Maths standard sample paper
Answers
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sec - a, b question isend u later on class board x look on that
Section C
27 Given that √5 is irrational, prove that 2√5 − 3is an irrational number.
OR
If HCF of 144 and 180 is expressed in the form 13m-16. Find the value of m.
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8
28 If the sum of first m terms of an AP is the same as the sum of its first n terms, show
that the sum of its first (m+n) terms is zero.
3
29 In the figure, ABCDE is a pentagon with BE||CD and BC||DE. BC is perpendicular to
CD. AB= 5cm, AE=5cm, BE= 7cm, BC= x-y and CD= x+y. If the perimeter of ABCDE is
27cm. find the value of x and y, given x, y ≠ 0.
A
B E
C D
OR
Solve the following system of equations:
21
+
47
= 110
+
= 162, , ≠ 0
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30 Obtain all the zeros of the polynomial x4+4x3-2x2-20x-15, if two of its zeroes are √5 and
−√5.
3
31 Two friends Seema and Aditya work in the same office at Delhi. In the Christmas
vacations, both decided to go to their hometowns represented by Town A and Town B
respectively in the figure given below. Town A and Town B are connected by trains
from the same station C (in the given figure)in Delhi.Based on the given situation,
answer the following questions:
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(i) Who will travel more distance, Seema or Aditya, to reach to their hometown?
(ii) Seema and Aditya planned to meet at a location D situated at a point D
represented by the mid-point of the line joining the points represented by
Town A and Town B. Find the coordinates of the point represented by the
point D
(iii) Find the area of the triangle formed by joining the points represented by A, B
and C.
32 If sin θ + cos θ = √3, then prove that tan θ + cot θ =1
OR
Evaluate:
(°) (°)
(°)× (°) + (30° + 90°) × (60° − 0°)
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33 Sides of a right triangular field are 25m, 24m and 7m. At the three corners of the field, a
cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the
field. Find the area of the field that cannot be grazed by these animals.
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10
34 A TV reporter was given a task to prepare a report on the rainfall of the city
Dispur of India in a particular year. After collecting the data, he analyzed
the data and prepared a report on the rainfall of the city. Using this report,
he drew the following graph for a particular time period of 66 days
Based on the above graph, answer the following questions:
(i) Identify less than type ogive and more than type ogive from the given graph.
(ii) Find the median rainfall of Dispur
(iii) Obtain the Mode of the data if mean rainfall is 23.4cm
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Section - D
35 Draw a triangle ABC with side BC=6.5cm, ∠B=30°, ∠A =105°. Then construct another
triangle whose sides are
times the corresponding sides of the triangle ABC.
OR
Construct a pair of tangents to a circle of radius 3 cm which are inclined to each other at
an angle of 60°
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0
10
20
30
40
50
60
70
0 10 20 30 40 50 60 70
Cumulative Frequency
Rainfall in cm
curve 1
curve 2
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36 Prove that if a line is drawn parallel to one side of a triangle to intersect the other two
sides in distinct points, then the other two sides are divided in the same ratio.
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37 A train covers a distance of 360 km at a uniform speed. Had the speed been 5km/hour
more, it would have taken 48 minutes less for the journey. Find the original speed of the
train.
OR
Solve the following equation:
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38 A petrol tank is in the form of a frustum of a cone of height 20 m with diameters of its
lower and upper ends as 20 m and 50 m respectively. Find the cost of petrol which can
fill the tank completely at the rate of Rs. 70 per litre. Also find the surface area of the
tank.
OR
Water is flowing at the rate of 15km/hour through a pipe of diameter 14cm into a
cuboidal pond which is 50m long and 44m wide. In what time will the level of water in the
pond rise by 21cm?
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39 The angle of elevation of an airplane from a point on the ground is 600. After a flight of
30 seconds, the angle of elevation becomes 300. If the airplane is flying at a constant
height of 3000√3 m, find the speed of the airplane.
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40 Daily wages of 110 workers, obtained in a survey, are tabulated below:
Compute the mean daily wages and modal daily wages of these workers.
Daily
Wages
(in Rs.)
100-120 120-140 140-160 160-180 180-200 200-220 220-240
Number
of
Workers
10 15 20 22 18 12 13
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