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MathsMediumNumerical2021 ยท 22 Jul Shift 1

Q87.Let A = {0, 1, 2, 3, 4, 5, 6, 7}. Then the number of bijective functions f : A โ†’A such that f(1) + f(2) = 3 โˆ’f(3) is equal to

What This Question Tests

This question evaluates the understanding of matrix multiplication and the condition for two matrices to commute (AB=BA), requiring careful calculation of matrix products and setting up a system of equations for elements of matrix B.

Concepts Tested

Matrix multiplicationCommutative property of matrices

Formulas Used

Matrix multiplication rules

๐Ÿ“š NCERT Sections This Tests

8.17 โ€” Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products

Chemistry Class 12 ยท Chapter 8

68% match

8.17 Complete each synthesis by giving missing starting material, reagent or products

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

Chemistry Class 11 ยท Chapter 3

67% 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).

9.8 โ€” Accomplish The Following Conversions:

Chemistry Class 12 ยท Chapter 9

67% match

9.8 Accomplish the following conversions: (i) Nitrobenzene to benzoic acid (ii) Benzene to m-bromophenol (iii) Benzoic acid to aniline (iv) Aniline to 2,4,6-tribromofluorobenzene (v) Benzyl chloride to 2-phenylethanamine (vi) Chlorobenzene to p-chloroaniline (vii) Aniline to p-bromoaniline (viii) Benzamide to toluene (ix) Aniline to benzyl alcohol.

๐Ÿ“‹ Question Details

Chapter
Matrices
Topic
Commutative matrices
Year
2021
Shift
22 Jul Shift 1
Q Number
Q87
Type
Numerical
NCERT Ref
Class 12 Mathematics Ch 3: Matrices

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