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MathsMediumMCQ2019 · 09 Apr Shift 1

Q74.If [10 11 ][10 21 ][10 31 ] [10 n −11 ] [10 781 ], [10 n1 ] (1) [10 –121 ] (2) [121 10 ] (3) [131 10 ] (4) [10 –131 ]

What This Question Tests

This problem involves recognizing a pattern in the product of specific 2x2 matrices, which simplifies to a single matrix with the sum of an arithmetic series as an element. After finding the value of 'n', the inverse of the last matrix in the product needs to be calculated.

Concepts Tested

Matrix multiplicationPattern recognition in matrix productsInverse of a 2x2 matrixSum of arithmetic series

Formulas Used

[[1,0],[a,1]] * [[1,0],[b,1]] = [[1,0],[a+b,1]]

Sum of first n natural numbers = n(n+1)/2

Inverse of A = [[a,b],[c,d]] is 1/(ad-bc) * [[d,-b],[-c,a]]

📚 NCERT Sections This Tests

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

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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 L–1 0.20 0.20 0.40 B/ mol L–1 0.30 0.10 0.05 r0/mol L–1s–1 5.07 × 10–5 5.07 × 10–5 1.43 × 10–4 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 ® C + D Experiment [A]/mol L–1 [B]/mol L–1 Initial rate of formation of D/mol L–1 min–1 I 0.1 0.1 6.0 × 10–3 II 0.3 0.2 7.2 × 10–2 III 0.3 0.4 2.88 × 10–1 IV 0.4 0.1 2.40 × 10–2 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 L–1 [B]/ mol L–1 Initial rate/ mol L–1 min–1 I 0.1 0.1 2.0 × 10–2 II – 0.2 4.0 × 10–2 III 0.4 0.4 – IV – 0.2 2.0 × 10–2 3.13 Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 s–1 (ii) 2 min–1 (iii) 4 years–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 ® 4NO2 + O2] in gas phase at 318K are given below: t/s 0 400 800 1200 1600 2000 2400 2800 3200 102 × [N2O5]/ 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35 mol L–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).

5.11Draw All The Isomers (Geometrical And Optical) Of:

Chemistry Class 11 · Chapter 5

67% match

5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+

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

Chemistry Class 12 · Chapter 8

67% match

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

📋 Question Details

Chapter
Matrices
Topic
Matrix multiplication, inverse of a matrix
Year
2019
Shift
09 Apr Shift 1
Q Number
Q74
Type
MCQ
NCERT Ref
Class 12 Mathematics Ch 3: Matrices

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