𝑖𝑚𝑖𝑡
𝑓(𝑥) = 𝑥→𝑐
𝐿𝑖𝑚𝑖𝑡
ℎ(𝑥) =
2, 𝑡ℎ𝑒𝑛 𝑥→𝑐
𝐿𝑖𝑚𝑖𝑡
𝑔(𝑥) =?
(a)<2 (b)>2
(c)=2 (d)nothing can be said
43. For a function if the right hand limit = left hand
limit then which of the following must be true;
(a)Function is continous (b)Function has same domain and range
(c)Function is defined (d)its limit exist
44. Which of the following cannot be the graph of a
function?
(a)(b)
(c)(d)
45. If h(x)=3x+2 and h(f(x))=x, then f(2)=?
(a)0 (b)2
(c)-2 (d)1
46. The domain of the function 𝑓(𝑥) =
|𝑥+2|
𝑥+2
is;
(a)R-{2} (b)R
(c)R-{ −
+
2} (d)R-{-2}
47. 𝑙𝑜𝑔2[𝑙𝑜𝑔3[𝑙𝑜𝑔2𝑥]] = 1 𝑡ℎ𝑒𝑛 𝑥 =?
(a)43 (b)34
(c)29 (d)22

9. 48. The domain of the function g(x)=𝑒√𝑥2−1
. ln(𝑥 − 1)
is;
(a)(1,∞) (b)[1,∞)
(c)R-{1} (d)[1,∞]
49. The graph of 𝑥2
+ 𝑦2
= 9 is symmetrical about
(a)x-axis (b)y-axis
(c)origin (d)All of these
50. The domain of y=√−𝑥 is;
(a)(0,∞) (b)
(c)(-∞,0) (d)(−∞, 0]
51. The range of the function f={(1,x),(2,y),(3,z)} is
(a){1,x,z} (b){1,y,z}
(c){1,2,3} (d){x,y,z}
52. The domain of definition of function
y= 1
√16−𝑥2
is______:
(a)(-4,4) (b)[-4,4]
(c)R-(-4,4) (d)(4, ∞)
53. If 𝑓(𝑥) =
𝑥−1
𝑥+1
, 𝑥 ≠ −1 𝑡ℎ𝑒𝑛 𝑓−1(𝑥) =?
(a)1+𝑥
𝑥−1
(b) 1+𝑥
1−𝑥
(c) 2
1+𝑥
(d) 1
𝑥−1
54. If f(x)=4𝑥 − 𝑥2, then f(a+1)-f(a-1) is equal to
(a)4(2-a) (b)2(4-a)
(c)4(2+1) (d)2(4+a)

10. 55. The range of the function 𝑓(𝑥) =
1+𝑥2
𝑥2
is____
(a)[0,1] (b)(0,1)
(c)(1,∞) (d)[1, ∞]
56. A function f:R→R is defined by 𝑓(𝑥) = { −1
1 , if 𝑥 ∈
𝑄 , 𝑖𝑓 𝑥 ∈ 𝑄′ then f(𝜋)-f(
22
7
)=?
(a)0 (b)2
(c)-2 (d)None of these
57. 𝑥→2
𝐿𝑖𝑚𝑖𝑡[𝑥] =?
(a)1 (b)2
(c)0 (d)Does not exist
58.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 𝑒𝑥−𝑒−𝑥
𝑠𝑖𝑛𝑥
=?
(a)1 (b)2
(c)0 (d)-1
59.
𝑥→0
𝐿𝑖𝑚𝑖𝑡 4𝑥−3𝑥
3𝑥−2𝑥 =?
(a)ln(
4
3
) (b)ln(
3
2
)
(c)ln(
4
3
)
ln(
4
3
)
(d)ln (
4
3
) − ln(
3
2
)
60.
𝑥→ 4
𝜋
𝐿𝑖𝑚𝑖𝑡 𝑠𝑖𝑛𝑥−𝑐𝑜𝑠𝑥
𝑥− 4
𝜋 =?
(a)2 (b)√2
(c) 1
√2
(d)2√2

11. CHAPTER#02
DIFFERENTIATION
1.