Maharashtra State Board
- 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
- What is the law of conservation of energy? Energy can neither be created nor destroyed. It can be converted from one form into another. Thus, the total amount of energy in the univers... 1
- Into which form are the chemical energy stored in the exploding firecrackers converted to? Energy is transformed from one form to another. In the example stated, the exploding firecrackers convert the chemical energy stored in them... 1
- Ajay and Atul have been asked to determine the potential energy of a ball of mass m kept on a table as shown As seen from the picture, the heights of the ball with respect to Ajay and Atul are different. Also, given that the potential energy is rela... 1
- What is the potential energy? Potential energy of the object is the energy stored in it because of its specific state or position. 1
- What is kinetic energy? Kinetic energy is the energy that an object has because of its motion. The kinetic energy gained by the object is the work done by a force t... 1
- Define energy. What is its unit? Energy is the capacity of a body to perform work. Unit of energy is the same as that of work. In the SI system, the unit is joule, while in... 1
- Pravin has applied a force of 100 N on an object, at an angle of 600 to the horizontal. The object gets displaced Given here is θ=60⁰ and F=100N, while W= 400J , SO s=? Take the equation W = F s Cos θ Replace with values 400= 100 × s × ½ Hence, 400 / 100... 1
- Calculate the work done to take an object of mass 20 kg to a height of 10 m. (g = 9 8 m/s2) Suppose mass of the object (m) = 20 kg, while height (s) = 10 m given that g = 9.8 m/s² The value for F = mg = 20 × (-9 8) (Because the disp... 2
- Write about the National Physical Laboratory. The National Physical Laboratory, conceptualized in 1943 was situated in New Delhi and functions under the Council of Scientific and Industr... 1