﻿ Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then VA/VB is  from Mathematics Class 12 JEE Year 2006 Free Solved Previous Year Papers

### Book Store

Currently only available for.
CBSE

# JEE Mathematics 2006 Exam Questions

#### Multiple Choice Questions

1.

All the values of m for which both roots of the equations x2 − 2mx + m2 − 1 = 0 are greater than −2 but less than 4, lie in the interval

• −2 < m < 0

• m > 3

• −1 < m < 3

• 1 < m < 4

C.

−1 < m < 3

Equation x2 − 2mx + m2 − 1 = 0
(x − m)2 − 1 = 0
(x − m + 1) (x − m − 1) = 0
x = m − 1, m + 1 − 2 < m − 1 and m + 1 < 4

m > − 1 and m < 3 − 1 < m < 3.

152 Views

2.

The two lines x = ay + b, z = cy + d; and x = a′y + b′, z = c′y + d′ are perpendicular to each other if

• aa′ + cc′ = −1

• aa′ + cc′ = 1

A.

aa′ + cc′ = −1

Equation of lines

111 Views

3.

If the roots of the quadratic equation x2 + px + q = 0 are tan30° and tan15°, respectively then the value of 2 + q − p is

• 2

• 3

• 0

• 1

B.

3

x2 + px + q = 0
tan 30° + tan 15° = − p
tan 30° ⋅ tan 15° = q

⇒ − p = 1 − q
⇒ q − p = 1
∴ 2 + q − p = 3

145 Views

4.

The value of

• i

• 1

• -i

• -1

C.

-i

131 Views

5.

Let W denote the words in the English dictionary. Define the relation R by :
R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then R is

• not reflexive, symmetric and transitive

• reflexive, symmetric and not transitive

• reflexive, symmetric and transitive

• reflexive, not symmetric and transitive

B.

reflexive, symmetric and not transitive

Clearly (x, x) ∈ R ∀ x ∈ W. So, R is reflexive. Let (x, y) ∈ R,
then (y, x) ∈ R as x and y have at least one letter in common. So, R is symmetric. But R is not transitive for example

Let x = DELHI, y = DWARKA and z = PARK then
(x, y) ∈ R and (y, z) ∈ R but (x, z) ∉ R

141 Views

6.

In an ellipse, the distance between its foci is 6 and minor axis is 8. Then its eccentricity is

• 3/5

• 1/5

• 2/5

• 4/5

A.

3/5

2ae = 6 ⇒ ae = 3
2b = 8 ⇒ b = 4
b2= a2(1 − e2)
16 = a2 − a2e2
a2= 16 + 9 = 25
a = 5
∴e = 3/a = 3/5

216 Views

7.

Suppose a population A has 100 observations 101, 102, … , 200, and another population B has 100 observations 151, 152, … , 250. If VA and VB represent the variances of the two populations, respectively, then VA/VB is

• 1

• 9/4

• 4/9

• 2/3

A.

1

(Here deviations are taken from the mean) Since A and B both have 100 consecutive integers, therefore both have same standard deviation and hence the variance.
387 Views

8.

A body falling from rest under gravity passes a certain point P. It was at a distance of 400 m from P, 4s prior to passing through P. If g = 10 m/s2 , then the height above the point P from where the body began to fall is

• 720 m

• 900 m

• 320 m

• 680 m

A.

720 m

Subtracting we get 400 = 8g + 4gt
⇒ t = 8 sec
∴
∴ Desired height = 320 + 400 = 720 m.
130 Views

9.

The locus of the vertices of the family of parabolas

A.

393 Views

10.

A straight line through the point A(3, 4) is such that its intercept between the axes is bisected at A. Its equation is

• x + y = 7

• 3x − 4y + 7 = 0

• 4x + 3y = 24

• 3x + 4y = 25

C.

4x + 3y = 24

The equation of axes is xy = 0
⇒ the equation of the line is

133 Views

Do a good deed today
Refer a friend to Zigya