1] Which of the following is irrational: [Marks:1] A.
2] Find the value of p such that (x -1) is the factor of the polynomial x3+10x2+ px . [Marks:1] A. p = 7
B. p = -7
C. p = 11
D. p = -11
3] Find remainder when is divided by [Marks:1] A. -1
What are the two factors of quadratic polynomial ? [Marks:1] A. (x+8) and (x-8)
B. (x+16) and (x-4)
C. (x-16) and (x-64)
D. (x-8) and (x-8)
5] Given lines l1 l2 and l3 in fig., are parallel. The value of x is : [Marks:1] A. 50o
6] [Marks:1] A. BC = EF
B. AC = EF
C. BC = DE
D. AC = DE
7] The area of an equilateral triangle with perimeter 18x is: [Marks:1] A.
8] The area of triangle, whose sides are 15 cm, 25 cm and 14 cm is [Marks:1] A.
9] Simplify: . [Marks:2]
11] Without actually calculating the cubes, find the value of 753 - 253 - 503. [Marks:2]
12] Lines PQ and RS intersect each other at point O. If POR: ROQ= 5:7, find all the remaining angles.
In figure, find the value of x. [Marks:2]
13] In the figure AD is the bisector of A, prove that AB > BD.
14] Where do the following points lie:
(D) (10,4) [Marks:2]
15] Simplify: . [Marks:3]
16] Represent the irrational number geometrically [Marks:3]
17] The polynomials p(x) = ax3 + 3x2 - 3 and q(x) = 2x3 - 5x + a, when divided by (x - 4) leave the remainders R1 and R2 . Find ‘a" if: R1 + R2 = 0. OR
Factorise the following polynomial.
2x3 - x2 - 13x - 6 [Marks:3]
18] (x + 2) is one of the factors of the polynomial x3 +13x2 + 32x + 20. Find its remaining factors. [Marks:3]
21] In ABC, BD and CE are two altitudes such that BD = CE. Prove that ABC is isosceles. [Marks:3]
22] A point O is taken inside an equilateral four sided figure ABCD such that its distances from the angular points D and B are equal. Show that AO and OC are in one and the same straight line.
24] A garden is in the shape of quadrilateral. The sides of the garden are 9m, 40m, 28m and 15m respectively in consecutive order and the angle between first two sides is a right angle. Find the area of the garden. [Marks:3]
26] If both a and b are rational numbers, find a and b for the following: [Marks:4]
27] The polynomials x3 + 2x2 - 5ax - 8 and x3 + ax2 - 12x - 6 when divided by (x - 2) and (x - 3) leave remainder p and q respectively. If q - p = 10, find the value of a. [Marks:4]
29] Factorise: x3 + 13x2 + 32x + 20.
If x and y be two positive real number such that 8x3 + 27y3 = 730 and 2x2y + 3xy2 = 15 then show that 2x + 3y = 10. [Marks:4]
30] How does Euclid's fifth postulate imply the existence of parallel lines? Give a mathematical proof. [Marks:4]
31] In fig., if AC = BC, DCA = ECB and DBC = EAC then Prove that BD = AE. [Marks:4]
32] In fig., l||m, show that 1 + 2 - 3 = 180o [Marks:4]
33] In figure, AC = AE, AB = AD and BAD = EAC show that BC = DE. [Marks:4]
34] Anju suggested a sketch plan to construct a lawn in her school playground by marking four points (-1,0) (1,0) (1,2) (-1,2) on a graph paper and also suggesting to plant a tree in the centre of the lawn. Plot these points on the graph paper and specify the type of the shape of the lawn suggested by Anju. Also, find the coordinates of the place where the tree is to be planted. What value is indicated from this action? [Marks:4]