CBSE
Class 10 Class 12
Download this Mathematics Pre Board Paper 1 for taking the test offline or sharing with your friends. Once you are done with all the answers to the questions, Go ahead with answer key to check your answers.
General Instructions:
| 1. | E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ABE ~ ∆CFB. | [1] |
| 2. |
Find the roots of the quadratic equation | [1] |
| 3. |
For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an A.P? | [1] |
| 4. |
Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear | [1] |
| 5. |
Write a rational number between ![<pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array)
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#6 {main}</pre>](/application/zrc/images/qvar/MAEN10041205.png) . | [1] |
| 6. | Write the value of sin2 69° + sin2 21°. | [1] |
| 7. |
A card is drawn at random from a well -shuffled fled pack of 52 playing cards. Find the probability of getting neither a red card nor a queen. | [2] |
| 8. | The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence, the sum of the ages of his children will be twice the ages of their father. Find the present age of the father. | [2] |
| 9. | Find the largest number which divides 245 and 1029 leaving remainder 5 in each case. | [2] |
| 10. |
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle. | [2] |
| 11. |
Three different coins are tossed together. Find the probability of getting | [2] |
| 12. | Three numbers are in A .P. if the sum of these numbers is 27 and the product 585, find the numbers. | [2] |
| 13. |
Consider the following distribution of daily wages of 50 workers of a factory.
Find the mean daily wages of the workers. | [3] |
| 14. |
A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (π = 22/7) | [3] |
| 15. |
In Fig. , PQ is tangent at point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA. | [3] |
| 16. |
In Fig. find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (use π =22/7)  | [3] |
| 17. |
Show that ΔABC, where A(–2, 0), B(2, 0), C(0, 2) and ΔPQR where P(–4, 0), Q(4, 0), R(0, 2) are similar triangles. | [3] |
In the given Fig. PB and QA are perpendiculars to segment AB. If PO = 5 cm, QO = 7 cm and area ∆POB = 150 cm2 find the area of ∆QOA.
| 18. |
Write the simplest value of 
| [3] |
| 19. |
Prove that | [3] |
| 20. |
The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p. | [3] |
If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.
| 21. | Tanvika went to a hotel in a town with her big family. They consumed 23 idlies, ISpoories, 7 dosas and 19 vadas. the bill was Rs. 108. Next day they consumed 34 idlies, 8 vadas, 22 poories and 7 dosas. The bill came to Rs. 114 if one idilie cost same as vada. What is the cost of one poori ? | [3] |
| 22. |
Find all the zeroes of the polynomial  given that  are two of its zeroes. | [3] |
| 23. |
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. | [4] |
| 24. |
What is the value of the median of the data using the graph in figure, of 'less than' ogive and 'more than ogive'? | [4] |
| 25. |
Construct a ΔABC in which AB = 6 cm, ∠A = 30o and ∠B = 60o. Construct another ΔAB'C' similar to ΔABC with base AB' = 8 cm | [4] |
| 26. |
The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60o. From a point Y, 40 m vertically above X, the angle of elevation of the top Q of the tower is 45o. Find the height of the tower PQ and the distance PX. | [4] |
| 27. |
In the given Fig, two triangles ABC and DBC lie on the same side of base BC. P is a point on BC such that PQ || BA and PR || BD. Prove that: QR || AD. | [4] |
| 28. |
In right-triangle ABC, right angled at B, if  Show that 
| [4] |
| 29. |
Find the sum of n terms of the series | [4] |
| 30. |
Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream. | [4] |
Solve for x:
is irrational.
