Table Of ContentIIT-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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