# Triangle and Marks

1]

when simplified is:

[Marks:1]

A.

negative and irrational

B.

negative and rational

C.

positive and irrational

D.

positive and rational

2]

The value of the polynomial x2 – x – 1 at x = -1 is

[Marks:1]

A.

Zero

B.

-1

C.

-3

D.

1

3]

The remainder when x2 + 2x + 1 is divided by (x + 1) is

[Marks:1]

A.

1

B.

4

C.

-1

D.

0

4]

In fig., AOB is a straight line, the value of x is:

[Marks:1]

A.

60°

B.

20°

C.

40°

D.

30°

5]

The number of line segment determined by three given non - collinear points is: [Marks:1]

A.

Two

B.

infinitely many

C.

Four

D.

Three

6]

The area of a right triangle with base 5 m and altitude 12 m is [Marks:1]

A.

50 m2

B.

15 m2

C.

9 m2

D.

30 m2

7]

Evaluate: 53 - 23 - 33

[Marks:1]

A.

80

B.

60

C.

120

D.

90

8]

The area of an equilateral triangle of side 14 cm is

[Marks:1]

A.

B.

C.

D.

9]

Simplify:

[Marks:2]

10]

Check whether (x + 1) is a factor of x3 + x + x2 + 1.

[Marks:2]

11]

In fig., OQ bisects AOB. OP is a ray opposite to ray OQ. Prove that POA=POB.

OR

In fig., AOC and BOC form a linear pair. If a - b = 80°, find the values of a and b.

[Marks:2]

12]

[Marks:2]

13]

The perpendicular distance of a point from the x - axis is 2 units and the perpendicular distance from the y - axis is 5 units. Write the coordinates of such a point if it lies in the: (i) I Quadrant (ii) II Quadrant

(iii) III Quadrant(iv) IV Quadrant

[Marks:2]

14]

The volume of a cuboid is given by the algebraic expression ky2 - 6ky +8k. Find the possible expressions of the dimensions of the cuboid. [Marks:2]

15]

Simplify the following expression:

[Marks:3]

16]

Evaluate: given that = 2.236.

OR

If , find a and b.

[Marks:3]

17]

Factorise: (2x - y - z)3 + (2y - z - x) + (2z - x - y)3.

OR

If a = 3 + b, prove that a3 - b3 - 9ab = 27.

[Marks:3]

18]

If a + b = 11, a2 + b2 = 61, find a3 + b3.

[Marks:3]

19]

OR

Prove that the sum of the angles of a triangle is 180°.

[Marks:3]

20]

In ABC, AC > AB and AD is the bisector of A. Show that ADC > ADB. [Marks:3]

21]

The side of a triangular park are 8m, 10m and 6m respectively. A small circular area of diameter 2m is to be left out and the remaining area is to be used for growing roses. How much area is used for growing roses? (use = 3.14) [Marks:3]

22]

In fig., l1||l2 and a1||a2. Find the value of x.

[Marks:3]

23]

ABCD is a quadrilateral in which AB = AD, BC = DC. AC and BD intersect at E. Prove that, AC bisects each of the angles A and C. [Marks:3]

24]

AP and BQ are bisectors of angles A and B of a quadrilateral ABCD. Prove that, 2APB = C + D

[Marks:3]

25]

The polynomials p(x) = ax3 + 4x2 + 3x - 4 and q(x) = x3 - 4x + a leave the same remainder when divided by x - 3. Find the remainder when p(x) is divided by (x - 2). [Marks:4]

26]

Factorise: 2x3 - 3x2 - 17x + 30.

[Marks:4]

27]

OR

In triangle ABC, the bisector of the exterior angle C and the bisector of interior angle B meet at a point D. Prove that, D=A [Marks:4]

28]

If both (x + 2) and (2x + 1) are factors of ax2 + 2x + b, prove that a - b = 0. OR

Factorise:

[Marks:4]

29]

If AD is the median of ABC, prove that AB + AC > 2AD.

[Marks:4]

30]

In fig., PQ and RS are perpendicular to QS, QA = BS and PB = AR. Prove that QPB = SRA.

[Marks:4]

31]

[Marks:4]

32]

[Marks:4]

33]

Plot the points (-2,2), (3, 2), (3,-2) and (-2,-2) on Cartesian plane. Name the figure formed by joining these points. Also, find the area of the figure so formed. [Marks:4]...

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