Objective Mathematics

97 Pages·2012·7.43 MB·English

IIT-JEE-2013

Objective Mathematics

{Mains & Advance}

Er.L.K.Sharma

B.E.(CIVIL), MNIT,JAIPUR(Rajasthan)

© Copyright L.K.Sharma 2012.

Er. L.K.Sharma an engineering graduate
from NIT, Jaipur (Rajasthan), {Gold
medalist, University of Rajasthan} is a well
known name among the engineering
aspirants for the last 15 years. He has
been
honored
with
"BHAMASHAH

AWARD" two times for the academic
excellence in the state of Rajasthan. He is
popular among the student community
for possessing the excellent ability to
communicate the mathematical concepts
in analytical and graphical way.

He has worked with many IIT-JEE coaching institutes of Delhi and
Kota, {presently associated with Guidance, Kalu Sarai, New Delhi as
senior mathematics faculty}. He has been a senior mathematics
{IIT-JEE} faculty at Delhi Public School, RK Puram for five years.

He is actively involved in the field of online teaching to the
engineering aspirants and is associated with iProf Learning
Solutions India (P) Ltd for last 3 years. As a premium member of
www.wiziq.com (an online teaching and learning portal), he has
delivered many online lectures on different topics of mathematics at
IIT-JEE and AIEEE level.{some of the free online public classes at
wizIQ can be accessed at http://www.wiziq.com/LKS }.

Since last 2 years many engineering aspirants have got tremendous
help with the blog “mailtolks.blogspot.com” and with launch of the
site “mathematicsgyan.weebly.com”, engineering aspirants get the
golden opportunity to access the best study/practice material in
mathematics at school level and IIT-JEE/AIEEE/BITSAT level. The
best part of the site is availability of e-book of “OBJECTIVE
MATHEMATICS for JEE- 2013” authored by Er. L.K.Sharma,
complete book with detailed solutions is available for free download
as the PDF files of different chapters of JEE-mathematics.

© Copyright L.K.Sharma 2012.

Contents

1. Quadratic Equations
1 - 8

2. Sequences and Series
9 - 16

3. Complex Numbers
17 - 24

4. Binomial Theorem
25 - 30

5. Permutation and Combination
31 - 36

6. Probability
37 - 44

7. Matrices
45 - 50

8. Determinants
51 - 57

9. Logarithm
58 - 61

10. Functions
62 - 70

11. Limits
71 - 76

12. Continuity and Differentiability
77 - 82

13. Differentiation
83 - 88

14. Tangent and Normal
89 - 93

15. Rolle's Theorem and Mean Value Theorem
94 - 97

16. Monotonocity
98 - 101

17. Maxima and Minima
102 - 108

18. Indefinite Integral
109 - 113

19. Definite Integral
114 - 122

20. Area Bounded by Curves
123 - 130

21. Differential Equations
131 - 137

22. Basics of 2D-Geometry
138 - 141

23. Straight Lines
142 - 148

24. Pair of Straight Lines
149 - 152

25. Circles
153 - 160

26. Parabola
161 - 167

27. Ellipse
168 - 175

28. Hyperbola
176 - 182

29. Vectors
183 - 191

30. 3-Dimensional Geometry
192 - 199

31. Trigonometric Ratios and Identities
200 - 206

32. Trigonometric Equations and Inequations
207 - 212

33. Solution of Triangle
213 - 218

34. Inverse Trigonometric Functions
219 - 225

IIT-JEE
Objective Mathematics

Er.L.K.Sharma

[ 1 ]
Mathematics for JEE-2013

Author - Er. L.K.Sharma

Multiple choice questions with ONE correct answer :

( Questions No. 1-25 )

1. If the equation | x – n | = (x + 2)2 is having exactly
three distinct real solutions , then exhaustive set of
values of 'n' is given by :

(a)
5
3
,
2
2










(b)
5
3
, 2,
2
2











(c)
5
3
,
2
2










(d)
9
7
, 2,
4
4











2. Let a , b , c be distinct real numbers , then roots of
(x – a)(x – b) = a2 + b2 + c2 – ab – bc – ac , are :

(a) real and equal
(b) imaginary

(c) real and unequal
(d) real

3. If
3
2
2
12
3
16
0
x
x
x





is having three positive
real roots , then ' ' must be :

(a) 4
(b) 8

(c) 0
(d) 2

4. If a , b , c are distinct real numbers , then number of
real roots of equation

(
)(
)
(
)(
)
(
)(
)
1
(
)(
)
(
)(
)
(
)(
)
x
a x
b
x
b x
c
x
c x
a
c
a c
b
a
b a
c
b
c b
a
















is/are :

(a) 1
(b) 4

(c) finitely many
(d) infinitely many

5. If ax2 + 2bx + c = 0 and a1x2 + 2b1x + c1 = 0 have a

common root and

1
1
1

,
,
a
b
c

a
b
c are in A.P. , then

a1 , b1 , c1 are in :

(a) A.P.
(b) G.P.

(c) H.P.
(d) none of these

6. If all the roots of equations

2 2
4
2
(
1)(1
)
(
1)(
1)
a
x
x
a
x
x








are imaginary , then range of 'a' is :

(a) (
,
2]


(b) (2 ,
)


(c) ( 2 , 2)

(d) ( 2 ,
)



7. Total number of integral solutions of inequation

2
3
4

5
6
(3
4) (
2)
0

(
5) (7
2 )

x
x
x

x
x







is/are :

(a) four
(b) three

(c) two
(d) only one

8. If exactly one root of 5x2 + (a + 1) x + a = 0 lies in the

interval
(1 , 3)
x 
, then

(a) a > 2

(b) – 12 < a < – 3

(c) a > 0

(d) none of these

9. If both roots of 4x2 – 20 px + (25 p2 +15p – 66) = 0 are
less than 2 , then 'p' lies in :

(a)
4 , 2
5









(b) (2 ,
)


(c)
4
1 , 5









(d) (
,
1)



10. If x2 – 2ax + a2 + a – 3
0
x
R



, then 'a' lies in

(a) [3 ,
)

(b) (
, 3]


(c) [–3 ,  )
(d) (
,
3]



11. If x3 + ax + 1 = 0 and x4 + ax2 + 1 = 0 have a common
root , then value of 'a' is

(a) 2
(b) –2

(c) 0
(d) 1

12. If x2 + px + 1 is a factor of ax3 + bx + c , then

(a) a2 + c2 + ab = 0

(b) a2 – c2 + ab = 0

(c) a2 – c2 – ab = 0

(d) a2 + c2 – ab = 0

13. If expression
2
2
2
2
2
2
2
2
2
2
(
)
(
)
(
)
a
b
c
x
b
c
a
x
c
a
b





is a perfect square of one degree polynomial of x ,
then a2 , b2 , c2 are in :

(a) A.P.
(b) G.P.

(c) H.P.
(d) none of these

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