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how to get 100 in maths class 12 board exam 2014

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

^{3 }+ x is a bijection.cos[tan-1{sin(cot-1 x)}] = [(1 + x^2)/(1 - x^2)]^-1

rnprove it!!!!

_{R}^{2 }and gof (x) = sin^{2}x. Then find f(x) and g(x).What do you mean by idempotent matrix?explain with example.

^{2}– 2x + 2 is onto function, find set A.(tan

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

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.

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.F(x)= sin^2x - sinx +1

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?

Find domain of 10

^{x}+10^{y}=10.11. 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 n(A)=n(B)=3, then how many bijective functions from A to B can be formed?

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

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

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

(a) 40 metres

(b) 39 metres

(c) 15 metres

(d) 10 metres

difference between all india and delhi cbse

Let S be the set of all real numbers.Show that the relation R={(a,b):a

^{2}+b^{2}=1} is symmetric but neither reflexive nor transitive.1. (fof)of

2. fo(fof)

If y=

(x+root(x^2+a^2))^n, prove that dy/dx=ny/(root(x^2+a^2)).A. 16000

B. 16500

C. 16050

D. 16005

^{2}+1, g(x) = x+1/x^{2}+1 and h(x) = 2x-3, find, f''[h'{g'(x)}].Please tell me the chapter wise marks distribution in physics, chemistry, and maths in boards...

if any two function f and g : R→ R

f(x) = 3x+4

and gof(x) = 2x-1

then find g(x) ?????

The first three terms of an AP are respectively 3y-1, 3y+5 and 5y+1. Then calculate the value of y.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}Prove that the function f: NN, defined by f(x) = x

^{2}+ x+1 is one one but not onto.period of function

f(x) = cos(tanx+cotx) *cos(tanx-cotx)which is the best maths guide book for class XII(CBSE)

Consider f: R+ → [−5, ∞) given by f(x) = 9x

^{2}+ 6x − 5. Show that f is one one,onto hence invertiblef(x) = (sin x + sin 3x + sin 5x + sin 7x)/( cos x + cos 3x + cos 5x + cos 7x) is

1) π/6

2) π/3

3) π/4

4) π/2

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

_{+}[9,infinity]f(x)=5x

^{2}+6x-9.Prove that f is invertible

USING COMPLETING SQUARE METHOD ONLY

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 that the function>[-7,∞) defined by f(x)=25x

f: [0,∞)^{2 }+ 10x -7 is one-one and onto^{. }Find f inverse.f: X → Y andg: Y → Z be two invertible functions. Thengofis also invertible with (gof)^{–1}=f^{ –1}og^{–1}.consider the set A containing n elements .Then the total number of injective functions from A onto itself isIf a and b are positive integers with no common factor , show that

[a/b] + [2a/b] + [3a/b] + ... + [(b-1)a/b] = (a-1)(b-1)/2,

where [.] denotes the greatest integer function.

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} .

then find L and 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.

Det =| log x 10 1|

| log y 13 1|

| log z 15 1|

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???

|cos6x| , where [] is greatest integer function and | | denotes modulus function . Answer is 2π/3

^{2}x + sin^{2}(x+pi/3)+ cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x)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

276 x+128 $\equiv $4(mod 7)

[Hint : 276 $\equiv $ 3, 128 $\equiv $2 (mod 7)]

pls someone solve these problems

1. show that f:R-R defined by f(x) = 2x

^{3}-7 for all x belonging to R is bijective2. f(x) = x+7 g(x) = x-7 x belonging to R find (fog)(7)

3.f(x) = x

^{3}g(x)= cos3x find fog(x)4.f:R-R f(x) = x/x

^{2}+1 find f (f (x))5. f:R-R f(x) = x

^{2 }- 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 ..