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how to get 100 in maths class 12 board exam 2014

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

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.(i) A

_{1}= {1,3,}, A_{2}= {2}, A_{3}= {4,7}.(ii) B

_{1}= {1,2,5,7}, B_{2}= {3},B_{3}= {4,6}.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,*).

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

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 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.

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._{7}= {1,2,3,4,5,6,7} does the following partition give rise to an equivalence relation? Why?A

_{1}= {1,2,5,7} A_{2}= {3} A_{3 = }{4,6}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

_{7}= {1,2,3,4,5,6,7}, does the following partitions give rise to an equivalence relation? Why?A

_{1}={1,2,5,7}, A_{2}={3}, A_{3}={4,6}.difference between all india and delhi cbse

## At six months’ intervals A deposited of Rs. 1000 in a savings account which credit interest at 10% p.a.,

compounded semi-annually. The first deposit was made when A’s son was 6 months old and last deposit

was made when his son was 8 years old. The money remained in the account and was presented to the

son on his 10th birthday. How much did he receive?

## (a) Rs.25740

(b) Rs.23740

(c) Rs.25860

(d) Rs.25760

If y=

(x+root(x^2+a^2))^n, prove that dy/dx=ny/(root(x^2+a^2)).^{7})e^{(x^5 Sgn(x)^9) is a.odd b.even c.neither d.constant}^{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...

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.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)

f:R → Rdefined by $f\left(x\right)=2{x}^{3}-7\mathrm{for}x\in \mathbf{R}$ is bijective.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

PLEASE ANSWER ASAP!!

ALSO EXPLAIN IT!!

_{+}[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={1,3,5}; B= {9,11} R = {(a,b) belongs to AxB:a-b is odd} Write the relation R

Find domain of 10

^{x}+10^{y}=10.F(x)= sin^2x - sinx +1

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

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} .

a. 11

b. 14

c. 13

d. 12

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.

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 .

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

find the identity element of a*b=ab/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???

^{2}x + sin^{2}(x+pi/3)+ cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x)^{2}for all real x, then f (x) isShow 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

^{5}C_{r}consider the set A containing n elements .Then the total number of injective functions from A onto itself ispls 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 ..