10th
- What made her decide to give a party in Loona Bimberton’s honour? What did she intend to give Loona on her birthday? Mrs. Packletide’s intension to show Loona down and humiliated her in front the crowd made her to decide to give party in Loona Bimberton’s h... 1
- Why did Mrs. Packletide wish to kill a tiger? Mrs. Packletide wished to kill a tiger because she wanted to show Loona Bimberton down, who had earned huge popularity by hunting a tiger. 1
- Why did not Nicola and Jacopo disclose their problems about their plans to the narrator Nicola and jacopo disclose their problem about their plans to the narrator because they were self made boys and didn't disclose their person... 1
- When the narrator asks the boys about their plan, they are evasive. Why don't they disclose their problems? When the narrator asks the boys about their plans, they are evasive, they do not disclose their problem as their self-respect does not allow... 1
- The narrator asks the boys, "Must you work so hard? You both look rather tired." The boys reply, We learn that the boys are self respectful and they do not want anyone to sympathize with their situation. 1
- Why were the boys in the deserted square at night? What character trait do they exhibit? The boys were in the deserted square at night as they were waiting for the last bus from Padua to sell the newspapers to the passengers. The... 1
- How were the boys useful to the author? The boys were very useful to the author as they helped the narrator in many ways. If he wanted a pack of American cigarettes or seats for th... 1
- Why was the author surprised to see Nicola and Jacopo working as shoeshine boys? The author was surprised to see Nicola and Jacopo working as shoeshine boys because he saw them selling fruits when he met them the first ti... 1
- Why were the narrator and his companion impressed by the two boys? The narrator and his companion were impressed by the two boys because of their brown skin, tangles hair and the dark earnest eyes of the boy... 1
- Why didn't Luigi, the driver, approve of the two boys? Luigi the driver, did not approved of the two boys of their shabby appearance. 1
- Which term of ap is first negative 50,45,40........ 12th term a+(n-1)d \\ = 50+(12-1)(-5) \\ = 50+(-55) =-5 2
- A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make Let x litres and y litres be the amount of acids from 50% and 25% acid solutions respectively. As per the question 50% of x + 25% of y = 40%... 1
- Find the values of a and b if the points A(–2,1), B(a,b) and C(4,–1) are collinear and a – b = 1. Answer: a = 1, b = 0 Three points are collinear when the area of the triangle formed by them is zero: x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂... 1
- If (3,3),(6,y),(x,7) and (5,6) are the vertices of a parallelogram taken in order, find the value of x and y. Answer: x = 8, y = 4 Let A(3, 3), B(6, y), C(x, 7), D(5, 6). The diagonals of a parallelogram bisect each other, so the mid-point of AC equa... 1
- If xcosθ – ysinθ = a, xsinθ + ycos θ = b, prove that x2+y2=a2+b2. Answer: Square both equations and add; the cross terms cancel and sin²θ + cos²θ = 1 gives x² + y² = a² + b² . Squaring the first equation: a... 1
- If cosφ + sinφ = √2 cosφ, prove that cosφ - sinφ = √ 2sin φ. Answer: From the given condition, cosφ = (sqrt2 + 1)sinφ , which rearranges to cosφ - sinφ = sqrt2sinφ . Given cosφ + sinφ = sqrt2cosφ . So... 1
- Prove that one of every three consecutive integers is divisible by 3. Answer: Every integer leaves remainder 0, 1 or 2 on division by 3; in each case exactly one of n, n + 1, n + 2 is a multiple of 3. Let the t... 1
- A bag contains 5 red and some blue balls, if probability of drawing a blue ball from the bag is twice that of Answer: 10 blue balls Let the number of blue balls be x . Total balls = 5 + x . P(red) = 5/5 + x,qquad P(blue) = x/5 + x Given P(blue) = 2 ×... 1
- A card is drawn at random from a well shuffled deck of playing cards. Find the probability that the card drawn Answer: (i) 11/13 (ii) 2/13 A deck has 52 cards, with 4 kings and 4 queens, so 8 cards are kings or queens. (ii) Either a king or a queen: P... 1
- Find the point on the y-axis which is equidistant from the points (5,–2) and (–3,2). Answer: (0, −2) Any point on the y-axis has x-coordinate 0, so let the point be P(0, y) . Let A(5, -2) and B(-3, 2) . Given PA = PB , so PA²... 1
- Which term of the sequence 4, 9, 14.... is 124? 2 Answer: 124 is the 25th term. The sequence 4, 9, 14, … is an AP with first term a = 4 and common difference d = 9 - 4 = 5 . Let a_n = 124 .... 1
- Find the LCM and HCF of 120 and 144 by using Fundamental Theorem of Arithmetic. Answer: HCF = 24, LCM = 720 Write each number as a product of primes (Fundamental Theorem of Arithmetic): 120 = 2³ × 3 × 5 144 = 2⁴ × 3² HCF... 1
- Determine whether the following system of equations has a unique solution, no solutions or infinitely many solution Answer: infinitely many solutions For a₁x + b₁y = c₁ and a₂x + b₂y = c₂ , compare the ratios of coefficients. Here a₁ = 3, b₁ = -7, c₁ = 5 a... 1
- If sec A+ tan A = p, then find the value of sec A – tan A. Answer: sec A - tan A = 1/p Use the identity sec²A - tan²A = 1 . Factorising the left side: (sec A + tan A)(sec A - tan A) = 1 Given sec A +... 1