maths-presentation.pdf

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)

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

(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
sin 𝑝𝑧
𝑚𝑧
(a)0 (b)∞
(c)1
𝑚
(d)𝑝
𝑚
13. Which one is true?
(𝐼) 𝑥 →∞
𝑒𝑥
= ∞ (𝐼𝐼) 𝑥 →∞
𝑒𝑥
= 0 (𝐼𝐼𝐼) 𝑥 →∞
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.

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
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

23.
𝑥 →∞
(
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
tan (
𝜃
2
) =?
(a)1 (b)0
(c)∞ (d)-1

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)∞

35.
𝑥→∞
(
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 =?

(a)1 (b)p
(c)0 (d)x
42. If 𝑓(𝑥) −
<
𝑔(𝑥) −
<
ℎ(𝑥)𝑎𝑛𝑑 𝑥→𝑐
𝑓(𝑥) = 𝑥→𝑐
ℎ(𝑥) =
2, 𝑡ℎ𝑒𝑛 𝑥→𝑐
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

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)

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

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