Q5. If A and B are two events such that P(A ∩B) = 0.1, and P(A ∣B) and P(B ∣A) are the roots of the equation – 12x2 −7x + 1 = 0, then the value of P(A∪B) is : P(A∩B) (1) 4 (2) 7 3 4 (3) 5 (4) 9 3 4
What This Question Tests
This question combines probability concepts, specifically conditional probability, with the properties of roots of a quadratic equation to find the probability of the union of two events.
Concepts Tested
Formulas Used
P(A|B) = P(A ∩ B) / P(B)
P(B|A) = P(A ∩ B) / P(A)
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
📚 NCERT Sections This Tests
9.8 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Probability
- Topic
- Conditional probability and properties of roots of quadratic equations
- Year
- 2025
- Shift
- 22 Jan Shift 2
- Q Number
- Q5
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 13: Probability
More from this Chapter
Q90.One ticket is selected at random from 50 tickets numbered 00, 01, 02, … , 49. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals (1) 1 (2) 1 14 7 (3) 5 (4) 1 14 50 JEE Main 2009 JEE Main Previous Year Paper
Q89.Four numbers are chosen at random (without replacement) from the set {1, 2, 3, … . , 20} . Statement-1: The probability that the chosen numbers when arranged in some order will form an AP is 1 . Statement-2: If the 85 four chosen numbers from an AP, then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1
Q90.An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is (1) 2 (2) 1 7 21 (3) 2 (4) 1 23 3 JEE Main 2010 JEE Main Previous Year Paper
Q89.Consider 5 independent Bernoulli's trials each with probability of success p . If the probability of at least one failure is greater than or equal to 31 , then p lies in the interval 32 (1) ( 34 , 1112 ] (2) [0, 12 ] (3) ( 1112 , 1] (4) ( 12 , 34 ]