Mathematics-5.Unit-3.03-Matrices and Determinants Test

1. The value of is : (A) ( − 5) (B) 5 ( − 5) (C) 5 ( + 5) (D) 5 ( − 5) 2. is equal to : (A) constant other than zero (B) zero (C) 100 (D) –1997 3. If a + b +c > 0 and a ≠ b ≠ c ≠ 0, then Δ = then : (A) Δ > 0 (B) Δ < 0 (C) Δ = 0 (D) Data insufficient 4. The determinant is equal to zero if : (A) a, b, c are in A.P. (B) a, b, c are in G.P. (C) a, b, c are in H.P. (D) none of these 5. The determinant is divisible by : (A) 1 + x (B) (1 + x)2 (C) x2 (D) none of these 6. is equal to : (A) a positive number (B) a negative number (C) Zero (D) none of these 7. If f(x) = , then dx is equal to : (A) 1/4 (B) –1/3 (C) 1/2 (D) 1 8. For positive numbers x, y, z, the numerical value of the determinant is : (A) 0 (B) 1 (C) 2 (D) none of these 9.  = is equal to : (A) p + q (B) a + b + c (C) x + y + z (D) 0 10. is equal to : (A) abc (B) a2b2c2 (C) ab + bc + ca (D) 0 11. is equal to : (A) 0 (B) 1 (C) –1 (D) none of these 12. If f (x) = then f (100) is equal to : (A) 0 (B) 1 (C) 100 (D) –100 13. is equal to : (A) 1 + ∑a2 (B) ∑a2 (C) (∑a)2 (D) ∑a 14. If A, B, C are the angles of a triangle and , then  is equal to: (A) constant other than zero (B) not a constant (C) 0 (D) none of these 15. If [.] denotes the greatest integer less than or equal to the real number under consideration and –1 ≤ x < 0; 0 ≤ y < 1 and 1 ≤ z < 2, then the value of the determinant is : (A) [z] (B) [y] (C) [x] (D) none of these 16. If  = = 0, then the non zero root of the equation is : (A) a+b +c (B) abc (C) – a – b –c (D) None of these 17. If f (x) = then the value of f(x) dx is equal to : (A) 0 (B) 1 (C) 2 (D) none of these 18. If A = , then A2 is equal to (A) unit matrix (B) null matrix (C) A (D) –A 19. If A′ is the transpose of a square matrix A, then (A) |A| ≠ |A′| (B) |A| = |A′| (C) |A| + |A′| = 0 (D) |A| = |A′| only when A is symmetric 20. If I = , J = and B = , then B equals (A) I cos + J sin (B) I sin + J cos (C) I cos – J sin (D) – I cos + J sin 21. If In is the identity matrix of order n, then (In)–1 (A) does not exist (B) equal to In (C) equals to O (D) nIn 22. If for a matrix A, A2 + I = O where I is the identity matrix, then A equals (A) (B) (C) (D) 23. If A = , then A40 equals (A) (B) (C) (D) none of these 24 If A [aij] is a square matrix of order n  n such that aii = k for all i, then trace of A is equal to (A) kn (B) (C) nk (D) none of these 25. If A = and I = , then the value of k so that A2 = 8A + kI is (A) 7 (B) − 7 (C) 0 (D) 5 26. If A = , then the value of |adj A| is (A) a27 (B) a9 (C) a6 (D) a2 27. If A and B are symmetric matrices of order n (A ≠ B), then (A) A + B is skew symmetric (B) A + B is symmetric (C) A + B is a diagonal matrix (D) A + B is a zero matrix 28. If A = and B = then AB = (A) A3 (B) B2 (C) O (D) I 29. If A = the A is (A) idempotent (B) nilpotent (C) symmetric (D) none of these 30. If A = , then 19A–1 is equal to (A) A′ (B) 2A (C) (D) A

Comments

Post a Comment

Popular posts from this blog

Planning to start your own coaching institute for JEE, NEET, CBSE or Foundation? Here's why not to waste time in developing study material from scratch. Instead use the readymade study material to stay focused on quality of teaching as quality of teaching is the primary job in coaching profession while study material is secondary one. Quality of teaching determines results of your coaching that decides success & future of your coaching while good quality study material is merely a necessary teaching aid that supplements your teaching (video in Hindi)

Image
Read more

Physics-30.24-Physics-Solids and Semiconductors

UNIT 24 - SOLIDS AND SEMICONDUCTORS 1. SOLID STATE ELECTRONICS (SEMICONDUCTORS) (A) Energy bands in solids: (i) In solids, the group of closely lying energy levels is known as energy band. (ii) In solids the energy bands are analogous to energy levels in an atom. (iii) In solids the atoms are arranged very close to each other. In these atoms there are discrete energy levels of electrons. For the formation of crystal these atoms come close together, then due to nucleus-nucleus, electron-electron and electron-nucleus interactions the discrete energy levels of atom distort and consequently each energy level spits into a large number of closely lying energy levels. (iv) The number of split energy levels is proportional to the number of atoms interacting with each other. If two atoms interact then each energy level splits into two out of which one will be somewhat above and another will be somewhat below the main energy level. In solids the number of atoms is very large ( 1023). Hence eac...
Read more

Physics-31.Rotational Mechanics

5.1 DEFINITION OF CENTRE OF MASS Centre of mass: Every physical system has associated with it a certain point whose motion characterizes the motion of the whole system. When the system moves under some external forces than this point moves as if the entire mass of the system is concentrated at this point and also the external force is applied at his point of translational motion. This point is called the centre of mass of the system. Centre of mass of system of n point masses or n particles is that point about which moment of mass of the system is zero, it means that if about a particular origin the moment of mass of system of n point masses is zero, then that particular origin is the centre of mass of the system. The concept of centre of mass is a pure mathematical concept. If there are n particles having mass m1, m2 ….m n and are placed in space (x1, y1, z1), (x2, y2, z2) ……….(x n, y n, z n) then centre of mass of system is defined as (X, Y, Z) where = Y = and Z = where...
Read more