Sujeet Kumar

Question 1.Find the principal values of the following : Question 2.Evaluate the following : Solution: Solution: (iii) tan-1√3 – sec-1(-2)Solution: (iv) cosec-1(−√2) + cot-1(√3)Solution: Question 3.Prove the following : Solution: Solution: Solution: Solution: Solution: = θ/2 …[∵ tan-1(tanθ) = θ]= RHS.

Question 1.Find the Cartesian co-ordinates of the point whose polar co-ordinates are : Let the cartesian coordinates be (x, y) Let the cartesian coordinates be (x, y) Question 2.Find the of the polar co-ordinates point whose Cartesian co-ordinates are. Question 4. Solution:By the sine rule, Question 5. Solution: Question 6.In ∆ABC, prove that a3sin(B – … Read more

Chapter 3 Trigonometric Functions Ex 3.1 Question 1.Find the principal solutions of the following equations : We know that,Hence, the required principal solution are (iv) cot θ = 0.Solution: Question 2.Find the principal solutions of the following equations:(i) sinθ = −1/2Solution:We know that,sin π/6 = 1/2 and sin (π + θ) = -sinθ,sin(2π – θ) = -sinθHence, the required … Read more

I) Choose the correct answer from the given alterna-tives in each of the following questions :Question 1. (a) a = – 2, b = 1(b) a = 2, b = 4(c) a = 2, b = –1(d) a = 1, b = –2Solution:(a) a = – 2, b = 1 Question 2. Solution: Question 3. … Read more

Question 1. Question 2.By R1 – R2, we get,By R1 – R3 and By R2 – R3, we get Question 3.Check whether the following matrices are invertible or not: ∴ A is a non-singular matrix.Hence, A-1 exist. = sec2θ – tan2θ = 1 ≠ 0.∴ A is a non-singular matrix.Hence, A-1 exist. = 3(5 – 0) – 4(5 – 0) + … Read more

Question 1.Solve the following equations by inversion method.(i) x + 2y = 2, 2x + 3y = 3Solution:The given equations can be written in the matrix form as :This is of the form AX = B, where ∴ A-1 = [−322−1]Now, premultiply AX = B by A-1, we get,A-1(AX) = A-1B∴ (A-1A)X = A-1B∴ IX = A-1B … Read more

Question 1.Find the co-factors of the elements of the following matricesHere, a11 = -11, M11 = 4∴ A11 = (-1)1+1(4) = 4a12 = 2, M12 = -3∴ A12 = (-1)1+2(- 3) = 3a21 = – 3, M21 = -2∴ A21 = (- 1)2+1(2) = -2a22 = 4, M22 = -1∴ A22 = (-1)2+2(-1) = -1. The co-factor of aij is given by Aij = (-1)i+jMij Question 2.Find the matrix … Read more

Question 1.Apply the given elementary transformation on each of the following matrices. Question 3. Question 4. Question 5. Question 6.We conclude from Ex. 5 and Ex. 6 that the matrix remains same by interchanging the order of the elementary transformations. Hence, the transformations are commutative. Question 7. Question 8. Question 9.

Question 1.Select and write the correct answer from the given alternatives in each of the following questions :i) If p ∧ q is false and p ∨ q is true, the ________ is not true.(A) p ∨ q(B) p ↔ q(C) ~p ∨ ~q(D) q ∨ ~pSolution:(b) p ↔ q. (ii) (p ∧ q) → … Read more

Question 1.Express the following circuits in the symbolic form of logic and writ the input-output table.(i)Solution:Let p : the switch S1 is closedq : the switch S2 is closedr : the switch S3 is closed~p : the switch S1‘ is closed or the switch S1is open~q : the switch S2‘ is closed or the switch S2 is open~r : … Read more