All questions

• ΔLMN ~ ΔPQR, 9 × A(ΔPQR) = 16 × A(ΔLMN). If QR = 20 then find MN. Answer: MN = 15 9 × A(triangle PQR) = 16 × A(triangle LMN) therefore A(triangle LMN)/A(triangle PQR) = 9/16 Since triangle LMN sim triangle... Similarity 1 answer
• Areas of two similar triangles are 225 sq.cm. 81 sq.cm. If a side of the smaller triangle is 12 cm, then find corresponding side of the bigger triangle. Answer: The corresponding side of the bigger triangle is 20 cm. Let the required side be x cm. The ratio of the areas of similar triangles e... Similarity 1 answer
• ΔABC and ΔDEF are equilateral triangles. If A(ΔABC) : A(ΔDEF) = 1 : 2 and AB = 4, find DE. Answer: DE = 4√(2) All equilateral triangles are similar (each angle is 60^° , AAA test), so triangle ABC sim triangle DEF . A(triangle ABC)... Similarity 1 answer
• In figure 1.66, seg PQ ∥ seg DE, A(ΔPQF) = 20 units, PF = 2 DP, then find A(□DPQE) by completing the following activity. Answer: A(□DPQE) = 25 sq. units Let DP = x, so PF = 2x and DF = DP + PF = x + 2x = 3x. In triangle FDE and triangle FPQ : ∠ FDE cong ∠ FPQ (... Similarity 1 answer
• In ΔABC and ΔPQR, in a one to one correspondence AB/QR = BC/PR = CA/PQ then (A) ΔPQR ~ ΔABC (B) ΔPQR ~ ΔCAB (C) ΔCBA ~ ΔPQR (D) ΔBCA ~ ΔPQR Answer: (B) triangle PQR sim triangle CAB Read the correspondence from the equal ratios: side AB ↔ side QR, BC ↔ PR, CA ↔ PQ. The vertex com... Similarity 1 answer
• If in ΔDEF and ΔPQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false? (A) EF/PR = DF/PQ (B) DE/PQ = EF/RP (C) DE/QR = DF/PQ (D) EF/RP = DE/QR Answer: (B) DE/PQ = EF/RP Since ∠ D cong ∠ Q and ∠ E cong ∠ R , by the AA test triangle DEF sim triangle QRP (D ↔ Q, E ↔ R, F ↔ P). So the c... Similarity 1 answer
• In ΔABC and ΔDEF ∠B = ∠E, ∠F = ∠C and AB = 3DE then which of the statements regarding the two triangles is true? (A) not congruent and not similar (B) similar but not congruent (C) congruent and similar (D) none Answer: (B) The triangles are similar but not congruent. ∠ B = ∠ E and ∠ C = ∠ F , so by the AA test triangle ABC sim triangle DEF . But AB... Similarity 1 answer
• ΔABC and ΔDEF are equilateral triangles, A(ΔABC) : A(ΔDEF) = 1 : 2. If AB = 4 then what is length of DE? (A) 2√2 (B) 4 (C) 8 (D) 4√2 Answer: (D) 4√(2) Equilateral triangles are similar, so the ratio of their areas equals the ratio of the squares of their sides: AB²/DE² = 1... Similarity 1 answer
• In figure 1.71, seg XY ∥ seg BC, then which of the following statements is true? (A) AB/AC = AX/AY (B) AX/XB = AY/AC (C) AX/YC = AY/XB (D) AB/YC = AC/XB Answer: (A) AB/AC = AX/AY Since XY ∥ BC, triangle AXY sim triangle ABC (AA test: ∠ A common, corresponding angles ∠ AXY cong ∠ ABC ). AX/AB... Similarity 1 answer
• In ΔABC, B-D-C and BD = 7, BC = 20 then find following ratios. (1) A(ΔABD)/A(ΔADC) (2) A(ΔABD)/A(ΔABC) (3) A(ΔADC)/A(ΔABC) Answer: (1) 7/13 (2) 7/20 (3) 13/20 DC = BC − BD = 20 − 7 = 13. Triangles ABD, ADC and ABC have the common vertex A and their bases BD, DC,... Similarity 1 answer
• Find the correct answer: The formula to find mean from a grouped frequency table is X̄ = A + (Σfᵢuᵢ / Σfᵢ) × h. In the formula uᵢ = ... Answer: (C) u_i = x_i - A/h In the step deviation method, the deviation d_i = x_i - A is divided by the class width h , giving u_i = x_i - A... Statistics 1 answer
• A balloon vendor has 2 red, 3 blue and 4 green balloons. He wants to choose one of them at random to give it to Pranali. What is the probability of the event that Pranali gets, (1) a red balloon (2) a blue balloon (3) a green balloon. Answer: (1) 2/9 (2) 1/3 (3) 4/9 n(S) = 2 + 3 + 4 = 9 (1) P(red) = 2/9 (2) P(blue) = 3/9 = 1/3 (3) P(green) = 4/9 Check: 2/9 + 3/9 + 4/9 = 1... Probability 1 answer
• A box contains 5 red, 8 blue and 3 green pens. Rutuja wants to pick a pen at random. What is the probability that the pen is blue? Answer: 1/2 n(S) = 5 + 8 + 3 = 16, n(A) = 8 P(A) = 8/16 = 1/2 Probability 1 answer
• Six faces of a die are marked A, B, C, D, E, A. If the die is rolled once, find the probability of - (1) 'A' appears on upper face. (2) 'D' appears on upper face. Answer: (1) 1/3 (2) 1/6 n(S) = 6 (six faces). (1) Two faces bear A: P = 2/6 = 1/3 . (2) One face bears D: P = 1/6 . Probability 1 answer
• A box contains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears (1) an odd number (2) a complete square number. Answer: (1) 1/2 (2) 1/6 n(S) = 30 (1) Odd numbers 1, 3, ..., 29: 15 numbers. P = 15/30 = 1/2 . (2) Perfect squares: 1, 4, 9, 16, 25 (5 numbe... Probability 1 answer
• A rectangular garden is 77 m by 50 m with a circular lake of diameter 14 m in it. A towel from a nearby terrace fell into the garden. Find the probability that it fell in the lake. Answer: 1/25 Area of garden = 77 × 50 = 3850 m² Radius of lake = 7 m. Area of lake = 22/7 × 7² = 154 m² P = 154/3850 = 1/25 Probability 1 answer
• A spinning arrow comes to rest at one of the numbers 1 to 8 (equally likely). Find the probability that it will rest at (1) 8 (2) an odd number (3) a number greater than 2 (4) a number less than 9. Answer: (1) 1/8 (2) 1/2 (3) 3/4 (4) 1 n(S) = 8 (1) P = 1/8 (2) Odd: 1, 3, 5, 7. P = 4/8 = 1/2 (3) Greater than 2: 3, 4, 5, 6, 7, 8. P = 6/8... Probability 1 answer
• There are six cards in a box, each bearing a number from 0 to 5. Find the probability that a card drawn shows, (1) a natural number. (2) a number less than 1. (3) a whole number. (4) a number is greater than 5. Answer: (1) 5/6 (2) 1/6 (3) 1 (4) 0 S = 0, 1, 2, 3, 4, 5, n(S) = 6 (1) Natural numbers 1 to 5: P = 5/6 (2) Less than 1: only 0. P = 1/6 (3)... Probability 1 answer
• A bag contains 3 red, 3 white and 3 green balls. One ball is taken out of the bag at random. What is the probability that the ball drawn is - (1) red. (2) not red (3) either red or white. Answer: (1) 1/3 (2) 2/3 (3) 2/3 n(S) = 9 (1) P(red) = 3/9 = 1/3 (2) Not red means white or green: 6 balls. P = 6/9 = 2/3 (3) Red or white: 6... Probability 1 answer
• Each card bears one letter from the word 'mathematics' The cards are placed on a table upside down. Find the probability that a card drawn bears the letter 'm'. Answer: 2/11 'mathematics' has 11 letters, so there are 11 cards: n(S) = 11. The letter m occurs twice: n(A) = 2. P(A) = 2/11 Probability 1 answer
• Out of 200 students from a school, 135 like Kabbaddi and the remaining students do not like the game. If one student is selected at random from all the students, find the probability that the student selected dosen't like Kabbaddi. Answer: 13/40 Students who do not like Kabbaddi = 200 - 135 = 65 . P = 65/200 = 13/40 Probability 1 answer
• A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - (1) prime number (2) multiple of 4 (3) multiple of 11. Answer: (1) 3/10 (2) 3/10 (3) 1/5 Tens digit: 1, 2, 3, 4 (not 0); units digit: any of 0 to 4. So n(S) = 4 × 5 = 20 . S = 10, 11, 12, 13, 14,... Probability 1 answer
• The faces of a die bear numbers 0, 1, 2, 3, 4, 5. If the die is rolled twice, then find the probability that the product of digits on the upper face is zero. Answer: 11/36 n(S) = 6 × 6 = 36 . The product is non-zero only when both numbers are from 1 to 5: 5 × 5 = 25 outcomes. So the product is zer... Probability 1 answer
• The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method. Answer: Mean time ≈ 4.36 hours ClassClass mark x_i Frequency f_i f_ix_i 0–2177 2–431854 4–651260 6–871070 8–109327 Total Σ f_i = 50 Σ f_ix_i... Statistics 1 answer