All questions
- If P(A) = \(\frac{1}{2}\), P(B) = 0, then P(A/B) is (A) 0 (B) \(\frac{1}{2}\) (C) not defined (D) 1 (C) not defined P(A) = 1/2 , P(B) = 0 P(A/B) = P(A∩B)/P(B) = P(A∩B)/0 = Not defined. 1
- If A and B are events such that P(A/B) = P(B/A), then (A) A ⊂ B (B) B = A (C) A ∩ B = ∅ (D) P(A) = P(B) (D) P(A) = P(B) is correct option : P(A/B) = P(B/A) ⇒ P(A∩B)/P(B) = P(A∩B)/P(A) ⇒ P(A) = P(B) 1
- If P(A) = \(\frac{6}{11}\), P(B) = \(\frac{5}{11}\) and P(A ∪B) = \(\frac{7}{11}\) P(A ∪ B) = P(A) + P(B) – P(A ∩ B) (i) P(A ∩ B) = P(A) + P(B) – P(A ∪ B) = 6/11 + 5/11 – 7/11 = 4/11 (ii) P(A/B)=P(A∩ B)/P(B))=4/11/5/11=4/5... 1
- Evaluate P(A ∪ B), if 2P(A) = P(B) = \(\frac{5}{13}\) and P(A/B) = \(\frac{2}{5}\) We have: 2P(A) = P(B) = 5/13 ⇒ P(A) = 5/26 , P(B) = 5/13 . So, P(A/B) = P(A∩B)/P(B) or 2/5 = P(A cap B)/5/13 ⇒ P(A ∩ B) = 2/5 × 5/13 = 2/13... 1
- If P(A) = 0.8, P(B) = 0.5 and P(B/A) = 0.4, find (i) P(A ∩ B) (ii) P(A/B) (iii) P(A ∪ B) (i) P(B/A) = P(A∩B)/P(B) ⇒ 0.4 = P(A∩B)/0.8 ∴ P(A ∩ B) = 0.4 × 0.8 = 0.32. (ii) P(A/B) = P(A∩B)/P(B) = 0.32/0.5 = 32/50 = 16/25 . (iii) P(A... 1
- Compute P(A/B), if P(B) = 0.5 and P(A ∩ B) = 0.32. P(A/B) = P(A∩B)/P(B) = 0.32/0.5 = 32/50 = 16/25 1
- Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E/F) and P(F/E). P(E/F) = E∩F/P(F) = 0.2/0.3 = 2/3 . P(F/E) = P(E∩F)/P(E) = 0.2/0.6 = 2/6 = 1/3 . 1
- Find X, if Y = \(\left[\begin{array}{ll} 3 & 2 \\ 1 & 4 \end{array}\right]\) and 2X + Y = 2X + Y = [beginarrayll 1 & 0 \\ -3 & 2 endarray] ∴ 2X = [beginarrayll 1 & 0 \\ -3 & 2 endarray] – Y = [beginarrayll 1 & 0 \\ -3 & 2 endarray... 1
- Solve the equation for x, y, z and t, if, 2\(\left[\begin{array}{ll} x & z \\ y & t \end{array}\right]\) 2 [beginarrayll x & z \\ y & t endarray] +3 [beginarrayll 1 & -1 \\ 0 & 2 endarray] = 3 [beginarrayll 3 & 5 \\ 4 & 6 endarray] or [beginarra... 1
- If x\(\left[\begin{array}{l} 2 \\ 3 \end{array}\right]\) + y\(\left[\begin{array}{l} -1 \\ 1 \end{array}\right]\) x [beginarrayl 2 \\ 3 endarray] + y [beginarrayl -1 \\ 1 endarray] = [beginarrayl 10 \\ 5 endarray] . or [beginarrayl 2x \\ 3x endarray] + [... 1
- The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books and 10 Let the number of books be represented by matrix A of order 1 x 3 as shown below : A = [10 dozen 8 dozen 10 dozen] = [120 96 120]. The cost... 1
- The restriction on n, k and p so that PY = WY will be defined are (A) k = 3, p = n (A) k = 3, p = n The order of matrix P is p x k and the order of matrix Y is 3 x k. PY is defined, when No. of columns in P = No. of rows in... 1
- If n = p, then the order of the matrix 7X – 5Z is (A) p x 2 (B) 2 x n (C) n x 3 (D) p x n (B) 2 x n The order of matrix X is 2 x n. The order of matrix Z is 2 x p. 7X – 5Z is defined when X and Z are of the same order. ⇒ n-p (give... 1
- What is the force between two small charged spheres having charges of 2 x 10-7C and 3 x 10-7C placed 30 cm apart q₁ = 2 x 10^(-7 )C, q₂ = 3 x 10^(-7 )C, r = 30 cm = 30 x 10^(-2 )m F = 9 x 10⁹ = 9 x 10⁹ x frac2 × 10⁻⁷ × 3 × 10⁻⁷(30 × 10⁻²)² = 0.06 x 10^(... 1
- The electrostatic force on a small sphere of charge 0.4 pC due to another small sphere of charge – 0.8 μC in air is 0.2 q₁ = 0.4 μC = 0.4 x 10^(-6 )C, q₂ = – 0.8μC = – 0 .8 x 10^(-6 )C, F = 0.2 N (a) F = 9 x 10⁹ r² = 9 x 10⁹ x fracq₁ q₂~F = frac9 × 10⁹ × 0.4 ×... 1
- An electric dipole with dipole moment 4 x 10-9 Cm is aligned at 30° with the direction of a uniform electric field p = 4 x 10^(-9 )Cm, θ = 30°, E = 5 x 10^(4 )NC⁻¹ τ = pE sin θ = 4 x 10⁻⁹ x 5 x 10⁴ x sin 30° = 4 x 10⁻⁹ x 5 x 10⁴ x 1 / 2 = 10 x 10^(-5 )Nm... 1
- A polythene piece rubbed with wool is found to have a negative charge of 3 x 10-7C. (a) Estimate the number q = 3 x 10^(-7 )C (a) q = ne, n = q / e = frac3 × 10⁻⁷1.6 × 10⁻¹⁹ ≈ 2 x 10¹² (Since polythene has negative charge, electrons are transferred... 1
- Consider a uniform electric field E = 3 x 103\(\hat { i } \) N/C. (a) What is the flux of this field through (a) E = 3 x 10^(3 )NC⁻¹, r = 10 x 10⁻²m Φ = E x Area = 3 x 10³ x (10 x 10⁻²)² = 30 Nm²C⁻¹ (b) Φ = E x Area x cos 60° = 30 x 1 / 2 = 15 Nm²C-... 1
- What is the net flux of the uniform electric field of Exercise.15 through a cube of side 20 cm oriented so that its Zero. The number of lines entering the cube is the same as the number of lines leaving the cube. 1
- Careful measurement of the electric field at the (a) Φ = fracqε₀ q = Φ x ε₀ = 8 x 10³ x 8.85 x 10⁻¹² = 0.07 μC (b) If the net outward flux through the surface of the box is zero, it cannot... 1
- A point charge of 2.0 pC is at the centre of a cubic Gaussian surface 9.0 cm on edge. Answer: Net flux = q/ε₀ ≈ 0.226\ mathrmN m² C⁻¹ for a 2.0 pC charge. By Gauss's law, the net flux through any closed surface depends only on... 1
- A point charge causes an electric flux of -1.0 x 103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm (a) If the radius of the gaussian surface is doubled, the electric flux through the new surface will still remain the same i.e. -1 x 10³Nm²C... 1
- An infinite line charge produces a field of 9 x 104 N/C at a distance of 2cm. Calculate the linear charge density. E = 9 x 10⁴ NC⁻¹, r = 2 cm = 2 x 10⁻²m E = 9 x 10⁹ x 2λ / 2 λ = fracEr9 × 10⁹ × 2 = frac9 × 10⁴ × 2 × 10⁻²9 × 10⁹ × 2 = 0.1µC/m 1
- Although ordinary rubber is an insulator, the special rubber tyres of aircraft are made slightly conducting The aircraft while in motion gets charged due to atmospheric air friction. The continuous charging may raise the sharp conducting metal part... 1