SECTION – A

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```SECTION – A
Question numbers 1 to 4 carry 1 mark each.
1
Find the product 3 2 . 4 2 . 12 32 .
2
Find one factor of (9x 1) (13x) .
1
3
An exterior angle of a triangle measures 140. If the interior opposite angles are in the ratio 3 : 1
1
2
1
2
then find the angles of the triangle.
4
What is the x-co odinate of any point on the y-axis ?
1
SECTION – B
Question numbers 5 to 10 carry 2 marks each.
3
5
and .
5
7
5
Insert three rational numbers between
2
6
For what value of k is the polynomial p(x)2x3kx23x10 exactly divisible by (x2) ?
2
7
In figure C is the mid-point of AB and D is the midpoint of AC. Prove that
2
1
4
8
In figure, if lines PQ and RS intersect at point T, such that PRT50, TSQ60 and
RPT100, find SQT.
Page 1 of 4
2
9
If a point P(2, 3) lies in first quadrant, then what will be the co-ordinates of a point Q opposite to it in
2
fourth quadrant having equal distance from x-axis ?
10
The semi-perimeter of a triangle is 132 cm. The product of the difference of
2
3
semi-perimeter and its respective sides is 13200 cm . Find the area of the triangle.
SECTION – C
Question numbers 11 to 20 carry 3 marks each.
11
12
If
1  2
1  2

 a  b 2 , then find a and b .
1  2
1  2
Find the value of a and b if
5  3
ab 3 .
7  4 3
3
3
13
If ab7 and a2b285, find a3b3.
3
14
If xa is a factor of x4a2x23xa, then find the value of a.
3
15
ABCD is a square. X and Y are points on the sides AD and BC such that AY= BX. Prove that
3
XAY=YBX
16
In the given figure ABC and DBC are two triangles on the same base BC and vertices A and D
are on the same side of BC, AD is extended to intersect BC at P. Show that :
(i)
Page 2 of 4
ABD ACD
(ii)
ABP ACP
3
17
If a transversal intersects two parallel lines, then prove that bisectors of alternate interior angles
3
are parallel.
18
In figure two sides AB and BC and median AM of ABC are respectively equal to sides DE and
3
DF and the median DN of DEF. Prove that ABCDEF.
19
Find the area of the trapezium in which parallel sides are 25 cm and 10 cm and non-parallel sides
3
are 14 cm and 13 cm.
20
The adjacent sides of a parallelogram ABCD are AB 34 cm, BC20 cm and diagonal AC = 42
3
cm. Find the area of the parallelogram.
SECTION – D
Question numbers 21 to 31 carry 4 marks each.
21
Varun was facing some difficulty in simplyfying
1
. His classmate Priya gave him a clue to
7 3
rationalise the denominator for simplification. Varun simplified the expression and thanked
Page 3 of 4
4
Priya for this goodwill. How Varun simplified
1

1 2
22
Prove that :
23
a2b2 

Simplify
3

1
? What value does it indicate ?
7 3
1
1
1

..........
 2
2  3
3  4
8  3
 b2c2

3

 c2a 2

4
3
4
 ab3 bc3 ca3
4
3
2
2
24
Without actual division prove that x 2x 2x 2x3 is exactly divisible by x 2x3.
4
25
Show by long division that 2x3 is a factor of p(x)4x48x35x2x3.
4
26
Find the value of k, if (x3) is a factor of p(x)2x35x23xk.
4
27
Show that the perimeter of a is greater than the sum of its three medians.
4
28
Prove that the sum of three angles of a triangle is 180. Using this result, find the value of x and
4
all three angles of a triangle if the angles are (2x7), (x25) and (3x12).
29
Prove that the angles opposite to equal sides of a triangle are equal.
4
30
In the given figure AB is a line segment and p is its mid-point. D and E are points on the same
4
side of AB such that BADABE and EPADPB. Show that :
(i)
31
DAP EBP
,
(ii)