Maths
maths maharashtra board 10th
- 2 mangles and 5 oranges together cost Rs. 30; but 4 mangoes and 3 oranges cost Rs. 46. Find the cost of a mango Answer: Mango = Rs. 10, Orange = Rs. 2 ("mangles" in the question is a typo for mangoes.) Let a mango cost Rs. x and an orange Rs. y . 2x +... 1
- The difference between the measures of angle A and angle B of a parallelogram ABCD is 180. Answer: ∠A = 99°, ∠B = 81° Adjacent angles of a parallelogram are supplementary. Taking ∠A as the larger angle: ∠ A + ∠ B = 180 (1) ∠ A - ∠... 1
- A piece of string 12m in length was cut into two pieces such that one piece is x metres and the other is y meters. Answer: The pieces are 5 m and 7 m. The two pieces together make the whole string: x + y = 12 (1) y is 2 m more than x : y = x + 2 (2) Subst... 1
- In a parallelogram ABCD, the measure of angle A is thrice the measure of angle B Answer: ∠A = 135°, ∠B = 45° ∠A and ∠B are adjacent angles of parallelogram ABCD, and adjacent angles of a parallelogram are supplementary: ∠... 1
- In a parallelogram ABCD, the measure of angle A is thrice the measure of angle B. Answer: ∠A = 135°, ∠B = 45° In a parallelogram, adjacent angles are supplementary: ∠ A + ∠ B = 180^° Given ∠ A = 3∠ B . Let ∠ B = x : 3x + x... 1
- 2 pens and 3 pencils cost Rs. 26, while 3 pens and 2 pencils cost Rs. 34. Find the cos Answer: Pen = Rs. 10, Pencil = Rs. 2 Let a pen cost Rs. x and a pencil Rs. y . 2x + 3y = 26 (1) 3x + 2y = 34 (2) Adding (1) and (2): 5x + 5y... 1
- The difference between two numbers is 16. The greater number is 1 more than twice the smaller number. Answer: The numbers are 31 and 15. Let the greater number be x and the smaller y . x - y = 16 (1) x = 2y + 1 (2) Substitute (2) in (1): 2y +... 1
- The sum of two numbers is 70. Three times the greater number is equal to four times the smaller number. Answer: The numbers are 40 and 30. Let the greater number be x and the smaller y . x + y = 70 (1) 3x = 4y ⇒ x = 4y/3 (2) Substitute (2) in (... 1
- Ina a cyclic quadrilateral ABCD, measure of angle A is double the measure of angle C. Answer: ∠A = 120°, ∠C = 60° Opposite angles of a cyclic quadrilateral are supplementary, so ∠ A + ∠ C = 180^° Given ∠ A = 2∠ C . Let ∠ C = x... 1
- The perimeter of an isosceles triangle is 27 cm and the length of the congruent sides is greater Answer: The sides are 11 cm, 11 cm and 5 cm (base). Let the base be x cm. Each congruent side is 1 cm more than twice the base: 2x + 1 cm. x... 1
- In a right – angled triangle, one of the acute angles exceeds the other by 200 Answer: The acute angles are 55° and 35°. In a right-angled triangle, the two acute angles add up to 90° (since the angle sum is 180° and on... 1
- The difference between two numbers is 5. Six times the smaller number is equal to four times the greater Answer: The numbers are 15 and 10. Let the greater number be x and the smaller y . x - y = 5 (1) 6y = 4x ⇒ 2x - 3y = 0 (2) From (1), x = y +... 1
- The perimeter of an isosceles triangle is 43cm. The length of its each congruent side is 1 cm less than twice the Answer: The sides are 17 cm, 17 cm and 9 cm (base). Let the base be x cm. Each congruent side is 1 less than twice the base: 2x - 1 cm. Peri... 1
- Cost of a table is three times the cost of a chair. One table and one chair together cost Rs. 800. Answer: The table costs Rs. 600. Let the cost of a chair be Rs. x . Then a table costs Rs. 3x . x + 3x = 800 4x = 800 ⇒ x = 200 Chair = Rs.... 1
- Ram has in all 35 coins, some of denomination 25 paise and some of 10 paise. Total amount is Rs. 6.20. Answer: 18 coins of 25 paise and 17 coins of 10 paise Let the number of 25 paise coins be x and of 10 paise coins be y . Rs. 6.20 = 620 pais... 1
- The sum of the present ages of Ram and Shyam is 36 years. Ram is elder than Shyam by 2 years. Find their present ages. Given data: The sum of the present ages of Ram and Shyam is 36 years: Ram + Shyam = 36 Ram is elder than Shyam by 2 years: Ram = Shyam + 2 W... 1
- The length of a rectangle is greater than twice its breadth by 4 cm. If the perimeter of the rectangle is 26 cm, Answer: Length = 10 cm, Breadth = 3 cm Let the breadth be x cm. The length is 4 cm more than twice the breadth, so length = 2x + 4 cm. Perim... 1
- The sum of the two numbers is 25 and the difference between them is 15. Find the two numbers. Let's solve the problem step by step: Let the two numbers be 'x' and 'y'. Given information: The sum of the two numbers is 25: x + y = 25. T... 1
- The sum of two numbers is 40 and the greater number is thrice the smaller number. Find the numbers. Let's solve the problem step by step: Let the smaller number be 'x' and the greater number be 'y'. Given information: The sum of two numbers... 1
- Suresh scored 15 marks more than Ramesh in Mathematics. If the sum of their marks in Mathematics is 275, Let the marks obtained by Ramesh in Mathematics be 'R' and the marks obtained by Suresh be 'S'. Given information: Suresh scored 15 marks mo... 1
- A boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream, it takes These types of questions are the real-time examples of linear equations in two variables. In water, the direction along the stream is called... 1
- If the cost of bananas is increased by Rs. 10 per dozen, one can get 3 dozen less for Rs.600. Let x be the original cost of 1 dozen bananas , for Rs. 600 we gets y dozens. xy =600 .................... 1 y=600over x By increasing the c... 1
- Find the first two terms of the sequence for which Sn is given below Sn=n^2 (n+1) Answer is 2 , 10 Solution :: To find the first term substitute n=1 in formula S₁=1²(1+1)=1(2)=2 To find the second term, substitute n = 2 in... 1
- Prove. Sec2 A + Cosec2 A = Sec2 A Cosec2 A Proof :: LHS = sec² A + cosec² A =1over(cos²A)+1over(sin²A)=(sin²A+cos²A)over(cos²A sin²A) =1over(cos²A sin²A)=sec²A cosec²A=RHS 1