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how to get 100 in maths class 12 board exam 2014

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

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

rnprove it!!!!

(tan

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

Show that the function f : R -- R defined byf(x) =x / x^{2}+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.

A. 16000

B. 16500

C. 16050

D. 16005

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.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.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,*).

how to prove that a given function is onto?

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

^{3 }+ x is a bijection.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

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

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.

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

Is ther no differnce in sign...??

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

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

R3 on R defined by (a,b) belongs to R3< => a2-4ab+3b2=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 invertibleLet a relation R on the Set N of natural numbers be defined as (x,y)

~~belongs to R if and only if x~~^{2}-4xy+3y^{2}=0 for all x,y belongs to N.Verify that R is reflexive but not symmetric and transiitve.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 R={(x,y): x,y belongs to Z, y=2x-4}.If(a,-2) and (4,b2) belongs to R , then write the values of a and b.

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?

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.

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

^{2}+ x+1 is one one but not onto._{+}[9,infinity]f(x)=5x

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

USING COMPLETING SQUARE METHOD ONLY

find range of f(x)=3sin(root(pi

^{2}/16) -x^{2})(A) 7

(B) 8

(C) 9

(D) 10

(E) 11

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

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???

^{x }and g(x) = logx ( x>0), find fog and gof. Is fog = gof?If y root(x2+1)=log(root(x2+1)-x), show that (x2+1) dy/dx+xy+1=0

(1) 20 m (2) 64 m (3) 32 m (4) 128 m

find the domain of the function f(x)=1/root(x+mod x)?plese mention imideiately

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]

the sum of the rational terms in the binomial expansion of (2^1/2 + 3^1/5)^10 ??

^{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

A binary operation * on the set {0,1,2,3,4,5} is defined as

a*b ={a+b if a+b<6 & a+b-6 if a+b>=6

Show that zero is the identity for this operation and each element 'a' of the set is invertible with 6-a, being the inverse of 'a'.

^{-1}+b^{-1}+c^{-1}?Show that

1.(a,a)€R for all a€Q

2(a,b)€R implies (b, a) €R

3(a,b) €R, (b, c) €R implies (a, c) €R

Let * be the binary operation on

Ngiven bya*b= L.C.M. ofaandb. Find(i) 5 * 7, 20 * 16 (ii) Is * commutative?

(iii) Is * associative? (iv) Find the identity of * in

N(v) Which elements of

Nare invertible for the operation *?