Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

711. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).

Area of the square lawn PQRS = 42 m x 42 m

Let OP = OS = xm
So, x² + x² = (42)²

⇒ 2x² = 42 x 42

⇒ x² = 21 x 42

Now,
area of sector POS=

$90 over 360 space x space πx squared space equals space 1 fourth space straight x space left parenthesis πx right parenthesis squared space.... space left parenthesis space straight i space right parenthesis equals 1 fourth space space straight x space 22 over 7 space straight x space 21 space straight x space 42 space straight m squared space.... space left parenthesis ii right parenthesis Also comma space Area space of space increment POS space equals space 1 fourth space straight x space Area space of space square space lawn space PQRS space equals space 1 fourth space straight x space left parenthesis space 42 space straight x space 42 right parenthesis squared space straight m squared space space space space space left parenthesis angle POQ space equals space 90 degree right parenthesis space.. space left parenthesis iii right parenthesis So comma space Area space of space flower space bed space PSP space equals space Area space of space Sector space POS space minus space Area space of space increment POS space equals space 1 fourth space straight x space 22 over 7 space straight x space 21 space straight x 42 space minus space 1 fourth space straight x space 42 space straight x space 42 space space left square bracket frome space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis right square bracket space equals space 1 fourth space straight x space 21 space straight x space 42 space straight x open parentheses 22 over 7 space minus space 2 close parentheses equals space 1 fourth space straight x space 21 space straight x space 42 space straight x space open parentheses 8 over 7 close parentheses straight m squared Therefore space area space of space the space two space flower space beds space equals space 2 space straight x space 1 fourth space straight x space 21 space straight x space 42 space straight x open parentheses space 8 over 7 close parentheses space space equals space 504 space straight m squared Hence comma space the space total space area space of space the space two space flower space beds space 504 space straight m squared$

3460 Views

712. From each end of a solid metal cylinder, metal was scooped out in the hemispherical form of the same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire. ( π = 22/7)

3312 Views

Short Answer Type

713.

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere?

9521 Views

714.

The 3/4th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in a cylindrical vessel.

4703 Views

715.

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

4315 Views

Long Answer Type

716.

In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of the hospital whose length is 25 m and breadth is 20 m. If the tank is filled completely then what will be the height of standing water used for irrigating the park. Write your views on recycling of water.

7864 Views

717.

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.

6743 Views

718.

The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts.

9459 Views

Short Answer Type

719.

In figure, ABCD is a rectangle. Find the values of x and y.

720.

If A(–2, 1), B(a, 0), C(4, b) and D(1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.