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!!!!

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}

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

let f:z-z:f(n)=3n and let g:z-z defined by

g(n)=n/3 if n multiple of 3

0 if n is not a multiple of 3

show that gof=Iz and fog not =Iz

(tan^{-1 x})^{2}+ (cot-^{1}_{x})^{2}= 5 pi^{2}/ 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.

what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

show that the function f: R ---->R given by f(x)=x^{3 }+ x is a bijection.

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 / x^{2} +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?

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

let f; N-R be a function defined as f(x) = 4x^{2}+12x +15. show that F:N - S where s is the range of f , is invertible. find the inverse of f.

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

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

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

rnprove it!!!!

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

let f:z-z:f(n)=3n and let g:z-z defined by

g(n)=n/3 if n multiple of 3

0 if n is not a multiple of 3

show that gof=Iz and fog not =Iz

(tan

^{-1 x})^{2}+ (cot-^{1}_{x})^{2}= 5 pi^{2}/ 8find value of x

^{i}θ(r > 0 and π < 0< 3π ) is aroot of the equation

Z

^{8}– Z^{7}+Z6 – 7^{5}+ z^{4}– z³ + Z^{2}–Z +1= 0.If the sum of all values of

θis kπ, then kis equal to...........?

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

denote the set of all natural numbers andNbe the relation onRNXdefined byN( a,b )R( c,d )both sided arrowad ( b + c ) = bc ( a + d )Prove that

is an equivalence relation onRNxN.^{2}/x^{2}+1 is surjective, then find the set Awhat are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

show that the function f: R ---->R given by f(x)=x

^{3 }+ x is a bijection.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 byf(x) =x / x^{2}+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?

If y=

(x+root(x^2+a^2))^n, prove that dy/dx=ny/(root(x^2+a^2)).let f; N-R be a function defined as f(x) = 4x

^{2}+12x +15. show that F:N - S where s is the range of f , is invertible. find the inverse of f.Please post answers of r.s. aggarwal of class 12 mathematics

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

_{R}^{2 }and gof (x) = sin^{2}x. Then find f(x) and g(x).