RankLab
Back to Questions
MathsMediumMCQ2022 ยท 29 Jul Shift 2

Q70.If the system of equations ๐‘ฅ+ ๐‘ฆ+ ๐‘ง= 6 2๐‘ฅ+ 5๐‘ฆ+ ๐›ผ๐‘ง= ๐›ฝ ๐‘ฅ+ 2๐‘ฆ+ 3๐‘ง= 14 has infinitely many solutions, then ๐›ผ+ ๐›ฝ is equal to (1) 8 (2) 36 (3) 44 (4) 48

What This Question Tests

This question assesses the understanding of the conditions for a system of linear equations to have infinitely many solutions, requiring the determinant of the coefficient matrix and related determinants to be zero.

Concepts Tested

Conditions for infinitely many solutions of a system of linear equations

Formulas Used

For infinitely many solutions: det(A) = 0 and det(Aโ‚“) = det(Aแตง) = det(Aโ‚‚) = 0 (or equivalent condition rank(A) = rank(A|B) < n)

๐Ÿ“š NCERT Sections This Tests

1.27 โ€” If The Solubility Product Of Cus Is 6 ร— 10โ€“16, Calculate The Maximum Molarity Of

Chemistry Class 11 ยท Chapter 1

70% match

1.27 If the solubility product of CuS is 6 ร— 10โ€“16, calculate the maximum molarity of CuS in aqueous solution.

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

Chemistry Class 11 ยท Chapter 3

70% 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).

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

Chemistry Class 11 ยท Chapter 5

69% 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