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JEE Mathematics Solved Question Paper 2010

Match The Following

Let R denote the set of all real numbers and RT denote the set of all positive real numbers. For the subsets A and B of R define f : A $\to$ B by f(x) = x² for x $\in$ A. Observe the two lists given below


A	f is one-one and onto, 1. A = R, B = R If	1	A = R⁺, B = R
B	f is one-one but not onto, If	2	A = B = R
C	f is onto but not one-one, if	3	A = R, B = R⁺
D	f is neither one-one nor onto If	4	A = B + R⁺

A. A B C D	(i) 1 2 3 4
B. A B C D	(ii) 4 2 1 3
C. A B C D	(iii) 4 1 3 2
D. A B C D	(iv) 4 2 1 3

Multiple Choice Questions

An urn A contains 3 white and 5 black balls. Another um B contains 6 white and 8 black balls. A ball is picked from A at random andthen transferred to B. Then, a ball is picked at random from B. The probability that it is a white ball is

$\frac{14}{40}$
$\frac{15}{40}$
$\frac{16}{40}$
$\frac{17}{40}$

3.
If a straight line L is perpendicular to the line 4x- 2y = 1 and forms a triangle of area 4 sq unit with the coordinate axes, then the equation of the line L is

2x + 4y + 7 = 0

2x - 4y + 8 = 0

2x + 4y + 8 = 0

4x - 2y - 8 = 0

2x + 4y + 8 = 0

A straight line L is perpendicular to the line 4x - 2y = 1 therefore the equation of the line is

$x + 2 y + λ = 0$ ...(i)

Also, the line (i) form a ti of area 4 unit² with the coordinate axes, then

$\frac{1}{2} |\begin{matrix} 0 & 0 & 1 \\ - λ & 0 & 1 \\ 0 & \frac{λ}{2} & 1 \end{matrix}| = 4 (- λ) (- \frac{λ}{2}) = 8 \Rightarrow λ^{2} = 16 \Rightarrow λ = 4$

$From Eq . (i) x + 2 y + 4 = 0 or 2 x + 4 y + 8 = 0$

$The image of the point (4, - 13) with respect to the line 5 x + y + 6 = 0 is$

(- 1, - 14)
(3, 4)
(1, 2)
(- 4, 13)

The image of the line x + y - 2 = 0 in the y-axis is

x - y + 2 = 0
y - x + 2 = 0
x + y + 2 = 0
x + y - 2 = 0

A straight line which makes equal intercepts on positive X and Y axes and which is at a distance 1 unit from the origin intersects the straight line $y = 2 x + 3 + \sqrt{2} at (x_{0}, y_{0}) . Then 2 x_{0} + y_{0} = ?$

$3 + \sqrt{2}$
$\sqrt{2} - 1$
1
0

The distance between the two lines represented by 8x² - 24xy + 18y² - 6x + 9y - 5 = 0 is

0
$\frac{3}{4 \sqrt{13}}$
$\frac{6}{\sqrt{13}}$
$\frac{7}{2 \sqrt{13}}$

A pair of perpendicular lines passes through the origin and also through the points of intersection of the curve x² + y² = 4 with x + y = a, where a > 0. Then a is equal to