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# JEE Mathematics 2007 Exam Questions

#### Multiple Choice Questions

1.

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

• 12 kg and 13 kg

• 5 kg and 5 kg

• 5 kg and 12 kg

• 5 kg and 13 kg

C.

5 kg and 12 kg

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2.

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

D.

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3.

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60º at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30º. The height of the tower is

C.

∆OAB is equilateral
∴ OA = OB = AB = a
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4.

The sum of the series 20C020C1 + 20C220C3 + …… - ….. + 20C10 is-

• 20C10

• 0

• 20C10

B.

(1 + x)20 = 20C0 + 20C1x + … + 20C10x10 + …+ 20C20x20
put x = − 1,
0 = 20C0 − 20C1 + … − 20C9 + 20C1020C11 + … + 20C20
0 = 2 (20C020C1 + … − 20C9) + 20C10
20C020C1 + … + 20C10 =

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5.

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, K) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interva

• 0 < k < 1/2

• k ≥ 1/2

• – 1/2 ≤ k ≤ 1/2

• k ≤ ½

B.

k ≥ 1/2

Equation of circle (x − h)2+ (y − k)2 = k2
It is passing through (− 1, 1) then
(− 1 − h)2+ (1 − k)2= k2
h2+ 2h − 2k + 2 = 0
D ≥ 0
2k − 1 ≥ 0 ⇒ k ≥ 1/2.

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6.

The differential equation of all circles passing through the origin and having their centres on the x-axis is

C.

General equation of all such circles is
x2+ y2 + 2gx = 0.
Differentiating, we get

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7.

If p and q are positive real numbers such that p2 + q2 = 1, then the maximum value of (p + q) is

• 2

• 1/2

D.

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8.  then the value of x
• 1

• 3

• 4

• 5

B.

3

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9.

The set S: {1, 2, 3, …, 12} is to be partitioned into three sets A, B, C of equal size. Thus, A ∪ B ∪ C = S, A ∩ B = B ∩ C = A ∩ C = φ. The number of ways to partition S is-

• 12!/3!(4!)3

• 12!/3!(3!)4

• 12!/(4!)3

• 12!/(3!)4

C.

12!/(4!)3

Number of ways

181 Views

10.

In the binomial expansion of (a - b)n, n ≥ 5, the sum of 5th and 6th terms is zero, then
a/b equals

• 5/n −4

• 6 /n −5

• n -5 /6

• n -4 /5

D.

n -4 /5

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