Q86.From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is σ2 , then 96σ2 is equal to ______
What This Question Tests
This question involves identifying the scenario as a hypergeometric distribution, then calculating the variance of the random variable X (number of defective items) using the appropriate formula for hypergeometric distribution.
Concepts Tested
Formulas Used
P(X=k) = [C(K,k) * C(N-K, n-k)] / C(N,n)
E[X] = np (for binomial), but hypergeometric is different
Var(X) = n * (K/N) * (N-K)/N * (N-n)/(N-1)
📚 NCERT Sections This Tests
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
1.17 — A Point Charge +10 Mc Is A Distance 5 Cm Directly Above The Centre
Physics Class 11 · Chapter 1
1.17 A point charge +10 mC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in Fig. 1.31. What is the magnitude of the electric flux through the square? (Hint: Think of the square as one face of a cube with edge 10 cm.) FIGURE 1.31
📋 Question Details
- Chapter
- Probability
- Topic
- Variance of a random variable (Hypergeometric Distribution)
- Year
- 2024
- Shift
- 05 Apr Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 13: Probability
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