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!!!! 

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

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

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

f(x) =x / x² +1 , ( x belongs R)

is neither one-one nor onto....

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.

Let S be the set of all real numbers.Show that the relation R={(a,b):a²+b²=1} is symmetric but neither reflexive nor transitive.

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 .

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,*).

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.

Let A=R-{3} and B=R-{2/3}, If f : A gives to B such that f (x)= (2x-4)/(3x-9), then prove that f is a bijective function

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

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

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.

1. Let f: R - R be a function given by f(x) = ax + b for all x element R. Find the constants a and b such that fof = I_R
2. Let f : R - R and g : R - R be two functions such that fog(x) = sin x² and gof (x) = sin²x. Then find f(x) and g(x).

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

show that function f:N ---> N, given by f(1) = f(2) = 1 and f(x) = x-1 , for every x > 2 , is onto but not one to one.

plz donot give the ncert soln as its not clear.

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)).

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}.

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.

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

Show that each of the relation R in the set A = {х Z :0 ≤ x ≤ 12} ,given by R ={(a,b) : | a-b| is a multiple of 4 is an equlance relarion . Find the set of elements related to 1

solution in the text book could not be followed kindly explain in detail.

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

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

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 ..

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 .

 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?

Let N be the set of all natural numbers and let R be a relation in N, defined by

R={(a,b): a is a factor of b}

Then, show that R is reflexive and transitive but not symmetric

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

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} .

If f:R -- R given by f(x) = x² +3x+1 and g:R-- R given by g(x) = 2x-3.Find gof and fog.

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???

if any two function f and g : R→ R

f(x) = 3x+4

and gof(x) = 2x-1

then find g(x) ?????

if n(A)=n(B)=3, then how many bijective functions from A to B can be formed?

 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]