All questions
- The distances covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distances. Answer: Median ≈ 223.13 km ClassFrequencyCumulative frequency (less than) 200–2104040 210–22060100 220–23080180 230–24050230 240–25020250 N... 1
- The prices of different articles and demand for them is shown in the following frequency distribution table. Find the median of the prices. Answer: Median price = ₹ 32 'Less than 20' is taken as the class 0–20. ClassFrequencyCumulative frequency (less than) 0–20140140 20–40100240... 1
- The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet. Answer: Mode ≈ 397.06 gram The highest frequency is 60, so the modal class is 250–500. L = 250 , f₁ = 60 , f₀ = 10 , f₂ = 25 , h = 250 Mode... 1
- Draw a histogram for the following frequency distribution. Answer: Histogram with rectangles of heights 150, 400, 460, 540, 600, 350 on the classes 50–70, ..., 150–170 Use of electricity (Unit)Number... 1
- In a handloom factory different workers take different periods of time to weave a saree. The number of workers and their required periods are given below. Present the information by a frequency polygon. Answer: Plot (9, 5), (11, 16), (13, 30), (15, 40), (17, 35), (19, 14) and join them, closing at (7, 0) and (21, 0) ClassClass markFrequencyP... 1
- The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon. Answer: Histogram with heights 8, 16, 22, 18, 14, 12; frequency polygon through (19, 0), (21, 8), (23, 16), (25, 22), (27, 18), (29, 14), (3... 1
- Draw a frequency polygon for the following grouped frequency distribution table. Answer: Plot (22, 38), (27, 46), (32, 35), (37, 24), (42, 15), (47, 12) and join them, closing at (17, 0) and (52, 0) The classes are not co... 1
- The following table shows the average rainfall in 150 towns. Show the information by a frequency polygon. Answer: Plot (10, 14), (30, 12), (50, 36), (70, 48), (90, 40) and join them, closing at (−10, 0) and (110, 0) ClassClass markFrequencyPoint... 1
- A pie diagram shows the percentages of vehicles passing a signal between 8 am and 10 am: Cars 30%, Tempos 12%, Buses 8%, Autos 10%, Two wheelers 40%. Find the central angles and, if two-wheelers are 1200, the total number of vehicles. Answer: (1) Cars 108°, Tempos 43.2°, Buses 28.8°, Auto rickshaws 36°, Two wheelers 144° (2) 3000 vehicles (1) Central angle = percentage/100... 1
- The following table shows causes of noise pollution. Show it by a pie diagram: Construction 10%, Traffic 50%, Aircraft take offs 9%, Industry 20%, Trains 11%. Answer: Central angles – Construction: 36°, Traffic: 180°, Aircraft take offs: 32.4°, Industry: 72°, Trains: 39.6° ComponentValueMeasure of... 1
- A pie diagram of 1000 students' favourite games: Cricket 81°, Football 63°, Hockey 54°, Other 72°, Kho-kho 45°, Kabaddi 45°. (1) How many like cricket? (2) How many like football? (3) How many prefer other games? Answer: (1) 225 (2) 175 (3) 200 Number of students = central angle/360 × 1000 (1) Cricket: 81/360 × 1000 = 225 (2) Football: 63/360 × 1000 =... 1
- Medical check up of 180 women was conducted in a health centre in a village. 50 of them were short of haemoglobin, 10 suffered from cataract and 25 had respiratory disorders. The remaining women were healthy. Show the information by a pie diagram. Answer: Central angles – Short of haemoglobin: 100°, Cataract: 20°, Respiratory disorders: 50°, Healthy: 190° ComponentValueMeasure of centr... 1
- On an environment day, students in a school planted 120 trees under plantation project. The information regarding the project is shown in the following table. Show it by a pie diagram. Answer: Central angles – Karanj: 60°, Behada: 84°, Arjun: 72°, Bakul: 66°, Kadunimb: 78° ComponentValueMeasure of central angle Karanj20 20/... 1
- In figure 1.55, ∠ABC = 75°, ∠EDC = 75°. State which two triangles are similar and by which test? Also write the similarity of these two triangles by a proper one to one correspondence. Answer: triangle ABC sim triangle EDC by the AA test. In triangle ABC and triangle EDC : ∠ ABC cong ∠ EDC (each is 75^° , given) ∠ ACB cong... 1
- Are the triangles in figure 1.56 similar? If yes, by which test? (In ΔPQR: PQ = 6, QR = 8, PR = 10; in ΔLMN: LM = 3, MN = 4, LN = 5) Answer: Yes, triangle PQR sim triangle LMN by the SSS test of similarity. Compare the corresponding sides: PQ/LM = 6/3 = 2, QR/MN = 8/4 = 2... 1
- Two poles of height 8 m and 4 m are perpendicular to the ground. If the length of shadow of smaller pole due to sunlight is 6 m then how long will be the shadow of the bigger pole at the same time? Answer: The shadow of the bigger pole is 12 m long. At the same time the sun's rays make the same angle with the ground, so ∠ PQR cong ∠ ABC... 1
- In ΔABC, AP ⊥ BC, BQ ⊥ AC, B-P-C, A-Q-C then prove that ΔCPA ~ ΔCQB. If AP = 7, BQ = 8, BC = 12 then find AC. Answer: triangle CPA sim triangle CQB by the AA test, and AC = 10.5 Proof: In triangle CPA and triangle CQB : ∠ CPA cong ∠ CQB (each 90^° ,... 1
- Given: In trapezium PQRS, side PQ ∥ side SR, AR = 5AP, AS = 5AQ then prove that, SR = 5PQ. Answer: triangle APQ sim triangle ARS (SAS test), so PQ/RS = 1/5 , i.e. SR = 5PQ. From the given data, AR = 5AP ⇒ AP/AR = 1/5 AS = 5AQ ⇒ AQ/... 1
- In trapezium ABCD, side AB ∥ side DC, diagonals AC and BD intersect in point O. If AB = 20, DC = 6, OB = 15 then find OD. Answer: OD = 4.5 In triangle AOB and triangle COD : ∠ ABO cong ∠ CDO (alternate angles, AB ∥ DC, BD is a transversal) ∠ AOB cong ∠ COD (vert... 1
- □ABCD is a parallelogram, point E is on side BC. Line DE intersects ray AB in point T. Prove that DE × BE = CE × TE. Answer: triangle BET sim triangle CED (AA test), which gives DE × BE = CE × TE. Side AB ∥ side DC (opposite sides of a parallelogram), and T... 1
- In the figure, seg AC and seg BD intersect each other in point P and AP/CP = BP/DP. Prove that, ΔABP ~ ΔCDP. Answer: triangle ABP sim triangle CDP by the SAS test of similarity. In triangle ABP and triangle CDP : AP/CP = BP/DP (given) ∠ APB cong ∠ C... 1
- In the figure, in ΔABC, point D on side BC is such that, ∠BAC = ∠ADC. Prove that, CA² = CB × CD. Answer: triangle BAC sim triangle ADC (AA test), so CA/CD = CB/CA , i.e. CA² = CB × CD . In triangle BAC and triangle ADC : ∠ BAC cong ∠ ADC... 1
- If ΔABC ~ ΔPQR and AB : PQ = 2 : 3, then fill in the blanks. A(ΔABC)/A(ΔPQR) = AB²/☐ = 2²/3² = ☐/☐ Answer: A(triangle ABC)/A(triangle PQR) = AB²/PQ² = 2²/3² = 4/9 By the theorem of areas of similar triangles, the ratio of the areas of two... 1
- If ΔABC ~ ΔPQR, A(ΔABC) = 80, A(ΔPQR) = 125, then fill in the blanks. A(ΔABC)/A(Δ....) = 80/125, therefore AB/PQ = ☐/☐ Answer: A(triangle ABC)/A(triangle PQR) = 80/125 = 16/25 , therefore AB/PQ = 4/5 For similar triangles, A(triangle ABC)/A(triangle PQR) = AB... 1