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how to get 100 in maths class 12 board exam 2014

A. 16000

B. 16500

C. 16050

D. 16005

cos[tan-1{sin(cot-1 x)}] = [(1 + x^2)/(1 - x^2)]^-1

rnprove it!!!!

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

f: X → Y andg: Y → Z be two invertible functions. Thengofis also invertible with (gof)^{–1}=f^{ –1}og^{–1}.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.

Find whether

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

consider the set A containing n elements .Then the total number of injective functions from A onto itself ishow 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 each of the relation R in the set A = {х Z :0 ≤ x ≤ 12} ,given by R ={(a,b) : | a-b| is a multiple of 4 is an equlance relarion . Find the set of elements related to 1

solution in the text book could not be followed kindly explain in detail.

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

^{2}/x^{2}+1 is surjective, then find the set Ahow to prove that a given function is onto?

Conduct a survey at population in your locality taking a sample of atleast 50 families. Prepare a project report with respect to the following points:

i) Represent the data showing age using class intervals.

ii) Compute the average income of the families.

iii) Literacy level of the population in terms of Elementary, Secondary, Senior Secondary, Graduation and above.

iv) Find the variance of the income of the families.

v) Represent the data in part (iii) with the help of bar graph.

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.urgent!!

show that the function f: R-----> R defined by f(x) = sin (2x+5) is neither one-one nor onto

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

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

If y=

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

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

(ii) symmetric and transitive

(iii) reflexive and symmetric

(iv) reflexive and transitive

^{2}+1, g(x) = x+1/x^{2}+1 and h(x) = 2x-3, find, f''[h'{g'(x)}].if A,B,C and A',B',C' are points on 2 parallel lines such that AB/A'B'=BC/B'C' then prove that AA',BB',CC'are concurrent if they are not parallel?

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

^{2}for all real x, then f (x) isThe first three terms of an AP are respectively 3y-1, 3y+5 and 5y+1. Then calculate the value of y.Prove that the function f: NN, defined by f(x) = x

^{2}+ x+1 is one one but not onto.what is trivially transitive relation.

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

^{3 }+ x is a bijection.which is the best maths guide book for class XII(CBSE)

Det =| log x 10 1|

| log y 13 1|

| log z 15 1|

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

^{2}+ 6x − 5. Show that f is one one,onto hence invertibleif 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

(A)

f(x) is one-one(B)

f(x) is not continuous(C)

f(x) is not one-one(D) domain of function is not the set of real numbers

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

1). {(1,1), (2,1), (3,1)}

2). {(1,1), (1,2)}

3). {(2,3), (3,1)}

4). {(1,1), (2,2), (3,3), (1,3), (3,1)}

Find domain of 10

^{x}+10^{y}=10.^{2}– 2x + 2 is onto function, find set A.URGENT ! URGENT! URGENT!

COMPLEX NUMBERS

Show that 1-i and 1-1/i are two conjugate complex numbers ,find the amplitude of the product of the numbers

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} .

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}.

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

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)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

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

let set A={1,2,3} .Then show that the number of relations containing (1,2) and (2,3) which are reflexive and transitive but not symmetric is three...

show that each of the relation in the set A = { x E Z : 0

x12 }, given by ,(a) R = {(a,b) : Ia-bI is a multiple of 4} . (b) R ={(a,b): a = b}is an equivalrnce relation - i understood this part, but the next one i didnt get it -Find the set of all elements related to 1 in each case...pls answer sir srry for my previous mistake i'll not repeat that again..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 ..

What is the range of f(x) = lx-1l / (x-1) ? How do we calculate range?