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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!!!!

Find the equation of the plane passing through intersection of the plane 4x-y+z=10 and x+y-z=4 and parallel to the line with direction ratios proportional to (2,1,1). Find also perpendicular Distance of (1,1,1) From this plane.

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

Prove that the function f: NN, defined by f(x) = x

^{2}+ x+1 is one one but not onto.(tan

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

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.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 given by f(x)=x

^{3 }+ x is a bijection.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?

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

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

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.^{2}+1, g(x) = x+1/x^{2}+1 and h(x) = 2x-3, find, f''[h'{g'(x)}].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)).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 ..

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

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

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

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

Consider f: R+ â†’ [âˆ’5, âˆž) given by f(x) = 9x

^{2}+ 6x âˆ’ 5. Show that f is one one,onto hence invertibleunder root of 4x-9 +

under root of 4x+9 = 5+ root7

in this question in the last step we equalize 8x=32 with what concept?

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

Find domain of 10

^{x}+10^{y}=10.R--->Rbe 2 functions defined as f(x) = |x| + x and g(x) = |x|-x for everyx~~E~~R.Then find fog and gof.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} .

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???

A. 16000

B. 16500

C. 16050

D. 16005

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.

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

consider the set A containing n elements .Then the total number of injective functions from A onto itself isSolve for x:

_{+}-->[5,infinity] given by f(x)=9x^{2}+6x-5 show that f is invertible and also find the inverse of f ?