Q60.Let θ = and A = . If B = A + A4 , then det (B) : 5 [−sinθcosθ cosθsinθ ] (1) is one (2) lies in (2, 3) (3) is zero (4) lies in (1, 2)
What This Question Tests
This question involves identifying a pattern in matrix powers (A²=I), simplifying the expression for B, and then calculating its determinant using trigonometric identities.
Concepts Tested
Formulas Used
det(A)
A²=I if A is orthogonal and det(A)=-1
Properties of I matrix
📚 NCERT Sections This Tests
3.10 — In A Reaction Between A And B, The Initial Rate Of Reaction (R0) Was Measured
Chemistry Class 11 · 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 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).
4.8 — A Closely Wound Solenoid 80 Cm Long Has 5 Layers Of Windings Of 400
Physics Class 11 · Chapter 4
4.8 A closely wound solenoid 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm. If the current carried is 8.0 A, estimate the magnitude of B inside the solenoid near its centre.
4.4 — A Horizontal Overhead Power Line Carries A Current Of 90 A In East To
Physics Class 11 · Chapter 4
4.4 A horizontal overhead power line carries a current of 90 A in east to west direction. What is the magnitude and direction of the magnetic field due to the current 1.5 m below the line?
📋 Question Details
- Chapter
- Matrices
- Topic
- Determinants, properties of matrices, powers of matrices
- Year
- 2020
- Shift
- 06 Sep Shift 2
- Q Number
- Q60
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 3: Matrices
More from this Chapter
Q87.Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr(A), the sum of diagonal entries of A . Assume that A2 = 1. Statement -1: If A ≠1 and A ≠−1, then det A = −1. Statement −2 : If A ≠1 and A ≠−1, then tr(A) ≠0. (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1
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 = ±1, then A−1 exists but all its entries (2) If det A ≠±1, then A−1 exists and all its entries are not necessarily integers are non-integers (3) If det A = ±1, then A−1 exists and all its entries (4) If det A = ±1, then A−1 need not exist are integers
Q74.Let A be a 2 × 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 × 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