downloaded from jeemain.guru
~-=.
f'4t1. '"
ALLIM
CAREER INSTITUT E
KOTA (RAJASTHAN)
0744-5156100 I www.all~
,downloaded from jeemain.guru
[ serlaJ) CONTENTS page)
No. No.
1. Logarithm 01
2. Trigonometric ration & Identities 02
3. Trigonometric equation 10
4. Quadratic equations 13
5. Sequences and Series 17
6. Permutation & Combination 23
7. Binomial Theorem 28
8. Complex number 31
9. Determinants 37
10. Matrices 42
11. Properties & Solution of triangle 50
12. Straight line 58
13. Circle 71
14. Parabola 81
15. Ellipse 89
16. Hyperbola 96
17. Function 103
18. Inverse trigonometric function 122 ;
19. Limit 130
20. Continuity 135
21. Differentiability 138
22. Methods of differentiation 141
23. Monotonicity 145
24. Maxima-Minima 149
25. Tangent & Normal 154
26. Indefinite Integration 157
27. Definite Integration 163
28. Differential equation 167
29. Area under the curve 173
30. Vector 175
31. 3D-Coordinate Geometry 185
32. Probability 193
33. Statistics 199
34. MathematlcaJ Reasoning 206
35. Sets 211
36. Relation 216
,downloaded from jeemain.guru
j
,downloaded from jeemain.guru
Mathematics Handbook
. LOGARITHM
LOGARIlHM OF A NUMBER :
The logarithm of the number N to the base 'a' Is the exponent indicating
the power to which the base 'a' must be raised to obtain the number N.
This number is designated as log. N .
(a) log, N - x, read as log of N to the base a <::> a' = N
If a = 10 then we write log N or log,oN and if a - e we write
In N or log,N (Natural log)
(h) Necessary conditions : N > 0 ; a > 0 ; a "' 1
(e) log) = 0
(d) log,a = 1
(e) logy' a =-1
(f) logf(x.y) = log,x + log.y; x, y > 0
(g) log, (;) = log, x - lpg, y ; x, y > 0
(h) log, x P = plog. x ; x > 0
1
(I) log . x=-log"x ; x > O
• q
1 1 .
(D og, x = log, a ; x > 0 , x "' 1
(k) log,x - Iog"x/Iogba ; x > 0, a, b > 0, b "' 1, a "' 1
(I) log, b.logb dog, d = log, d ; a, b, c, d > 0, "' 1
(m) a""'" = x; a > 0, a "' 1
(n) a""'" - c"""' ; a,b,c > 0 ; b "' 1
X < y if a>1
(0) Iog x < Iog y <::> [
• • x>y if 0 < a<1
(P) log,x = log.y => x - y ; x, Y > 0 ; a > 0, a "' 1
(q) eln, ' _ a'
(r) log,02 - 0 .3010 ; log103 - 0.4771; In2 - 0 .693, in10 - 2.303
(5) If a > 1 then log. x < p=>O < x < a P
(t) If a > 1 then log. x > P => x > a P
(u) If 0 < a < 1 then log. x < p => x > a P
(vi If 0 <a < 1 then log. x > p=>O < x < a P
1
~-=.
f'4t1. '"
ALLIM
CAREER INSTITUT E
KOTA (RAJASTHAN)
0744-5156100 I www.all~
,downloaded from jeemain.guru
[ serlaJ) CONTENTS page)
No. No.
1. Logarithm 01
2. Trigonometric ration & Identities 02
3. Trigonometric equation 10
4. Quadratic equations 13
5. Sequences and Series 17
6. Permutation & Combination 23
7. Binomial Theorem 28
8. Complex number 31
9. Determinants 37
10. Matrices 42
11. Properties & Solution of triangle 50
12. Straight line 58
13. Circle 71
14. Parabola 81
15. Ellipse 89
16. Hyperbola 96
17. Function 103
18. Inverse trigonometric function 122 ;
19. Limit 130
20. Continuity 135
21. Differentiability 138
22. Methods of differentiation 141
23. Monotonicity 145
24. Maxima-Minima 149
25. Tangent & Normal 154
26. Indefinite Integration 157
27. Definite Integration 163
28. Differential equation 167
29. Area under the curve 173
30. Vector 175
31. 3D-Coordinate Geometry 185
32. Probability 193
33. Statistics 199
34. MathematlcaJ Reasoning 206
35. Sets 211
36. Relation 216
,downloaded from jeemain.guru
j
,downloaded from jeemain.guru
Mathematics Handbook
. LOGARITHM
LOGARIlHM OF A NUMBER :
The logarithm of the number N to the base 'a' Is the exponent indicating
the power to which the base 'a' must be raised to obtain the number N.
This number is designated as log. N .
(a) log, N - x, read as log of N to the base a <::> a' = N
If a = 10 then we write log N or log,oN and if a - e we write
In N or log,N (Natural log)
(h) Necessary conditions : N > 0 ; a > 0 ; a "' 1
(e) log) = 0
(d) log,a = 1
(e) logy' a =-1
(f) logf(x.y) = log,x + log.y; x, y > 0
(g) log, (;) = log, x - lpg, y ; x, y > 0
(h) log, x P = plog. x ; x > 0
1
(I) log . x=-log"x ; x > O
• q
1 1 .
(D og, x = log, a ; x > 0 , x "' 1
(k) log,x - Iog"x/Iogba ; x > 0, a, b > 0, b "' 1, a "' 1
(I) log, b.logb dog, d = log, d ; a, b, c, d > 0, "' 1
(m) a""'" = x; a > 0, a "' 1
(n) a""'" - c"""' ; a,b,c > 0 ; b "' 1
X < y if a>1
(0) Iog x < Iog y <::> [
• • x>y if 0 < a<1
(P) log,x = log.y => x - y ; x, Y > 0 ; a > 0, a "' 1
(q) eln, ' _ a'
(r) log,02 - 0 .3010 ; log103 - 0.4771; In2 - 0 .693, in10 - 2.303
(5) If a > 1 then log. x < p=>O < x < a P
(t) If a > 1 then log. x > P => x > a P
(u) If 0 < a < 1 then log. x < p => x > a P
(vi If 0 <a < 1 then log. x > p=>O < x < a P
1
