Maharashtra State Board
- Narrate in 100 words an incident, that illustrates the way a friend of yours ‘made you feel happy and accepted That was my first day at school. I was just five years old. When my parents left me in school and I entered the classroom. I felt so lonely... 1
- “I’m not afraid of anything”, returned Jo with a toss of the head. “I don’t believe you are !” exclaimed the boy. With a toss of the head Jo emphatically told that she was not afraid of anything. The boy was not surprised at her claim and agreed with her... 1
- “The pretty one is Meg, and the curly-haired one is Amy, I believe?” – Laurie. “How did you find that out?” – Jo. Laurie wanted to confirm from Jo whether the pretty one was Meg and the curly-haired was Amy. With surprise in her voice Jo enquired how he(... 1
- Jo flourished her broom as she called out… “How do you do? Are you sick? Laurie opened the window and croaked out as Flourishing her broom Jo asked Laufie about his well-being and enquired whether he was sick. Laurie opened the window and croaked out as hoa... 1
- Change into indirect speech. Question (a) “Do you like your school?” asked the boy. “Don’t go to school The boy wanted to know whether she (Jo) liked school to which Jo answered quite emphatically that she did not go to school. She further adde... 1
- The Extract deals with the atmosphere of two homes. Collect the words associated with – Home Library Garden Home: old, brown, bare, shabby, stately stone mansion, comfort, luxury, big coach house, lovely things, rich curtains, lifeless, lawn, encha... 1
- Find proverbs, maxims and idioms related to ‘friendship’. Birds of a feather flock together. A friend in need is a friend in deed. Friendship is love with understanding. To get on like a house on fi... 1
- Give a brief account of the interaction between Grandpa and Jo. Grandpa and Jo had an interesting interaction as Jo had come out of her initial fear after having a closer look at him. Grandpa had overhear... 1
- Write down in your own words the way Laurie confirmed the names of the March sisters. The March family sometimes forgot to put the curtain down at the window and that helped Laurie, their neighbor, to observe minutely inside t... 1
- Bring out the contrast between the two houses with the help of the following points: House of March House of Laurence 1. Old, brown house 2. Rather bare and shabby 3. Children played all around 4. A lively household having fo... 1
- Jo’s decision to make friends with the lonely boy next door proves to be a good one. Elaborate. Jo was bold, friendly and warm person who observed the boy next door closely and came to the conclusion that he was hungry for friends and f... 1
- z – z¯ = 6i ( z – z¯ = 6i) z – z¯ = (2 + 3i) – (2 – 3i) = 2 + 3i – 2 + 3i = 6i 1
- (1 + 2i) 2 (1 – i) Let z = (1 + 2i)² (1 – i) = (1 + 4i + 4i²) (1 – i) = [1 + 4i + 4(-1)] (1 – i) ….[∵ i² = -1] = (-3 + 4i) (1 – i) = -3 + 3i + 4i – 4i² = -3 +... 1
- (1 + ω)(1 + ω2)(1 + ω4)(1 + ω8) ω is the complex cube root of unity. ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² and ω + ω² = -1 (1 + ω)(1 + ω²)(1 + ω⁴)(1 + ω⁸... 1
- (1 – ω – ω2)3 + (1 – ω + ω2)3 ω is the complex cube root of unity. ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² and ω + ω² = -1 (1 – ω – ω²)³ + (1 – ω + ω²)³... 1
- (1 + ω – ω2) 6 = 64 Proof: since 1 + ω = -ω² , the expression becomes (-2ω²)⁶ = 64 . Here ω is a complex cube root of unity, so ω³ = 1 and 1 + ω + ω² = 0 , whic... 1
- If ω is the complex cube root of unity, show that (i) (2 – ω)(2 – ω2) = 7 ω is the complex cube root of unity. ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² and ω + ω² = -1 L.H.S. = (2 – ω)(2 – ω²) = 4 –... 1
- If ω is a complex cube root of unity, prove that (1 – ω + ω2)6 + (1 + ω – ω2)6 = 128. ω is the complex cube root of unity. ∴ ω³ = 1 and 1 + ω + ω² = 0 Also, 1 + ω² = -ω, 1 + ω = -ω² ∴ L.H.S. = (1 – ω + ω²)⁶ + (1 + ω – ω²)⁶ = [... 1
- 18i complex number Let √18i = a + bi, where a, b ∈ R. Squaring on both sides, we get 18i = a² + b² i² + 2abi 0 + 18i = a² – b² + 2abi …..[∵ i² = -1] Equating r... 1
- i131 + i49 complex number i¹³¹ + i⁴⁹ = (i⁴)³² . i³ + (i⁴)¹² . i = (1)³² (-i) + (1)¹² . i = -i + i = 0 2
- 2x + i9 y(2 + i) = x i7 + 10 i16 2x + i⁹ y(2 + i) = x i⁷ + 10 i¹⁶ 2x + (i⁴)² . i . y(2 + i) = x(i²)³ . i + 10 . (i⁴)⁴ 2x + (1)² . iy(2 + i) = x(-1)³ . i + 10(1)⁴ ……..[∵ i² =... 1
- A 0.1 m solution of K2SO4 in water has a freezing point of – 4.3 °C. Given: Molality of K₂SO₄ solution = m = 0.1 m Freezing point of solution = T_f = – 4.3 °C K_f of water = 1.86 K kg mol^(–1)To find: van’t Ho... 1
- Write the equation relating boiling point elevation to the concentration of the solution. The boiling point elevation is directly proportional to the molality of the solution. Thus, Δ Tb ∝ m ∴ Δ Tb ∝ Kb m where, m is the molality... 1
- The distance between two consecutive bright fringes in a biprism experiment using light of wavelength 6000 Å Given : λ₁ = 6000 Å = 6 x 10⁻⁷ m, λ_(2 )= 4800 Å = 4.8 x 10⁻⁷ m, W₁ = 0.32 mm =3.2 x 10⁻⁴ m Distance between consecutive bright fringes, W =... 1