1.Binomial theorem no. of
Lx + x? term
(1 +X) = 1 + 2 x
ifx <<< 1 then T, =a + (n-1) d
(1 +X) = 1 + 2x last -1st Common
MR*
feel term term diff.
(Carrier + love) = Carrier + 2 love
Because carrier >>> love no. of terms.
n
S, 2 2a +(n-1) a
AX <<<K X.
NOTE:- n = no. of terms not last term.
+ (1- x)" = 1 - nx
+(1-X)" = 1+ GP series
+ (1 + X)=1 - nx Next term = Previous term x Common ratio
a , ar, arar
2. Imp formula
Ex 16, 8, 4, 2., 1, 1/2, 1/4, so on
(a+ b = a + b + 2ab nth term
(a - b = a+ b - 2ab r (Common ratio) =
(n-1)" term
a - b= (a + b) (a - b)
(a + b) = a + b + 3ab (a + b) Sum =
1-r
valid when r< 1.
(a - bj = a' - b - 3ab (a - b) 1 1 1 1
a +b' = (a + b) (a + b- ab) Ex
r= 1/4 1
a- b = (a - b) (a? + b+ ab) 1/2
1 1
3. AP series Sum =
i12- 2
2
Next term = Previous term + Common
difference Ex 1
a,at d , a+2d,a+ 3d,at 4d..
Ex 2, 5, 8, 11, 14, 17, so on. r
d= Cowmmon difference
=nth term- (n-1 'h term Sum
, 4. Quadratic equation (c) log,x = 1
ax +bx +C =0 log,9
() logn= 1
a, b, & Care constant in
which acan not be zero
n
log.x
(e) log=n logx
X= -bt Vb?-4ac () log,a x log, b =1
2a.
g) log,a =1
Sum of roots = a
, Products of roots = a
log,1 =O
Q. Find roots of equationx -5X +6 = 0;
find value of a, b &cby comparing with log2 = 0.30
ax + bx + C=O
Ans. a = 1, b= -5 & c=6 logo1 =O
X.=(-5) +V-s)?-4x2x6 log.o3 = 0.48 s O.s
2x1
=5+l1=z log,(sin 90°) =o
2
X, = 2 log.o5 + log20 = 2
Q. x - 4X = O
log,3 = logio3 -48
= 4X log.2 30
X= 4
wrong + Concept of Anti-log
log e = Y
x(x - 4) =0 By taking Anti-log
X=0; X=4 correct (convert
X= e
into concept of
power)
Q. x- 4X +3=0then find roots. MR*katadka
Ans. x - 3x - x+ 3=o
X(K-3) -1 (x -3) =0 log ’ Concept of Power
(x - 3) (x - 1) = o
=
TResult ’ log
X= 3, X = 1 Base
2 =3
S. Logarithms Base wahi rahega
log y' = log x on the base y interchange hoga) (Power Result
log, x = 2.303 log.oX G. Rule of
Power
(a) log, (xy) = log, x+ log, y 4 IfPower of
any
log x - log y non-zero
then result will be one number is zero
EX- 8°=1
Physics
Lx + x? term
(1 +X) = 1 + 2 x
ifx <<< 1 then T, =a + (n-1) d
(1 +X) = 1 + 2x last -1st Common
MR*
feel term term diff.
(Carrier + love) = Carrier + 2 love
Because carrier >>> love no. of terms.
n
S, 2 2a +(n-1) a
AX <<<K X.
NOTE:- n = no. of terms not last term.
+ (1- x)" = 1 - nx
+(1-X)" = 1+ GP series
+ (1 + X)=1 - nx Next term = Previous term x Common ratio
a , ar, arar
2. Imp formula
Ex 16, 8, 4, 2., 1, 1/2, 1/4, so on
(a+ b = a + b + 2ab nth term
(a - b = a+ b - 2ab r (Common ratio) =
(n-1)" term
a - b= (a + b) (a - b)
(a + b) = a + b + 3ab (a + b) Sum =
1-r
valid when r< 1.
(a - bj = a' - b - 3ab (a - b) 1 1 1 1
a +b' = (a + b) (a + b- ab) Ex
r= 1/4 1
a- b = (a - b) (a? + b+ ab) 1/2
1 1
3. AP series Sum =
i12- 2
2
Next term = Previous term + Common
difference Ex 1
a,at d , a+2d,a+ 3d,at 4d..
Ex 2, 5, 8, 11, 14, 17, so on. r
d= Cowmmon difference
=nth term- (n-1 'h term Sum
, 4. Quadratic equation (c) log,x = 1
ax +bx +C =0 log,9
() logn= 1
a, b, & Care constant in
which acan not be zero
n
log.x
(e) log=n logx
X= -bt Vb?-4ac () log,a x log, b =1
2a.
g) log,a =1
Sum of roots = a
, Products of roots = a
log,1 =O
Q. Find roots of equationx -5X +6 = 0;
find value of a, b &cby comparing with log2 = 0.30
ax + bx + C=O
Ans. a = 1, b= -5 & c=6 logo1 =O
X.=(-5) +V-s)?-4x2x6 log.o3 = 0.48 s O.s
2x1
=5+l1=z log,(sin 90°) =o
2
X, = 2 log.o5 + log20 = 2
Q. x - 4X = O
log,3 = logio3 -48
= 4X log.2 30
X= 4
wrong + Concept of Anti-log
log e = Y
x(x - 4) =0 By taking Anti-log
X=0; X=4 correct (convert
X= e
into concept of
power)
Q. x- 4X +3=0then find roots. MR*katadka
Ans. x - 3x - x+ 3=o
X(K-3) -1 (x -3) =0 log ’ Concept of Power
(x - 3) (x - 1) = o
=
TResult ’ log
X= 3, X = 1 Base
2 =3
S. Logarithms Base wahi rahega
log y' = log x on the base y interchange hoga) (Power Result
log, x = 2.303 log.oX G. Rule of
Power
(a) log, (xy) = log, x+ log, y 4 IfPower of
any
log x - log y non-zero
then result will be one number is zero
EX- 8°=1
Physics
