﻿ Let a1, a2, a3, … be terms of an A.P. If  equals from Mathematics Class 12 JEE Year 2006 Free Solved Previous Year Papers

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# JEE Mathematics 2006 Exam Questions

#### Multiple Choice Questions

11.

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the mid points of the chords of the circle C that subtend an angle of 2π/3  at its centre is

• x2+y2 = 3/2

• x2 + y2 = 1

• x2+y2 = 27/4

• x2+y2 = 9/4

D.

x2+y2 = 9/4

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12.

If the expansion in powers of x of the function  is a0 + a1x + a2x2 + a3x3 + … , then an is

D.

(1-ax)-1(1-bx)-1 = (1+ax+a2x2+.....)(1+bx+b2x2+....)
therefore coefficient of xn = bn +abn-1 +a2bn-2 +.....+an-1b +an =

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13.

If (a, a2 ) falls inside the angle made by the lines y =x/2, x >0 and y = 3x, x > 0, then a belongs to

• (0,1/2)

• (3, ∞)

• (1/2, 3)

• (-3, -1/2)

C.

(1/2, 3)

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14.

Let a1, a2, a3, … be terms of an A.P. If  equals

• 41/11

• 7/2

• 2/7

• 11/47

D.

11/47

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15.

If the lines 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 are two diameters of a circle of area 49π square units, the equation of the circle is

• x2 + y2 + 2x − 2y − 47 = 0

• x2 + y2 + 2x − 2y − 62 = 0

• x2 + y2 − 2x + 2y − 62 = 0

• x2 + y2 − 2x + 2y − 47 = 0

D.

x2 + y2 − 2x + 2y − 47 = 0

Point of intersection of 3x − 4y − 7 = 0 and 2x − 3y − 5 = 0 is (1 , − 1), which is the centre of the circle and radius = 7.
∴ Equation is (x − 1)2 + (y + 1)2 = 49
⇒ x2 + y2 − 2x + 2y − 47 = 0.

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16.

The value of ,where [x] denotes the greatest integer not exceeding x is

• af(a) − {f(1) + f(2) + … + f([a])}

• [a] f(a) − {f(1) + f(2) + … + f([a])}

• [a] f([a]) − {f(1) + f(2) + … + f(a)}

• af([a]) − {f(1) + f(2) + … + f(a)}

B.

[a] f(a) − {f(1) + f(2) + … + f([a])}

Let a = k + h, where [a] = k and 0 ≤ h < 1

{f(2) − f(1)} + 2{f(3) − f(2)} + 3{f(4) − f(3)}+…….+ (k−1) – {f(k) − f(k − 1)} + k{f(k + h) − f(k)}

= − f(1) − f(2) − f(3)……. − f(k) + k f(k + h)
= [a] f(a) − {f(1) + f(2) + f(3) + …. + f([a])}

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17.

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area enclosed by the park is

• 3x2/2

• x3/8

• x2/2

• πx2

C.

x2/2

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18.

For natural numbers m, n if (1 − y)m (1 + y)n = 1 + a1y + a2y2 + … , and a1 = a2 = 10, then (m, n) is

• (20, 45)

• (35, 20)

• (45, 35)

• (35, 45)

D.

(35, 45)

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19.

If z2 + z + 1 = 0, where z is a complex number, then the value of

• 18

• 54

• 6

E.

12

z2 + z + 1 = 0 ⇒ z = ω or ω2

∴ The given sum = 1 + 1 + 4 + 1 + 1 + 4 = 12
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20.

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

• 5040

• 6210

• 385

• 1124

C.

385

10C1 + 10C2 + 10C3 + 10C4
= 10 + 45 + 120 + 210 = 385
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