﻿ The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is from Mathematics Class 12 JEE Year 2005 Free Solved Previous Year Papers

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# JEE Mathematics 2005 Exam Questions

#### Multiple Choice Questions

61.

Three houses are available in a locality. Three persons apply for the houses. Each applies to one house without consulting others. The probability that all the three apply for the same house is

• 2/9

• 1/9

• 8/9

• 7/9

B.

1/9

For a particular house being selected

Probability = 1/3

Prob(all the persons apply for the same house) =

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62.

For any vector   the value of  is equal to

C.

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63.

If  are non -coplanar vector λ is a real number then

• exactly one value of λ

• no value of λ

• exactly three values of λ

• exactly two values of λ

B.

no value of λ

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64.

The angle between the lines 2x = 3y = − z and 6x = − y = − 4z is

• 0o

• 90o

• 45o

• 30o

B.

90o

Angle between the lines 2x = 3y = - z & 6x = -y = -4z is 90°
Since a1a2 + b1b2 + c1c2 = 0

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65.

If the plane 2ax − 3ay + 4az + 6 = 0 passes through the midpoint of the line joining the centres of the spheres

x2 + y2 + z2 + 6x − 8y − 2z = 13 and x2 + y2 + z2 − 10x + 4y − 2z = 8, then a equals

• -1

• 1

• -2

• 2

C.

-2

Plane 2ax – 3ay + 4az + 6 = 0 passes through the mid point of the centre of spheres x2 + y2 + z2 + 6x – 8y – 2z = 13 and x2 + y2 + z2 – 10x + 4y – 2z = 8 respectively centre of spheres are (-3, 4, 1) & (5, - 2, 1) Mid point of centre is (1, 1, 1) Satisfying this in the equation of plane,
we get 2a – 3a + 4a + 6 = 0
⇒ a = -2.

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66.

The distance between the line  and the plane

• 10/9

• 3/10

• 10/3

B.

Distance between the line

equation of plane is x + 5y + z = 5 ∴ Distance of line from this plane = perpendicular distance of point (2, -2, 3) from the plane

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67.

If a vertex of a triangle is (1, 1) and the mid-points of two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is

• (-1, 7/3)

• (-1/3, 7/3)

• (1, 7/3)

• (1/3, 7/3)

C.

(1, 7/3)

Vertex of triangle is (1, 1) and midpoint of sides through this vertex is (-1, 2) and (3, 2) ⇒ vertex B and C come out to be (-3, 3) and (5, 3)
therefore centroid  is

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68.

The value of

• a π

• π/2

• π/a

B.

π/2

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69.  depends on
• only y

• only x

• both x and y

• neither x nor y

D.

neither x nor y

which does not depend on x and y.
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70.

Let a, b and c be distinct non-negative numbers. If the vectors

• the Geometric Mean of a and b

• the Arithmetic Mean of a and b

• equal to zero

• the Harmonic Mean of a and b

A.

the Geometric Mean of a and b

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