An urn A contains 3 white and 5 black balls. Another um B contain

Subject

Mathematics

Class

JEE Class 12

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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

Advertisement

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


D.

1740

Case Ist: Let a white ball be transfered from the first bag to the second bag.

The probability of selecting white ball from the first bag is

P133 + 5 = 38

Now, the second bag has 7 white and 8 black balls. The probability of selecting a white ballfrom the second bag is

P277 + 8 = 715

The probability that both these events take place simultaneously

= P1 × P2 = 38 × 715 = 740

Case IInd: Let a black ball be transfered fromthe first bag to the second bag. Its probability is

P3 = 53 + 5 = 58

Now, the second  9 black balls.bag contains 6 white and

The probability of drawing a white ball from the second bag is P466 + 9 = 615

Therefore, the probability of both these events taking place simultaneously

     = P3 ×P4 = 58 × 615 = 14

 The required probability = P1P2 + P3P4         = 740 + 14        = 7 + 1040 = 1740


Advertisement
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)


Advertisement
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


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


Advertisement
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


Advertisement