Question
Solution
1/4 - √ 8 + 3 + 2√2/3 - 2√2 – 3 - 2√2/3 + 2√2 = a + b√2 Rationalizing each we get 1/4 - √8 → 1/4 -√8 × 4 + √8 / 4 + √8 = 4 + √8 / 8 Same for other values = 3 + 2√2 / 3 – 2√2 = 17 + 12√2 = 3 - 2√2 / 3 + 2√2 = 17 - 12√2 = 4 + √8 / / + 17 + 12√2 – 17 + 12√2 On solving 1/2 + 97√2/4 = a + b√2 So, a = 1/2 and b = 97/4 (3 × 1/2 + 4 × 97/4) = 3/2 + 97 = 197/2
If (x² + 1/x2) = 4, which of the options below is a possible value of x² - 1/x2 ?
The difference between the length and breadth of a rectangle is 13 m. If its perimeter is 186 m, then its area is
The length of a 744 metre long wire is 12 times the perimeter of a rectangular French garden. Find the area of the rectangular garden given that its len...
The lateral surface area of a cube is 484 cm2 . The length of a cuboid is 10% more than the side of the cube. The breadth of the cuboid is 9 ...
If the areas of three adjacent faces of a rectangular box which meet in a corner are 12cm2, 15cm2 and 20cm2 respective...
A solid cylinder of radius 7 cm and height 15 cm is melted and recast into small cones each of radius 3.5 cm and height 6 cm. How many cones are formed?
Which of the following two will provide more volume?
I) A cuboid of edges 6 cm, 7 cm and 8 cm
II) A cube of edge 7 cm
- A cone has a radius of 18 cm and its curved surface area is 1980 cm². Find its height.
Find the lateral surface area of a pyramid with a rectangular base measuring 12 meters by 8 meters and a slant height of 18 meters.
- The length of a rectangle is the same as the side of a square. If the area of the square is 625 m² and that of the rectangle is 500 m², what is the perim...
