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If (1+x+x^2)^n=a0+a1x+a2x^2+....+a(2n)x^...

If `(1+x+x^2)^n=a_0+a_1x+a_2x^2+....+a_(2n)x^(2n)`, then `a_0+a_2+a_4+.....+a_(2n)` is

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Given that (1+x+x^2)^n=a_0+a_1x+a_2x^2+.....+a_(2n)x^(2n) find i) a_0 + a_1 +a_2 .. . . .+ a_(2n) ii) a_0 - a_1 + a_2 - a_3 . . . . + a_(2n) iii) (a_0)^2 - (a_1)^2 . . . . .+ (a_(2n))^2

If (1 + x +x^2)^n = a_0 +a_1x + a_2x^2 + ….+a_(2n)x^(2n) then prove that a_0 +a_2 +a_4+……+a_(2n) = (3^n +1)/(2)

If (1 +x+x^2)^25 = a_0 + a_1x+ a_2x^2 +..... + a_50.x^50 then a_0 + a_2 + a_4 + ... + a_50 is :

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 + a_2 +a_4 + …….= (1+ (-13)^n)/(2)

If (3 + 7x - 9x^2)^n = a_0 +a_1x + a_2 x^2 + ……+a_(2n)x^(2n) prove the a_0 +a_1 +a_2 + ……+a_(2n) = 1

If (1+2x +3x^2)^10 = a_0 +a_1x +a_2x^2 + ……+a_20x^20 then a_1 = ?

If (1-x+x^2)^n=a_0+a_1x+a_2x^2+ .........+a_(2n)x^(2n),\ find the value of a_0+a_2+a_4+........+a_(2n)dot

If (1+x)^n=a_0+a_1x+a_2x^2+....+a_nx^n , then (a_0-a_2+.....)^2+(a_1-a_3+.....)^2 is equal to (A) 3^n (B) 2^n (C) ((1-2^n)/(1+2^n)) (D) none of these

If (18x^2+12x+4)^n = a_0 +a_(1x)+ a_(2x)^2 +......+ a_(2n)x^(2n) , prove that a_r= 2^n3^r ( "^(2n)C_r + "^(n)C_1 "^(2n-2)C_r + "^(n)C_2 "^(2n-4)C_r + ....

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+….+a_(2n)x^(2n) where a_(0) , a(1) , a(2) are unequal and in A.P., then (1)/(a_(n)) is equal to :

RESONANCE DPP ENGLISH-JEE MAINS-All Questions
  1. Make the following expressions free from modulus sign: (x in R) |2x-...

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  2. Simplify (sqrt5-sqrt2)(sqrt5+sqrt2)

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  3. If (1+x+x^2)^n=a0+a1x+a2x^2+....+a(2n)x^(2n), then a0+a2+a4+.....+a(2n...

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  4. Make the following expressions free from modulus sign : (x in R) (...

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  5. Simplify the following expressions : (sqrt5-sqrt2)(sqrt5+sqrt2)

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  6. The possible number of ordered triplets (m, n, p) where m,np in N is (...

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  7. Evaluate the following: 4!-3!

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  8. Let O be an interior points of triangleABC such that vec(OA)+vec(OB)+3...

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  9. Make the following expressions free from modulus sign: (x in R) |x^2...

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  10. If (cos^2x+1/(cos^2x)) (1+tan^2 2y)(3+sin3z)=4, then x is an integral ...

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  11. Given abclt0 and a+b+cgt0. If (|a|)/(a)+(|b|)/(b)+(|c|)/(c)=x, then fi...

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  12. Make the following expressions free from modulus sign : (x in R) (...

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  13. Investigate for the maxima and minima of the function f(x)=int1^x[2(t...

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  14. Make the following expressions free from modulus sign : (x in R) (...

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  15. Find the equation of the largest circle with centre (1, 0) that can be...

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  16. One side of square ABCD is on the line y=2x-17 and other two vertices ...

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  17. Make the following expressions free from modulus sign : (i) |x^(2) -...

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  18. If vec a,vec b,vec c are three non-coplanar vectors represented by co...

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  19. A die is rolled and showing any number is directly proportional to tha...

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  20. Make the following expressions free from modulus sign: (x in R) |x^2...

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