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What is the inverse of x[x] ?
[x] is greatest integer function.

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Ans. For inverse of a function to be defined it should be bijective function.
f(x) = x−n when x∈(n,n+1) and f(x)=0 when x = n
=> f(x) is not oneone function but is many to one function.
=> f(x) is not bijective function
So f^{1}(x) is not defined.
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Can phi be included in any relation R from A to B...??

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Sin y =x sin (a+y)
Prove that : dy/dx= sin x/12xcosx+ x^2

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Sin^{1(tan5π/4)}

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{tex}\tan{5\pi\over4}{/tex} = {tex}\tan({\pi + {\pi\over4}}){/tex} = {tex}\tan{\pi\over4}{/tex}
{tex}\sin^{1}({\tan{\pi\over4}}){/tex} = {tex}\sin^{1}({1}){/tex} = {tex}\pi\over2{/tex}
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If f (x) = 3x^2 9x+7 for any square matrix A then write f (A)

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{tex}f\left( A \right) = 3{A^2}  9A + 7I{/tex}
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Find the principal value of sin^{1}(√31/2√2)

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tan^{1 }x3/x4. +. tan^{1} x+3/x+4. =. π/4

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I think it is x2 and x +2 instead of x3 and x +3 respectively
Ans.
{tex}tan^{1} ({x2\over x4})+ tan^{1}( {x+2\over x+4}) = {\pi \over 4}{/tex}
Using{tex}tan^{1} x + tan^{1}y = tan^{1} ({x+y\over 1xy}){/tex}
=> {tex}tan^{1} ({{x2\over x4} + {x+2\over x+4}\over 1( {x2\over x4} \times {x+2\over x+4})}) = {\pi \over 4}{/tex}
=> {tex}tan^{1}({2x^216\over 12}) = {\pi \over 4}{/tex}
{tex}=> {2x^216\over 12}= tan^{1} {\pi \over 4}{/tex}
{tex}=> {2x^216\over 12}= 1{/tex}
{tex}=> 2x^216= 12{/tex}
{tex}=> 2x^2= 4 => x^2 = 2{/tex}
{tex}x = \sqrt 2{/tex}
if you use 3 answer ll be {tex}x = \sqrt {17\over 2}{/tex}
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Find the matrix A such that
Matrix of ( 2. 1. (1. 8
1. 0. * A=. 1. 2
3. 4) 9. 22)

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There are 4 cards numbered 1,3,5and 7 one number on one card . Two cards are drawn at random! Without replacement . Let x denote the sum of the numbers on the two cards .Find the mean and variance of x

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Find the value of x such that the points are coplanar A(3,2,1), B(4,x,5),. C(4,2,2) and D(6,5,1)

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Ans.
Points are A(3,2,1), B(4,x,5), C(4,2,2) And D(6,5,1).
Position Vector of A = {tex}3\hat i + 2\hat j + \hat k{/tex}
Position Vector of B = {tex}4\hat i + x\hat j + 5\hat k{/tex}
Position Vector of C = {tex}4\hat i + 2\hat j 2\hat k{/tex}
Position Vector of D = {tex}6\hat i + 5\hat j \hat k{/tex}
{tex}=> \overrightarrow {AB} = \hat i + (2x)\hat j + 4\hat k{/tex}
{tex}=> \overrightarrow {AC} = \hat i + 0\hat j 3\hat k{/tex}
{tex}=> \overrightarrow {AD} = 3\hat i + 3\hat j 2\hat k{/tex}
As points are coplaner, then triple scaler product is zero,
So,
{tex}\begin{bmatrix} 1& (x2) & 4 \\[0.3em] 1 & 0 & 3 \\[0.3em] 3 & 3 & 2 \end{bmatrix} = 0{/tex}
Expanding along R_{2}
=> 1[2(x2) 12] (3)[33(x2)] = 0
=> 2x 4+12 +99x +18 = 0
=> 7x +35 = 0
=> 7x = 35
=> x = 5
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Using the method of integration find the area of the triangle ABC , coordinates of whose vertices are A(4,1). B(6,6),. C(8,4)

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Find the coordinates of the point where the line through the points (3,4,5)and (2,3,1),crosses the plane determined by the points (1,2,3),(4,2,3)and (0,4,3).

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(1,2,7)
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Will teachers will do linent marking or strict marking in mathematics

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What is the minimum passing marks required for mathematics in class12?

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33% marks are required to pass any subject.
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find the area enclosed between the parabola 4y= 3x^{2 and the straight line 3x 2y+12=0}

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how will be the evalution of maths examination conducted today be?

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integration of sin inverse x divide by x

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For what value of k ,the system of linear equatoin
X+y+z=2
2x+yz=3
3x+2y+kz=4

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Important. Question given by u r from ncert only?

Are most of the questions given tomorrow in the exam are from ncert examples?
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Yeah......it is for sure.but dont depend on it fullt.practice other problems also.
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Find the shortest distance between the line xy+1=0 and thr curve y^{2}= x

pls teachers answer it quickly i really need ur help
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A signal which can be green or red with probability 4/5 and 1/5 respectivEly, is received by station A and then transmitted to station B. The probability of each receiving the signal correctly is 3/4. If the signal received at station B is green, then find the probability that original signal is green.

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3 no.s are selected at random from first 6 +ve integers. x denotes the smallest of 3 no.s selected . find the probabiloty distribution of x?

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How many marks are allotted to questions on 3D geometry?

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One 6 marks question will surely come
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The probablity of specific problems being solved independently by A and B are 1/2 and 1/3 respectively. If both tried to solve the problem independently find the probablity of
1. Both of them solved
2. None of them solve
3. The problem is solved

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i) 2/3
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if A=
1  2 
3  5 
then find the value of A^20095A^2008

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in a town there are 486 families having 6 children each . if probability of survival of a girl is 1/3 and that of boy is 2/3 . find the number of families having 2 girls and 4 boys

does this ques belong to 12 class or somehow 9 too?
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