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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

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

what are real numbers?

what are natural numbers?

what are integers?

what is difference between them?

tell thm in detail with examples

(A) 7

(B) 8

(C) 9

(D) 10

(E) 11

how to calculate the number of binary operations on any set A , say of 4 elements?

If y=

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

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?

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

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

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

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

^{-1}+b^{-1}+c^{-1}?^{2}+1, g(x) = x+1/x^{2}+1 and h(x) = 2x-3, find, f''[h'{g'(x)}].Consider f: R+ â†’ [âˆ’5, âˆž) given by f(x) = 9x

^{2}+ 6x âˆ’ 5. Show that f is one one,onto hence invertible_{R}^{2 }and gof (x) = sin^{2}x. Then find f(x) and g(x).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

_{+}[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?

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

Is ther no differnce in sign...??

f: X → Y andg: Y → Z be two invertible functions. Thengofis also invertible with (gof)^{–1}=f^{ –1}og^{–1}.^{3}kg/m3 and viscosity of water = 103 Pa.s) close to (A) 11,000 (B) 550 (C) 5500 (D) 1100Find domain of 10

^{x}+10^{y}=10.^{th }word in the list is :(a) W

(b) D

(c) M

(d) C

the binary operation *:R x R--->R is defined as a*b=2a+b.Find (2*3)*4

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

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

$65.Thenumberofpositiveintegralsolutionsoftheequation{x}_{1}{x}_{2}{x}_{3}{x}_{4}{x}_{5}=1050is\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\left(a\right)1800\left(b\right)1600\left(c\right)1400\left(d\right)1875$

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???

a. 11

b. 14

c. 13

d. 12

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

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]

find identity element and inverse of each element of X

plz answer asap its urgent

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

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

under root of 4x-9 +

under root of 4x+9 = 5+ root7

in this question in the last step we equalize 8x=32 with what concept?

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

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

12 grams (g) of a chemical are added to a metal. The amount, A, in grams of the chemical remaining during a reaction with a metal plate, decrease by 0.5 g every second. If instead the plate were dissolved, the amount, , in grams of chemical remaining, would decrease by a factor of 2 every four seconds. How much greater is A than in grams after 12 seconds?

how to solve this question

can anyone explain it elaborately

chapter (exponential growth)