how to get 100 in maths class 12 board exam 2014

cos[tan-1{sin(cot-1 x)}] = [(1 + x^2)/(1 - x^2)]^-1

prove it!!!! 

What do you mean by idempotent matrix?explain with example.

(tan^{-1 _x})²+ (cot-^1_x)²= 5 pi²/ 8

find value of x

if * is a binary operation on R defined by a*b= a+b+ab. prove that * is commutative and associative. find the idebtify element. also show that every element of R is invertible wxcept -1.

Let N denote the set of all natural numbers and R be the relation on N X N defined by

( a,b ) R ( c,d ) both sided arrow ad ( b + c ) = bc ( a + d )

Prove that R is an equivalence relation on N x N.

if any two function f and g : R→ R

f(x) = 3x+4

and gof(x) = 2x-1

then find g(x) ?????

1. Show that the relation R defined by R={(a,b):a-b is divisible by 3;a,b E N}is an equivalence relation .

Find the number of one-one functions from a finite set A to A ,where n(A) = p

what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples 

how to calculate the number of binary  operations on any set A , say of 4 elements?

11. Let A=QxQ.Let * be a binary operation on A defined by : (a,b)*(c,d) = (ac,ad+b).Find i) Identity element of (A,*) ii) the invertible element of (A,*).

Show that the function f : R -- R defined by

f(x) =x / x² +1 , ( x belongs R)

is neither one-one nor onto....

1] if cos-1 x/2 + cos-1 y/3 = theta, then prove that 9x2 - 12xy cos theta + 4y2 = 3b sin square theta .

2] simplify : cos-1 (3/5 cos x + 4/5 sin x )

3] if tan-1 a + tan-1 b + tan-1 c = pie , then prove that a + b + c = a.b.c

4] prove:

a) 2 tan-1 x = tan-1 ( 2x/ 1 - x2 )

b) sec2 ( tan-1 2 ) + cosec2 ( cot-1 3 ) = 15

how to prove that a given function is onto?

let f; N-R be a function defined as f(x) = 4x²+12x +15. show that F:N - S where s is the range of f , is invertible. find the inverse of f.

in a state with population of 75 x 10 raise to 6 ,45% of them know hindi,22%know english,18%know sanskrit.,12% know hindia and english,8%know english and sanskrit,10%know hindi and sanskrit,and 5%know ol three .

then answer wt is the nmbr of ppl who do not know any of these languagae,

how many ppl know hindi only

how many know sanskrit only

how many know eng only

nmbr of ppl who know only one language

and nmbr of ppl who know two language

Please post answers of r.s. aggarwal of class 12 mathematics

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

 LET A BINARY OPERATION*IS DEFINED BY a*b=ab/5 for all a,b belongs R-{0} THEN FIND THE VALUE x given by 2*(x*5)=10

difference between all india and delhi cbse

If y=(x+root(x^2+a^2))^n, prove that dy/dx=ny/(root(x^2+a^2)).

Is it necessary that fo(g+h) is always equal to (fog) + (foh)? Explain using an example.

Please tell me the chapter wise marks distribution in physics, chemistry, and maths in boards...

1. The first three terms of an AP are respectively 3y-1, 3y+5 and 5y+1. Then calculate the value of y.

Prove that the function f: NN, defined by f(x) = x² + x+1 is one one but not onto.

Show that the function f : [0,∞) >[-7,∞) defined by f(x)=25x^₂ + 10x -7 is one-one and onto^_. Find f inverse.

show that the function f: R ---->R given by f(x)=x³ + x is a bijection.

evaluate integral 5^x / 1 + 5^x - 5 ^2x .dx

which is the best maths guide book for class XII(CBSE)

Show that the function f: R-->R defined by f(x)= 3x^3+ 5 for all x belongs to R is bijective.

Consider f: R+ → [−5, ∞) given by f(x) = 9x² + 6x − 5. Show that f is one one,onto hence invertible

Find whether f:Z - Z defined by f(x) = x² + 5 for all x belongs Z is one one or not.

if the binary operation * on the set Z of integers is defined by a * b = a + b -5, then write the identity element for the operation * in Z

Find the value of m for which the function f(x)=2x2-5x+3 / 4x-m takes all real values for x belonging to R.

 How is aggregate calculated in CBSE report card of class 12th, if the Medical student has Maths as optional subject and Physical education is additional?

show tht the R on the set A={1,2,3,4,5},given by

R={(x,y):mod of a-b is evn},is an equivalence relation.

show that all the elements of[1,3,5} are related to each other al the elemnts of{2,4} are related to each other.But,no element of{1,3,5}related to any element of {2,4}.

Find domain of 10^x+10^y =10.

URGENT ! URGENT! URGENT!

COMPLEX NUMBERS

Show that 1-i and 1-1/i are two conjugate complex numbers ,find the amplitude of the product of the numbers

1. Show that f:N=N given be f(x)={x+1, if x is odd
2. x-1, if x is even } is bijectve .

the binary operation *:R x R--->R is defined as a*b=2a+b.Find (2*3)*4

Are equations of tangent and normal to parabola whether x2 =4ay or y2 =4ax is same...???

Is ther no differnce in sign...??

write the smallest equivalence relation R on set A ={1, 2, 3} .

for the set A={1,2,3} define the relation R in set A as follows:

R={(1,1) (2,2) (3,3) (1,3)}. write the ordered pairs to be added to R to make it the smallest equivalent relation.

If y root(x2+1)=log(root(x2+1)-x), show that (x2+1) dy/dx+xy+1=0

In a college of 300 students,every student reads 5 newspaper and every newspaper is read by 60 students. what is the number of newspaper???

(1-2x-3x²) / (3x-x²-5) >0 ;then what is the value of x?

For any relation R in any set A, we can define the inverse relation R^-1 by a relation a R^-1 b if and only if bRa.Prove that R is symmetric if and only if R=R^-1

 Show that the relation (R) defined by (a,b)R(c,d) -> a+d=b+c on the set N X N is an equivalence relation

pls someone solve these problems

1. show that f:R-R defined by f(x) = 2x³ -7 for all x belonging to R is bijective

2. f(x) = x+7 g(x) = x-7 x belonging to R find (fog)(7)

3.f(x) = x³ g(x)= cos3x find fog(x)

4.f:R-R f(x) = x/x² +1 find f (f (x))

5. f:R-R f(x) = x² - 3x + 2 find f (f (x))

6.f(x) = mode x  g(x) = [x] f:R-R find  fog(5/ 2) gof ( - square root 2)  where [ greatest integer function]

let f:n-n defined by f(x)= n+1/2, if n is odd

n/2, if n i even

state whether f is bijective ?

i know how to prove that f is 1-1 . i need help for if f is onto or not ..