State true or false : If f(x)=(x+1/x)^(2...

State true or false : If `f(x)=(x+1/x)^(2n)+(x-1/x)^(2n)` the `f(x)` is a polynomial function which is an even function.

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Statement I The function f(x) = int_(0)^(x) sqrt(1+t^(2) dt ) is an odd function and g(x)=f'(x) is an even function , then f(x) is an odd function.

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1+x) then (1) g(x) is an odd function (2)g(x) is an even function (3) graph of f(x) is symmetrical about the line x=1 (4) f'(1)=0

Statement 1: If f(x) is an odd function,then f'(x) is an even function.Statement 2: If f'(x) is an even function,then f(x) is an odd function.

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Find a polynomial function f(x) such that f(2x)=f'(x)f''(x)

If f(x)=|(1,x,x+1),(2x, x(x-1(, x(x+1)),(3x(x-1), x(x-1)(x-2), x(x-1)(x+1))| then (A) f(x) is a polynomial of degree 4 (B) f(x) is an odd function (C) f(x) is a costant function (D) f(x) is an even function

If int(x^(2)-x+1)/((x^(2)+1)^((3)/(2)))e^(x)dx=e^(x)f(x)+c, then f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1)f(x) has two points of extrema

If f is a real valued function, not identically zeroand satisfying f(x_1 + x_2)) + f(x_1 - x_2) = 2 f(x_1)f(x_2)forall x_1,x_2 , then f(x) is (1) An odd function(2) An even function (3) Neither even nor odd(4) f(0) = 1/2

The function f(x)=lim_(n rarr oo)(x^(^^)(2n)-1)/(x^(^^)(2n)+1)^(-) is identical with the function

A DAS GUPTA-Binomial Theorem for Positive Integrel Index-Exercise

If n is even then the coefficient of x in the expansion of (1+x)^n*(1-...
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The sum of ""^21C0+""^21C1+""^21C2+...+""^21C10 is equal to .
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The coefficient of x^(n) y^(n) in the expansion of [(1 + x)(1+y) (x...
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The number of terms in the expansion of (1+2x+x^2)^n is :
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The number of terms in the expansion of (1+7sqrt(2x))^9+(1-7sqrt(2x))^...
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In the expansion of (x^(3) - (1)/(x^(2)))^(15) , the constant term,i...
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The largest coefficient in the expansion of (1+x)^24 is
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3^(51) when divided by 8 leaves the remainder 2 2. 6 3. 3 4. 5 5. 1
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The sum of the series ""^20C0+""^20C1+""^20C2+...+""^20C9 is =
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If C(r) stands for ""^(n)C(r), then the sum of the series (2((n)/(2))!...
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If pa n dq are ositive, then prove that the coefficients of x^pa n dx^...
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The number of dissimilar terms in the expansion of (a+2b+3c)^8 is
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In the expansion of (1+x)^(2m)(x/(1-x))^(-2m) the term independent of ...
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State true or false : The integral part of (8+3sqrt7)^20 is odd.
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State true or false : In the expansion of (x^2/y+y^2/x)^15 there is no...
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State true or false: In the expansion of (1+2x+x^2)^9 there is exactly...
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State true or false : In the expansion of (x+1/x)^13 every term is a f...
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State true or false : If f(x)=(x+1/x)^(2n)+(x-1/x)^(2n) the f(x) is a ...
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State whether the statements are true or false : ""^16C0-""^16C1+""^16...
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