RankLab
Back to Questions
MathsMediumNumerical2021 · 26 Aug Shift 2

Q84.Let a1, a2, … , a10 be an A. P. with common difference −3 and b1, b2, … , b10 be a G. P. with common ratio 2. Let ck = ak + bk, k = 1, 2, … , 10. If c2 = 12 and c3 = 13, then ∑10k=1 ck is equal to ______.

What This Question Tests

This question tests the understanding of general terms and sum formulas for both arithmetic and geometric progressions, requiring the solution of a system of equations to find initial terms.

Concepts Tested

Arithmetic Progression (AP)Geometric Progression (GP)Sum of APSum of GP

Formulas Used

ak = a1 + (k-1)d

bk = b1 * r^(k-1)

Sn_AP = n/2 * (2a1 + (n-1)d)

Sn_GP = b1 * (r^n - 1) / (r - 1)

📚 NCERT Sections This Tests

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

Chemistry Class 12 · Chapter 8

70% match

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

2.2A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its

Physics Class 11 · Chapter 2

70% match

2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.

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

Chemistry Class 11 · 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 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).