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how to get 100 in maths class 12 board exam 2014

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

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

rnprove it!!!!

what is trivially transitive relation.

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

A. 16000

B. 16500

C. 16050

D. 16005

(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.

^{2}– 2x + 2 is onto function, find set A.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.Find the value of m for which the function f(x)=2x2-5x+3 / 4x-m takes all real values for x belonging to R.

what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

(Answer is 0)

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,*).

^{2}- q^{2}) = 7pq where p and q are positive, then p:q will be?Show that the function f : R -- R defined byf(x) =x / x^{2}+1 , ( x belongs R)is neither one-one nor onto....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...

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

f: X → Y andg: Y → Z be two invertible functions. Thengofis also invertible with (gof)^{–1}=f^{ –1}og^{–1}.how to prove that a given function is onto?

then find L and a

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

Chapters are as follows :

1.relation and function

2. matrices

3. determinants

f(x)=1/log(to the base e)|x| is continuous is

A 1

B 2

C 3

D 4

E infinitely many

Explain.

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

URGENT ! URGENT ! URGENT!

(CONIC SECTIONS :PARABOLA,HYPERBOLA AND ELLIPSE)

Find the equation of conic section whose focus is (ac,0) ,directrix is the line ex=a and eccentricity is e.State whether the conic section is ellipse or a hyperbola..

If y=

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

Ans - 54

_{1}=1+i then the minimum value of |z-z_{1}| is ???^{x}w.r.t sin^{-1}x^{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...

Further, 70 persons in the group and Muslims and the remaining

Hindus. Then the number of Bengali Muslims in the group is

(a) 30 or more

(b) Exactly 20

(c)Between 15 and 25

(d) Between 20 and 25

The 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.Find whether

f:Z- Zdefined by f(x) = x^{2}+ 5 for all x belongs Z is one one or not.^{-1}+b^{-1}+c^{-1}?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)

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

^{2}+ 6x âˆ’ 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

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) Mrs. Panikkar is Chanchala.

(b) Anita's husband had 8 bottles.

(c)Mr. Narayan had 12 bottles.

(d) Mrs. Rao is Dipti.

(permutations and combinations )

Find domain of 10

^{x}+10^{y}=10.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 binary operation *:R x R--->R is defined as a*b=2a+b.Find (2*3)*4

for proving that a function is one - one or injective,

f: R-R

we consider ( x1,x2) belonging to R

f(x1) = f(x2)

how does proving x1 = x2 imply that they are injective?

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

Is ther no differnce in sign...??

Is it necessary that fo(g+h) is always equal to (fog) + (foh)? Explain using an example.

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

^{2}for all real x, then f (x) isfor 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

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

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)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

AandBbe sets . Show that f :AXB--->BXAsuch thatf (a,b)=(b,a)is bijective function.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]

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

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 ..