#   Annual Sample Paper – II : 2013 – 14

```Annual Sample Paper – II : 2013 – 14
Std. : IX
Q:1
Sub. : Maths
SECTION : A (All questions are compulsory in this section)
(A) Find amount and C.I. on ` 19,000 in 3 years at 8% p.a.
2
(B) If x +
(03)
1
1
3
=
7
,
find
x
+
x2
x3
(03)
(C) The sum of three consecutive natural numbers divisible by 3 is x, form an
equation. Also find the three numbers.
(04)
Q:2
(A) Solve for x.
1
3
 x – 1 –
(03)
1
 x – 2 = 1
4
(B) In ABC , D and E are the mid-points of AC and BC respectively. Find the values
of (a) ABC (b) DE if AB = 4.4 cm.
(03)
(C) A man invested ` 40,000 for 3 years at the C.I. rate of 8% p.a. After 2 years the
rate of interest was raised to 10%.
(04)
(1) Find the total interest earned by him.
(2) Find the amount he received after 3 years.
Q:3
(A) A map of a rectangular field is drawn to a scale of 1 : 5000.
(03)
(1) Find the actual length of the field if the length of the same in the map is 25
cm.
(2) If the actual width of the field is 1 km., find its width in the map.
(B) In the figure AB = 6 cm. AC = 10 cm, find the values of
(03)
(a) sin 
(b) cos 
(c)
10 cm
6 cm
cosec + sec
(C) In the given figure MN KL GH and AB = AC. If DE = 2.2 cm, find DF.
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(04)
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Q:4
(A) If sin =
(a)
5
13
then find
tan 
1
cos
(03)
(b)
5sin – cos
tan
(B) The edge of a cube measures 5 cm, find (a) its volume (b) its surface area and
the length of a diagonal.
(03)
(C) Raju lends ` 10,000 to John at the simple interest rate of 10% for 3 years and `
10,000 to Rahim at the compound interest rate of 15% for 2 years. Find the sum
of money that John and Rahimwill return to Raju when they repay the loan.
Who will pay more and by how much ?
(04)
(a) If AD = 3 cm, DB = 4 cm, EC = 12 cm, find AE.
(b) If AE = 2.7 cm, EC = 4.5 cm, AD = 2.4 cm, find BD.
SECTION : B
(Attempt any four questions from this section)
Q:5
(A) Find x if the mean of three numbers is 8 and the mean of those three numbers
and x is 7.
(03)
(B) Evaluate : 2sin2 30° – 3cos2 45° + tan2 60°
(03)
(C) Find the area of the triangle whose sides are in the ratio 5:6:7 and the
perimeter is 54 cm.
(04)
Q:6
(A) Two cubes of edge 14 cm each are joined end to end to form a cuboid, find the
volume and the total surface area of the cuboid.
(03)
(B) Solve using elimination method.
3x – 7y = 7,
(03)
11x + 5y – 87
(C) The denominator of a fraction is 1 more than double of the numerator. If both
the numerator and denominator are increase by 4, the fraction becomes
assuming the numerator as x, find the fraction.
Q:7
(A) (1) Factorize : 25x2 + 20x + 3
4
2
  a
3
5
(04)
(03)

(2) Simplify :  – 1  
+ 1
2
a
  16–a

(B)
ABC is right angled at B and D is any point on AB DE is perpendicular to AC. If
AD = 4 cm, AB = 16 cm and AC = 24 cm, find AE.
(03)
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(C) A two-digit number is 7 itmes the sum of its digits. The number formed by
reversing the degits is 18 less than the original number. Find the number.
(04)
(a) volume
Q:8
(b) C. S. A
(c)
T. S. A
(A) The money spent by 30 students during the tiffin hour were as follows..
Find the mean.
(03)
Money Spent (in `)
No. of Students
0
5
5
2
10
12
20
7
25
2
30
2
Total
30
(B) Draw the graph of the equating given below using the slope and y - intercept
(03)
X=y+2
(C) (1) Evaluate :
1283 + 2723
1282 – 128 × 272 + 2722
(04)
(2) Factorize : (x + 2) (x + 3) –12
Q:9
(A) Construct a histogram of the given data.
Class-interval
Frequency
0-30
7
30-60
4
60-90
5
(03)
90-120 120-150
10
6
Total
32
(B) (1) Find the median of first 6 prime numbers.
(03)
(2) Find the median of the following data.
Variate
10
11
12
13
14
Frequency
1
2
3
4
5
(C) For the collection of data be grouped into the class intervals 56-59, 59-62, 6265, 65-68, 68-71 then answer the following
(04)
(1) What is the type of these clas intervals ?
(2) What are the class limits and class boundaries of the class interval 68-71 ?
(3) What are the class size and the class mark of the class interval 68-71 ?
Where data is
60, 65, 63, 70, 65, 62, 65, 63, 64, 60, 68, 58, 62, 65, 63, 65, 64, 60, 62, 63.
Q : 10
(A) The area of a trapemium is 240cm2 and its parallel sides are in the ratio 2:1. If
the distance between the parallel sides is 50 cm then find the longer of the
parallel sides.
(03)
(B) In how many years will a sum of ` 5000 become ` 6655 at the compound
interest rate of 10% per annum ?
(03)
(C) The curved surface area of a right circular cylinder is 1760 cm2 and its radius is
14cm. Find its
(04)
(1) height
(2) Volume and capacity in litres
(3) curved surface area and
(4) Total surface area
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