Q70.Let ๐ด= ๐๐๐2 ร 2, where ๐๐๐โ 0 for all ๐, ๐ and ๐ด2 = ๐ผ, Let a be the sum of all diagonal elements of ๐ด and ๐= ๐ด Then 3๐2 + 4๐2 is equal to (1) 4 (2) 14 (3) 7 (4) 3
What This Question Tests
The question tests the understanding of matrix properties like A^2 = I, determinant, and trace for a 2x2 matrix, and then uses these properties to evaluate an expression.
Concepts Tested
Formulas Used
A = [[a,b],[c,d]]
A^2 = I
det(A) = ad-bc
Trace(A) = a+d
๐ NCERT Sections This Tests
3.10 โ In A Reaction Between A And B, The Initial Rate Of Reaction (R0) Was Measured
Chemistry Class 11 ยท Chapter 3
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 Lโ1 0.20 0.20 0.40 B/ mol Lโ1 0.30 0.10 0.05 r0/mol Lโ1sโ1 5.07 ร 10โ5 5.07 ร 10โ5 1.43 ร 10โ4 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 Lโ1 [B]/mol Lโ1 Initial rate of formation of D/mol Lโ1 minโ1 I 0.1 0.1 6.0 ร 10โ3 II 0.3 0.2 7.2 ร 10โ2 III 0.3 0.4 2.88 ร 10โ1 IV 0.4 0.1 2.40 ร 10โ2 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 Lโ1 [B]/ mol Lโ1 Initial rate/ mol Lโ1 minโ1 I 0.1 0.1 2.0 ร 10โ2 II โ 0.2 4.0 ร 10โ2 III 0.4 0.4 โ IV โ 0.2 2.0 ร 10โ2 3.13 Calculate the half-life of a first order reaction from their rate constants given below: (i) 200 sโ1 (ii) 2 minโ1 (iii) 4 yearsโ1 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 Lโ1 (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).
14.2 โ Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 ยท Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
13.5 โ The Q Value Of A Nuclear Reaction A + B ยฎ C + D Is Defined By
Physics Class 12 ยท Chapter 13
13.5 The Q value of a nuclear reaction A + b ยฎ C + d is defined by Q = [ mA + mb โ mC โ md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H โ12 H+12 H (ii) 126 C+126 C โ1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
๐ Question Details
- Chapter
- Matrices
- Topic
- Properties of matrices, determinant, trace
- Year
- 2023
- Shift
- 06 Apr Shift 1
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
More from this Chapter
Q87.Let A be a 2 ร 2 matrix with real entries. Let I be the 2 ร 2 identity matrix. Denote by tr(A), the sum of diagonal entries of A . Assume that A2 = 1. Statement -1: If A โ 1 and A โ โ1, then det A = โ1. Statement โ2 : If A โ 1 and A โ โ1, then tr(A) โ 0. (1) Statement โ1 is false, Statement โ2 is true (2) Statement โ1 is true, Statement โ2 is true, Statement โ2 is a correct explanation for Statement โ1 (3) Statement โ1 is true, Statement โ2 is true; (4) Statement โ1 is true, Statement โ2 is false. Statement โ2 is not a correct explanation for Statement โ1
Q88.Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If det A = ยฑ1, then Aโ1 exists but all its entries (2) If det A โ ยฑ1, then Aโ1 exists and all its entries are not necessarily integers are non-integers (3) If det A = ยฑ1, then Aโ1 exists and all its entries (4) If det A = ยฑ1, then Aโ1 need not exist are integers
Q74.Let A be a 2 ร 2 matrix Statement-1 : adj(adj A) = A Statement-2 : |adj A| = |A| (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true
Q75.The number of 3 ร 3 non-singular matrices, with four entries as 1 and all other entries as 0 , is (1) 5 (2) 6 (3) at least 7 (4) less than 4