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how to get 100 in maths class 12 board exam 2014

_{1}=1+i then the minimum value of |z-z_{1}| is ???cos[tan-1{sin(cot-1 x)}] = [(1 + x^2)/(1 - x^2)]^-1

rnprove it!!!!

^{2}– 2x + 2 is onto function, find set A.What do you mean by idempotent matrix?explain with example.

(tan

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

(i) Let f(x)= x^3+x^2+ax+4 be bijective , then find a .

(ii) Let f(x)=x^3+bx^2+cx+d is bijective , then find the condition.

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.

Write the range of the principal branch of sec

^{-1}x defined on domain R-(-1,1).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.in a state with population of 75 x 10 raise to 6 ,45% of them know hindi,22%know english,18%know sanskrit.,12% know hindia and english,8%know english and sanskrit,10%know hindi and sanskrit,and 5%know ol three .

then answer wt is the nmbr of ppl who do not know any of these languagae,

how many ppl know hindi only

how many know sanskrit only

how many know eng only

nmbr of ppl who know only one language

and nmbr of ppl who know two language

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}.

what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

A. 16000

B. 16500

C. 16050

D. 16005

how to calculate the number of binary operations on any set A , say of 4 elements?

if any two function f and g : R→ R

f(x) = 3x+4

and gof(x) = 2x-1

then find g(x) ?????

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,*).

f(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

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?

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 is trivially transitive relation.

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

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)).^{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...

Every arbitrary equivalence relation

Rin a setXdividesXinto mutually disjoint subsets (A_{i}) called partitions or subdivisions ofXsatisfying the following conditions:All elements of

Sir , I can't under stand the line means. Plz explain in brief.A_{i}are related to each other for alliThe first three terms of an AP are respectively 3y-1, 3y+5 and 5y+1. Then calculate the value of y.276 x+128 $\equiv $4(mod 7)

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

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

^{2}+ x+1 is one one but not onto.^{2}- q^{2}) = 7pq where p and q are positive, then p:q will be?show that the function f: R ---->R given by f(x)=x

^{3 }+ x is a bijection.f: X → Y andg: Y → Z be two invertible functions. Thengofis also invertible with (gof)^{–1}=f^{ –1}og^{–1}.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 invertible^{2}/x^{2}+1 is surjective, then find the set Aif 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

∀a, b ∈ Z, a ∗ b = a + 3b − 1.

Prove that the operation is binary.

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

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

USING COMPLETING SQUARE METHOD ONLY

Find whether

f:Z- Zdefined by f(x) = x^{2}+ 5 for all x belongs Z is one one or not.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?

a) [-8,8]

b) [-8,0]

c) [-6,6]

d) [0,8]

e) there is no interval

Find domain of 10

^{x}+10^{y}=10.(1-2x-3x

^{2}) / (3x-x^{2}-5) >0 ;then what is the value of x?Is it necessary that fo(g+h) is always equal to (fog) + (foh)? Explain using an example.

f: R → R given byf(x) = 3 – 2 sinxis(a) one-one (b) onto (c) bijective (d) None of these

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}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...??

Q.39. A newspaper costs Rs. 11 to print on a daily basis. Its sale price (printed) is Rs. 3. The newspaper gives a sales incentive of 40 % on the printed price, to the newspaper vendors. The newspaper makes up for the loss through advertisements, which are charged on the basis of per column centimetre rates. The advertisement rates of the newspaper are Rs. 300 per cc (column centimetre). It has to give an incentive of 15 % on the advertising bill to the advertising agency. If the newspaper has a circulation of 12,000 copies, what is the approximate minimum advertising booking required if the newspaper has to break-even on a particular day. (Assume there is no wastage)

(a) 300 cc

(b) 350 cc

(c) 435 cc

(d) 450 cc

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

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.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.

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???

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

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

Show that the function f: R-->R defined by f(x)= 3x^3+ 5 for all x belongs to R is bijective.

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 ..

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