A pair of perpendicular lines passes through the origin and also

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMatch The Following

1.

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 B by f(x) = x2 for x  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
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 QuestionsMultiple Choice Questions

2.

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

  • 1440

  • 1540

  • 1640

  • 1740


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


4.

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

  • (- 1, - 14)

  • (3, 4)

  • (1, 2)

  • (- 4, 13)


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5.

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


6.

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 = 2x + 3 + 2 at x0, y0. Then 2x0 + y0 = ?

  • 3 + 2

  • 2 - 1

  • 1

  • 0


7.

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

  • 0

  • 3413

  • 613

  • 7213


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8.

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

  • 2

  • 3

  • 4

  • 5


A.

2

The intersection point of the curve x2 + y2 = 4with x + y = a, where a > 0             x2 + a - x2 = 4   x2 + a2 + x2 - 2ax = 42x2 - 2ax + a2 - 4 = 0x2 - ax + a22 - 2 = 0x = + a ± a2 - 4a22 - 22x = a ± a2 - 2a2 + 82 = a ±8 - a22Since, here the point of intersection sholud be real number, iff 8 - a2  0ie, a2  8, a  22a  2.82Hence, the value is a = 2 according to option


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9.

If 3x2 - 11xy + 10y2 - 7x + 13y + k = 0 denotes a pair of straight lines, then the point of intersection of the lines is

  • (1, 3)

  • (3, 1)

  • (- 3, 1)

  • (1, - 3)


10.

The equation of the radical axis of the pair of circles  7x2 + 7y2 - 7x + 14y + 18 = 0  and 4x2 + 4y2 - 7x + 8y + 20 = 0 is

  • x - 2y - 5 = 0

  • 2x - y + 5 = 0

  • 21x - 68 = 0

  • 23x - 68 = 0


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