**Sample Paper- 2013**

**Subject: Mathematics**

**Class- X**

^{th}**General Instructions:**

(i)
All
questions are compulsory. There are three sections A, B, C and D in the
question paper.

(ii)
Section
A: Q. Nos. 1 to 8 carry 1 mark each.

##
Section B: Q. Nos.9 to 14 carry 2 marks each*. *

Section C: Q. Nos. 15 to 24 carry 3 mark
each.

Section D: Q. Nos. 25 to 34 carry 4 mark
each.

(iii)
There is
no overall choice, however internal choices has been provided in one question
of 2 marks, three questions of 3 marks and 2 questions of 4 marks. You have to
attempt only one of the alternatives in all such questions.

**Section A**

1.
If the equation x

^{2}+ 4x + k = 0 has real and distinct roots, then
(a)
K< 4 (b) k > 4 (c) k ≥ 4 (d) k ≤ 4

2.
If x > y > 0, x

^{2}+ y^{2}= 13 and x y = 6, then y =
(a)
4 (b) 3 (c) 2 (d) none of these

3.
If
the area of the triangle formed by the points (k, 4/3) , (-2, 6) and (3, 1) is
5 sq units , then k is

(a)
3 (b) 5
(c) 2/3 (d) 3/5

4. The sum of n term of
an AP is 3n2 + 5n, then 164 is its

(a)
24

^{th}term (b) 27^{th}term (c) 29^{th}term (d) none of these
5. If first term of an
AP is a and nth term is b, then its common difference is

(a) (b-a)/n+1 (b) (b-a)/n-1 (c) (b-a)/n (d) none of these

6.
The
height of a tower is 100√3 m. the angle of elevation of its top from a point
100 m away from its foot is

(a)
30

^{o}
(b)
45

^{o}
(c)
60

^{o}
(d)
None
of these

7.
Which
was the first book on Probability?

(a) Dealing with
possibilities

(b) World of chances

(c ) Book on games
of chance

(d) None of the
above

8.
A
letter is chosen at random from the letters of the word ‘ASSASSINATION’. Find
the probability that the letter chosen is a consonant.

(a)
1/13

(b)
2/13

(c)
7/13

(d)
6/13

**Section B**

9.
Find
the value of K so that the sum of the roots of the equation 3x

^{2 }+ (2k+1) x – k – 5 = 0 is equal to the product of roots.
10. Show that the roots
of the equation. (x - a) (x - b) + (x - b) (x - c) + (x - c) (x - a) = 0 are
always real and they cannot be equal unless a = b = c.

11.
Solve
for x, 4√6 x

^{2}-13 x -2√6 = 0 by using a completing the square.
12. Prove that the
tangents drawn at the ends of a diameter of a circle are parallel.

13. Find the distance
between the points P (-4, 0) and Q (2,-5).

**Or**

Show that the points
A(1,2), B(5,4), C(3,8) and D(-1,6) are the vertices of a square.

14.
Divide a line segment of length 8 cm internally in the ratio
4:5. Also, give justification of the construction.

**Section C**

15. Find the centre of a
circle passing through the points (6, -6), (3, -7) and (3, 3). Also find the
radius.

16. One
natural number is 3 times the other number. Sum of their squares exceeds 13
times of the greatest number by 4. Find both the numbers.

17. What is the
probability that a leap year, selected at random will contain 53 Sundays?

18. Find the 103

^{th }term of the AP 4, 4 ½, 5, 5 ½, 6 ……..**Or**

The fourth term of an AP is 0. Prove that its 25

^{th}term is triple its 11^{th}term.
19. Prove that a

_{m + n }+ a_{m - n }=2a_{m}
20. For what value of n, the nth term of the
following two A.P.’s are equal?

21. 20, 25, 30, 35… And -17, -10, -3, 4…

22. Two
concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of
the larger circle which touches the smaller circle

23. Prove that opposite sides of a quadrilateral
circumscribing a circle subtend supplementary angles at the centre of the circle.

24. A copper wire 0.4 cm in diameter is evenly
wound about a cylinder whose length is 24 cm and diameter 20 cm so as to cover
the whole surface. Find the length and weight of the wire assuming the specific
gravity to be 10 gm/cm

^{3}.
25. 500 men took a dip
in an 80 m long and 50 m broad tank. What is the rise in the water level if the
average displacement of water by a man is 4 sq m?

**Section D**

26. If the
sides of a right angled triangle are x, x + 1 and x - 1, find the hypotenuse.

27. Find the ratio in
which the line 2x + y - 4 = 0 divides the line segment joining A (2, -2) and B
(3, 7)

28. A metallic cylinder has radius 3 mm and
height 5 mm. It is made of a metal A. to reduce its weight, a conical hole is
drilled in the cylinder as shown in the figure and

it completely filled with a lighter metal B.
the conical hole has a radius

of 1.5 mm and its depth is 8/9 mm. calculate
the ratio of the volume

of the metal A to the volume of metal B in
the solid.

29. The adjoin figure shows the cross section of
an ice cream consisting of a cone surmounted by a hemisphere. The radius of the
hemisphere is 3.5 cm and the height of the cone is 10.5 cm. the outer shell
ABCDFE is shaded and it is not filled with ice

Cream. AE = DC = 0.5 cm, and AB is parallel
to EF, BC is parallel to FD

Calculate:

(i)
The
volume of the ice cream in the cone (the un shaded

Portion including the hemi sphere)

(ii)
The
volume of the outer shell (the shaded portion)

30.
Two
circles touch externally. The sum of their areas is 130 Ï€
sq cm and the distance between the centers is 14 cm. find the radii of the
circles.

31. In the given figure, a crescent is formed by
two circles which touch at A. C is the centre of the larger circle. The width
of the crescent at BD = 9 cm and at EF it is 5 cm. find the radii of two
circles and the area of the shaded region.

32. Two
pillars of equal heights stands on either side of a road which is 150m wide. At
a point on the road between the pillars, the angles of elevation of the tops of
the pillars are 60° and 30°. Find the height of each pillar and the position of
the point on the road.

**Or**

A
ladder 10 metres long reaches a point 10 meters below the top of a vertical
flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60

^{o}. Find the height of the flagstaff.
33. Construct
a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose
side’s are2/3 of the corresponding sides
of the first triangle.

Give the justification of the
construction.

34. A bag contains only black and white balls. The probability of picking at
random a black ball from the bag is 7/10.

**(i)**

**What is the probability of picking a white ball from the bag?**

**(ii)**Can you say how many black and white balls are in the bag?

Hemant Kumar

Delhi Public School

Mathura Refinery Nagar, Mathura

Email Id: hkumarsharma@gmail.com

## No comments:

## Post a Comment