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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!!!!

^{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

_{R}^{2 }and gof (x) = sin^{2}x. Then find f(x) and g(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.A. 16000

B. 16500

C. 16050

D. 16005

if n(A)=n(B)=3, then how many bijective functions from A to B can be formed?

what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

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}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,*).

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

Show that the function f : R -- R defined byf(x) =x / x^{2}+1 , ( x belongs R)is neither one-one nor onto....F(x)= sin^2x - sinx +1

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?

Find domain of 10

^{x}+10^{y}=10.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.period of function

f(x) = cos(tanx+cotx) *cos(tanx-cotx)Please post answers of r.s. aggarwal of class 12 mathematics

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

1. (fof)of

2. fo(fof)

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

^{2}+ x+1 is one one but not onto.f: X → Y andg: Y → Z be two invertible functions. Thengofis also invertible with (gof)^{–1}=f^{ –1}og^{–1}.^{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...

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

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

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

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

^{2}+ 6x âˆ’ 5. Show that f is one one,onto hence invertibleconsider the set A containing n elements .Then the total number of injective functions from A onto itself isif 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

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}.

_{+}[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?

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 alliif any two function f and g : R→ R

f(x) = 3x+4

and gof(x) = 2x-1

then find g(x) ?????

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...??

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.

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

a) n/12

b) n/4

c) n/2

d) 2n/5

e) 2n/3

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.

Please answer all with explanation

In two different societies, there are some college going students - including girls as well as

boys.

Satish forms two sets with these students, as his college project.

Let A = {a1 , a2 , a3 , a4 , a5} and B {b1 , b2 , b3 , b4} where ai ?s and bi ?s are the school going

students of first and second society respectively.

Satish decides to explore these sets for various types of relations and functions.

Using the information given above, answer the following :

(i) Satish wishes to know the number of reflexive relations defined on set A. How many

such relations are possible?

(a) 0

(b) 2

5

(c) 2

10

(d) 220

(ii) Let R : A? A , R = { (x, y) : x and y are students of same sex } . Then relation R is

(a) reflexive only

(b) reflexive and symmetric but not transitive

(c) reflexive and transitive but not symmetric

(d) an equivalence relation

(iii) Satish and his friend Rajat are interested to know the number of symmetric relations

defined on both the sets A and B, separately. Satish decides to find the symmetric

relation on set A, while Rajat decides to find the symmetric relation on set B. What is

difference between their results?

(a) 1024

(b) 2

10 (15)

(c) 2

10 (31)

(d) 2

10 (63)

(iv) Let R : A? B , R = { (a1 ,b1 ), (a1 ,b2 ), (a2 ,b1 ), (a3 ,b3 ), (a4 ,b2 ), (a5 ,b2 ) } then R is

(a) neither one-one nor onto

(b) one-one but, not onto

(c) only onto, but not one-one

(d) not a function

(v) To help Satish in his project, Rajat decides to form onto function from set A to B. How

many such functions are possible?

(a) 342

(b) 240

(c) 729

(d) 1024

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

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...

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???

Let * be a binary operation on Q

^{+}defined by a*b=ab/100 for all a,b belongs to Q^{+}.The inverse of 0.1 is?^{2}x + sin^{2}(x+pi/3)+ cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x)A speaks the truth 8 times out of 10 times. A die is tossed. He reports that it was 5. What is the probability that it was actually 5?

is it the questn of total probabilty , or bayes theorem . identify kaise krna h isko experts .

shukria .

Det =| log x 10 1|

| log y 13 1|

| log z 15 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

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 ..