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# JEE Mathematics 2008 Exam Questions

#### Multiple Choice Questions

1.

The conjugate of a complex number is . Then the complex number is

C.

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2.

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°.
Then the height of the pole is

B.

BD = AB = 7 + x
Also AB = x tan 60° = x√3
∴ x√3 = 7+x

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3.

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

• a = 0, b = 7

• a = 5, b = 2

• a = 1, b = 6

• a = 3, b = 4

D.

a = 3, b = 4

Mean of a, b, 8, 5, 10 is 6

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4.

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi−major axis is

• 8/3

• 2/3

• 5/3

• 4/3

A.

8/3

Major axis is along x-axis.

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5.

The perpendicular bisector of the line segment joining P (1, 4) and Q (k, 3) has y−intercept − 4. Then a possible value of k is

• 1

• 2

• -2

• -4

D.

-4

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6.

The solution of the differential equation    satisfying the condition y (1) = 1 is

• y = ln x + x

• y = x ln x + x2

•  y = xe(x−1)

• y = x ln x + x

D.

y = x ln x + x

y = vx

Since, y (1) = 1, we have y = x log x + x

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7.

The point diametrically opposite to the point P (1, 0) on the circle x2+ y2 + 2x + 4y − 3 = 0 is

• (-3,4)

• (-4,3)

• (-3,-4)

• (3,4)

C.

(-3,-4)

Centre (− 1, − 2)
Let (α, β) is the required point

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8.

Statement − 1: For every natural number n ≥ 2

Statement −2: For every natural number n ≥ 2,

• Statement −1 is false, Statement −2 is true

• Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

• Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

• Statement − 1 is true, Statement − 2 is false.

C.

Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

Hence Statement −2 is not a correct explanation of Statement −1.
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9.

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P (A ∪ B) is

• 3/5

• 0

• 1

• 2/5

C.

1

A = {4, 5, 6} , B = {1, 2, 3, 4} .
Obviously P (A ∪ B) = 1.

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10.

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

• (0, 2)

• (1, 0)

• (0,1)

• (2,0)

B.

(1, 0)

vertex (0,1)

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