RankLab
Back to Questions
MathsHardMCQ2022 ยท 28 Jun Shift 2

Q62.The number of ways to distribute 30 identical candies among four children C1, C2, C3 and C4 so that C2 receives atleast 4 and atmost 7 candies, C3 receives atleast 2 and atmost 6 candies, is equal to (1) 205 (2) 615 (3) 510 (4) 430 JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper

What This Question Tests

This question tests the ability to solve distribution problems with identical items and specific upper and lower bounds for some recipients, typically solved using the stars and bars method combined with inclusion-exclusion.

Concepts Tested

Stars and Bars methodInclusion-Exclusion PrincipleGenerating functions (implicit)

Formulas Used

Number of non-negative integer solutions to x1 + x2 + ... + xk = n is C(n+k-1, k-1)

๐Ÿ“š NCERT Sections This Tests

5.28 โ€” How Many Ions Are Produced From The Complex Co(Nh3)6Cl2 In Solution?

Chemistry Class 11 ยท Chapter 5

70% match

5.28 How many ions are produced from the complex Co(NH3)6Cl2 in solution? (i) 6 (ii) 4 (iii) 3 (iv) 2 139 Coordination Compounds Reprint 2025-26

5.12 โ€” Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of

Chemistry Class 11 ยท Chapter 5

68% match

5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?

3.10 โ€” In A Reaction Between A And B, The Initial Rate Of Reaction (R0) Was Measured

Chemistry Class 11 ยท Chapter 3

68% match

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 Lโ€“1 0.20 0.20 0.40 B/ mol Lโ€“1 0.30 0.10 0.05 r0/mol Lโ€“1sโ€“1 5.07 ร— 10โ€“5 5.07 ร— 10โ€“5 1.43 ร— 10โ€“4 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 Lโ€“1 [B]/mol Lโ€“1 Initial rate of formation of D/mol Lโ€“1 minโ€“1 I 0.1 0.1 6.0 ร— 10โ€“3 II 0.3 0.2 7.2 ร— 10โ€“2 III 0.3 0.4 2.88 ร— 10โ€“1 IV 0.4 0.1 2.40 ร— 10โ€“2 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 Lโ€“1 [B]/ mol Lโ€“1 Initial rate/ mol Lโ€“1 minโ€“1 I 0.1 0.1 2.0 ร— 10โ€“2 II โ€“ 0.2 4.0 ร— 10โ€“2 III 0.4 0.4 โ€“ IV โ€“ 0.2 2.0 ร— 10โ€“2 3.13 Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 sโ€“1 (ii) 2 minโ€“1 (iii) 4 yearsโ€“1 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 Lโ€“1 (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).

๐Ÿ“‹ Question Details

Chapter
Permutation & Combination
Topic
Distribution of Identical Items (Stars and Bars)
Year
2022
Shift
28 Jun Shift 2
Q Number
Q62
Type
MCQ
NCERT Ref
Class 11 Mathematics Ch 7: Permutations and Combinations

More from this Chapter

Q85.The set S = {1, 2, 3, โ€ฆ , 12) is to be partitioned into three sets A, B, C of equal size. Thus, A โˆชB โˆชC = S, A โˆฉB = B โˆฉC = A โˆฉC = ฯ• . The number of ways to partition S is (1) 12! (2) 12! 3!(4!)3 3!(3!)4 (3) 12! (4) 12! (4!)3 (3!)4

2007
Medium

Q74.In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement -1: The number of different ways the child can buy the six ice-creams is 10C5 . Statement โˆ’2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row. (1) Statement โˆ’1 is false, Statement โˆ’2 is true (2) Statement โˆ’1 is true, Statement โˆ’2 is true, Statement โˆ’2 is a correct explanation for Statement โˆ’1 (3) Statement โˆ’1 is true, Statement โˆ’2 is true; (4) Statement โˆ’1 is true, Statement โˆ’2 is false. Statement โˆ’2 is not a correct explanation for Statement โˆ’1.

2008
Medium

Q75.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent? (1) 8 โ‹…6C4 โ‹…7C4 (2) 6.8 โ‹…7C4 (3) 6 โ‹…7 โ‹…8C4 (4) 7 โ‹…6C4 โ‹…8C4

2008
Hard

Q63.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is (1) less than 500 (2) at least 500 but less than 750 (3) at least 750 but less than 1000 (4) at least 1000

2009
Medium
More Mathematics questions