Q80.Let 9 distinct balls be distributed among 4 boxes, ๐ต1, ๐ต2, ๐ต3 and ๐ต4. If the probability that ๐ต3 contains 9 exactly 3 balls is ๐3 then ๐ lies in the set : 4 (1) {๐ฅโ๐ : | ๐ฅ- 3 | < 1} (2) {๐ฅโ๐ : | ๐ฅ- 2 | โค1} (3) {๐ฅโ๐ : | ๐ฅ- 1 | < 1} (4) {๐ฅโ๐ : | ๐ฅ- 5 | โค1}
What This Question Tests
This question involves applying the binomial probability distribution to calculate the probability of a specific number of distinct balls ending up in one particular box, given they are distributed randomly among four boxes.
Concepts Tested
Formulas Used
P(X=k) = nCk * p^k * (1-p)^(n-k)
๐ NCERT Sections This Tests
4.8 โ A Closely Wound Solenoid 80 Cm Long Has 5 Layers Of Windings Of 400
Physics Class 11 ยท Chapter 4
4.8 A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
3.10 โ In A Reaction Between A And B, The Initial Rate Of Reaction (R0) Was Measured
Chemistry Class 11 ยท Chapter 3
3.10 In a reaction between A and B, the initial rate of reaction (r0) was measured for different initial concentrations of A and B as given below: A/ mol Lโ1 0.20 0.20 0.40 B/ mol Lโ1 0.30 0.10 0.05 r0/mol Lโ1sโ1 5.07 ร 10โ5 5.07 ร 10โ5 1.43 ร 10โ4 What is the order of the reaction with respect to A and B? 3.11 The following results have been obtained during the kinetic studies of the reaction: 2A + B ยฎ C + D Experiment [A]/mol Lโ1 [B]/mol Lโ1 Initial rate of formation of D/mol Lโ1 minโ1 I 0.1 0.1 6.0 ร 10โ3 II 0.3 0.2 7.2 ร 10โ2 III 0.3 0.4 2.88 ร 10โ1 IV 0.4 0.1 2.40 ร 10โ2 Determine the rate law and the rate constant for the reaction. 3.12 The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table: Experiment [A]/ mol Lโ1 [B]/ mol Lโ1 Initial rate/ mol Lโ1 minโ1 I 0.1 0.1 2.0 ร 10โ2 II โ 0.2 4.0 ร 10โ2 III 0.4 0.4 โ IV โ 0.2 2.0 ร 10โ2 3.13 Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 sโ1 (ii) 2 minโ1 (iii) 4 yearsโ1 3.14 The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample. 3.15 The experimental data for decomposition of N2O5 [2N2O5 ยฎ 4NO2 + O2] in gas phase at 318K are given below: t/s 0 400 800 1200 1600 2000 2400 2800 3200 102 ร [N2O5]/ 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35 mol Lโ1 (i) Plot [N2O5] against t. (ii) Find the half-life period for the reaction. (iii) Draw a graph between log[N2O5] and t. (iv) What is the rate law ? Chemistry 86 Reprint 2025-26 (v) Calculate the rate constant. (vi) Calculate the half-life period from k and compare it with (ii).
1.18 โ A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 ยท Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
๐ Question Details
- Chapter
- Probability
- Topic
- Binomial Probability Distribution
- Year
- 2021
- Shift
- 25 Jul Shift 1
- Q Number
- Q80
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 13: Probability
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