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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!!!!

A. 16000

B. 16500

C. 16050

D. 16005

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.

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.

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.^{2}+1, g(x) = x+1/x^{2}+1 and h(x) = 2x-3, find, f''[h'{g'(x)}].what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

Q112. Two common tangents to the circle x

^{2}+ y^{2}^{ }= 2a^{2}and parabola y^{2}= 8ax are(a) x = $\pm $(y +2a ) (b) y = $\pm $(x + 2a)

(c) x = $\pm $ (y + a) (d) y = $\pm $(x + a)

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,*).

how to prove that a given function is onto?

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

Is ther no differnce in sign...??

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

Let a relation R on the Set N of natural numbers be defined as (x,y)

~~belongs to R if and only if x~~^{2}-4xy+3y^{2}=0 for all x,y belongs to N.Verify that R is reflexive but not symmetric and transiitve.Show that the function f : R -- R defined byf(x) =x / x^{2}+1 , ( x belongs R)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

consider the set A containing n elements .Then the total number of injective functions from A onto itself isLET 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

If y=

(x+root(x^2+a^2))^n, prove that dy/dx=ny/(root(x^2+a^2)).difference between all india and delhi cbse

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

^{3 }+ x is a bijection.Please tell me the chapter wise marks distribution in physics, chemistry, and maths in boards...

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

The first three terms of an AP are respectively 3y-1, 3y+5 and 5y+1. Then calculate the value of y.which is the best maths guide book for class XII(CBSE)

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

^{2}+ x+1 is one one but not onto.(A) 7

(B) 8

(C) 9

(D) 10

(E) 11

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

^{2}+ 6x âˆ’ 5. Show that f is one one,onto hence invertibleFind the equation of the plane passing through intersection of the plane 4x-y+z=10 and x+y-z=4 and parallel to the line with direction ratios proportional to (2,1,1). Find also perpendicular Distance of (1,1,1) From this plane.

if 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

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?

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

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

USING COMPLETING SQUARE METHOD ONLY

Find domain of 10

^{x}+10^{y}=10.Plzz answer ASAP

the binary operation *:R x R--->R is defined as a*b=2a+b.Find (2*3)*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???

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

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

Solve this :Q. Let the product of all the divisors of 1440 be P. If P is divisible by 24

^{x}, then the maximum value of x is :(a) 28 (b) 30

(c) 32 (d) 36

^{x }and g(x) = logx ( x>0), find fog and gof. Is fog = gof?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]

^{2}x + sin^{2}(x+pi/3)+ cosx*cos(x+pi/3), and g(5/4)=1 then find gof(x)The curve represented by x =3(cost + sint) , y=4(cost - sint) is

a. ellipse

b. parabola

c. hyperbola

d. circle

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

^{3}kg/m3 and viscosity of water = 103 Pa.s) close to (A) 11,000 (B) 550 (C) 5500 (D) 1100A binary operation * on the set {0,1,2,3,4,5} is defined as

a*b ={a+b if a+b<6 & a+b-6 if a+b>=6

Show that zero is the identity for this operation and each element 'a' of the set is invertible with 6-a, being the inverse of 'a'.