If (1 + 2x + 3x2)10 = a0 

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181.

If (1 + 2x + 3x2)10 = a0 + a1x + a2x2 + . . . + a20x20, then a2a1 = ?

  • 10.5

  • 21

  • 10

  • 5.5


A.

10.5

(1 + 2x + 3x2)10 = a0 + a1x + a2x2 + . . . + a20x20  = 1 + x2 + 3x10,Then by binomial expansion=C010 + C110x2 + 3x + C210x22 + 3x2 + . . . Now, the coefficient of x in this expansion = 3 C110ie, a1 = 2 10 = 20and coefficient of x2 in this expansion= 3 .  C110 + 4 . C210ie, a2 = 3 10 + 4 45          = 30 + 180          = 210So, a2a1 = 21020 = 10.5


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182.

The condition that the x3 - bx2 + cx - d = 0 are in progression is

  • c3 = b3d

  • c2 = b2d

  • c = bd3

  • c = bd2


183.

n = 1 2n2n + 1! = ?

  • 1e

  • e2

  • e

  • 2e


184.

If 12 × 4 + 14 × 6 + 16 × 8 + . . . n terms = knn × 1,then k =?

  • 14

  • 12

  • 1

  • 18


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185.

k = 1r = 0k13kCrk = ?

  • 13

  • 23

  • 1

  • 2


186.

1xx + 1x + 2 . . . x + n = A0x + A1x + 1 + Anx + n, 0  i  r  Ar = ?

  •  - 1rr!n - r!

  • - 1rr!n - r!

  •  1r!n - r!

  •  r!n - r!


187.

1 + 13 . 22 + 15 . 24 + 17 . 26 + ... =?

  • loge2

  • loge3

  • loge4

  • loge5


188.

Given that, 2 + 2 + c  0 and that the system of equations

   + bx + ay + bz = 0;    + cx +by +cz = 0; + by +  +cz = 0has a non-trival solution, then a, b and c lie in

  • Arithmetic Progression

  • Geometric Progression

     

  • Harmonic Progression

  • Arithmetico- geometric Progression


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189.

If a, b and c form a geometric progression with common ratio r, then the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y2 = 0 is

  • - r22

  • - r2

  • r2

  • r


190.

The point (3, 2) undergoes the following three transformations in the order given

(i) Reflection about the line y = x.

(ii) Translation by the distance 1 unit in the positive direction of x-axis.

(iii) Rotation by an angle π4 about the origin in  anti-clockwise direction.

Then, the final position of the point is

  • - 18, 18

  • (- 2, 3)

  • 0, 18

  • (0, 3)


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