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Unformatted text preview: Design of Question Paper
Mathematics  Class X Time : Three hours Max. Marks :80
Weightage and distribution of marks over different dimensions of the question paper shall be as follows: A. Weightage to content units S.No. Content Units Marks 1. Number systems 04 2. Algebra 20 3. Trigonometry 12 4. Coordinate Geometry 08 5. Geometry 16 6. Mensuration 10 7. Statistics & Probability 10 Total 80
B Weightage to forms of questions
S.No. Forms of Questions Marks of each M Total
question Questions marks 1. Very Short answer questions 01 10 10
(VSA) 2. Short answer questionsl (SAI) 02 05 10 3. Short answer questionsll (SAII) 03 1O 30 4. Long answer questions (LA) 06 05 30
Total 30 80 C. Scheme of Options All questions are compulsory. There is no overall choice in the question paper. However,
internal choice has been provided in one question of two marks each, three questions of three
marks each and two questions of six marks each. D. Weightage to diffculty level of Questions S.No. Estimated difficulty level of questions Percentage of marks
1 . Easy 15
2. Average 70
3 Difficult 15 Based on the above design, separate Sample papers along with their blue print and marking
scheme have been included in this document for Board’s examination.The design of the question
paper will remain the same whereas the blue print based on this design may change. MathematicsX
Blue Print I F f
G" SA  LA Total
(3 Marks) (6 Marks)
each each Number systems 1 (1) 3(1) 6(1 Coordinate 2(1) 6(2)
Geometry )
)
Geometry 2(2) 2(1) 6(2) ) Statistic and 2(2) 2(1) 6(1)
Probability Time :Three hours Sample Question Paper I
Mathematics  Class X Max.Marks :80 General Instructions. 1.
2. All Questions are compulsory. The question paper consists of thirty questions divided into 4 sections A, B, C and D.
Section A comprises of ten questions of 01 mark each, section B comprises of five
questions of 02 marks each, section C comprises of ten questions of 03 marks each and
section D comprises of five questions of 06 marks each. All questions in Section A are to be answered in one word, one sentence or as per the
exact requirement of the question. There is no overall choice. However, internal choice has been provided in one question of
02 marks each, three questions of 03 marks each and two questions of 06 marks each.
\bu have to attempt only one of the alternatives in all such questions. In question on construction, drawings should be neat and exactly as per the given
measurements. Use of calculators is not permitted.However you may ask for mathematical tables. Section A Write the condition to be satisfied by q so that a rational number a has a terminating decimal expansion. The sum and product of the zeroes of a quadratic polynomial are  1/2 and 3 repectively
What is the quadratic polynomial? For what value of k the quadratic equation x2  kx + 4 = 0 has equal roots? cosecze  $9020 Given that tan9=—1 ,what is the value of 2 2
cosec 0+sec 0 J5 Which term of the sequence 114, 109, 104 is the first negative term ? 10. Acylinder, a cone and a hemisphere are of equal base and have the same height.What is
the ratio in their volumes? In the given figure, DE is parallel to BC and AD = 1cm, BD = 20m. What is the ratio of the
area of A ABC to the area of AADE? In the figure given below, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10cm, and CO = 20m, what is the length of PC? B C Cards each marked with one of the numbers 4,5,6....20 are placed in a box and mixed
thoroughly. One card is drawn at random from the box. What is the probability of getting an
even prime number ? A student draws a cumulative frequency curve for the marks obtained by 40 students of a
class, as shown below. Find the median marks obtained by the students of the class. 4;
O NCO
OO cumulative frequency (No of students) _\
O O 10 20 30 40 50 60 70 80
upper limits of class intervals (Marks) 11 12. 13 14 15. (i)
(ii) Section B Without drawing the graphs, state whether the following pair of linear equations will
represent intersecting lines, coincident lines or parallel lines : 6x3y+10=0
2xy+9=0 Justify your answer. cos 70° _ +cos 57° cosec 33°  2cos 60°
sm 20° Without using trigonometric tables, find the value of Find a point on the yaxis which is equidistant from the points A(6,5) and B (4.3). In the figure given below, AC is parallel to BD, AE DE A _=_7 '
ls CE BE . Justify your answer. B A bag contains 5 red, 8 green and 7 white balls. One ball is drawn at random from the bag,
find the probability of getting a white ball or a green ball.
neither a green ball not a red ball.
OR One card is drawn from a well shuffled deck of 52 playing cards. Find the probability of getting (0
(ii) 16 17. 18. a nonface card A black king or a red queen.
Section C Using Euclid’s division algorithm, find the HCF of 56, 96 and 404.
OR Prove that 3\/§ is an irrational number If two zeroes of the polynomial x4+3x320x26x+36 are \/§ and  J5 , find the other zeroes
of the polynomial. Draw the graph of the following pair of linear equations 19. 20. 21 x + 3y = 6 2x  3y = 12 Hence find the area of the region bounded by the
x=0, y=0and2x3y: 12 A contract on construction job specifies a penalty for delay of completion beyond a
certain date as follows: Rs 200 for lst day, Rs. 250 for second day, Rs. 300 for third
day and so on. If the contractor pays Rs 27750 as penalty, find the number of days for
which the construction work is delayed. 1+cosA+ sinA Prove that : _ =2cosecA
Sln A 1+cosA
OR
Prove that:
sinA+cosA sinAcosA _ 2
sin A  cos A sinA+cosA _ sinzAcos2 A Observe the graph given below and state whether triangle ABC is scalene, isosceles or
equilateral. Justify your answer. Also find its area. 22. 23. 24 25 26. 27. 28 Find the area of the quadrilateral whose vertices taken in order are A (5,3) B(4, 6),
C(2,1) and D (1,2). Construct a AABC in which CA = 6cm, AB = 5cm and BAC = 45°, then construct a triangle similar to the given triangle whose sides are 2 of the corresponding sides of the A ABC. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a
right angle at the centre of the circle. A square field and an equilateral triangular park have equal perimeters.lf the cost of
ploughing the field at rate of Rs 5/ mzis Rs 720, find the cost of maintaining the park at the
rate of Rs 1O/m2. OR An iron solid sphere of radius 30m is melted and recast into small sperical balls of
radius 1cm each.Assuming that there is no wastage in the process, find the number of
small spherical balls made from the given sphere. Section D Some students arranged a picnic. The budget for food was Rs 240. Because four students
of the group failed to go, the cost of food to each student got increased by Rs 5. How
many students went for the picnic? OR A plane left 30 minutes late than its scheduled time and in order to reach the destination
1500km away in time, it had to increase the speed by 250 km/h from the usual speed.
Find its usual speed. From the top of a building 100 m high, the angles of depression of the top and bottom of
a tower are observed to be 45° and 60° respectively. Find the height of the tower. Also
find the distance between the foot of the building and bottom of the tower. OR The angle of elevation of the top a tower at a point on the level ground is 30°.After walking
a distance of 100m towards the foot of the tower along the horizontal line through the foot
of the tower on the same level ground , the angle of elevation of the top of the tower is 60°.
Find the height of the tower. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the other two sides. Using the above, solve the following: A ladder reaches a window which is 12m above the ground on one side of the street.
Keeping its foot at the same point, the ladder is turned to the other side of the street to
reach a window 9m high. Find the width of the street if the length of the ladder is 15m. 29. 30 The interior of building is in the form of a right circular cylinder of radius 7m and height 6m,
surmounted by a right circular cone of same radius and of vertical angle 60°. Find the
cost of painting the building from inside at the rate of Rs 3O/m2 The following table shows the marks obtained by 100 students of class X in a school
during a particular academic session. Find the mode of this distribution. Marks No. of students
Less then 10 7 Less than 20 21 Less than 30 34 Less than 40 46 Less than 50 66 Less than 60 77 Less than 70 92 Less than 80 100 MathematicsX
Blue Print 11 Form of
Quest'm‘s VSA SA  SA   LA Total
(1 Mark) (2 Marks) (3 Marks) (6 Marks)  Coordinate 2(1) 6(2) 8(3)
Geometry
 Statistics and 2(2) 2(1) 6(1) 10(4)
Probability 20 Time :Three hours Sample Question Paper  II
Mathematics  Class X Max. Marks : 80 General Instructions : 1.
2. All questions are compulsory. The question paper consists of thirty questions divided into 4 Section A,B,C and D. Section
A comprises of ten questions of 01 marks each, section B comprises of five questions of
02 marks each, section C comprises of ten questions of 03 marks each and section D
comprises of five questions of 06 marks each. All questions in Section A are to be answered in one word, one sentence or as per the
exact requirement of the question. There is no overall choice. However, internal choice has been provided in one question of
02 marks each, three questions of 03 marks each and two questions of 06 marks each.
\bu have to attempt only one of the alternatives in all such questions. In question on construction, drawings should be neat and exactly as per the given
measurements. Use of calculator is not permitted. However, you may ask for mathematical tables. Section A
State the Fundamental Theorem of Arithmetic. The graph of y=f(x) is given below. Find the number of zeroes of f(x).
Y 21 10. 11. 12. Give an example of polynomials f(x), g(x), q(x), and r(x) satisfying
f(x) = g(x)  q(x) + r(x) where deg r(x) = 0. What is the nature of roots of the quadratic equation
4x212x9=O? If the adjoining figure is a
sector of a circle of radius 10.5 cm, find the perimeter of the sector. (Take TC = g ) V C The length of tangent from a pointA at a distance of 5 cm from the centre of the circle is 4
cm. What will be the radius of the circle? Which measure of central tendency is given by the xcoordinate of the point of intersection
of the ‘more than’ ogive and ‘less than’ ogive? A bag contains 5 red and 4 black balls.A ball is drawn at random from the bag. What is the
probability of getting a black ball? What is the distance between two parallel tangents of a circle of the radius 4 cm? The height of a tower is 10m. Calculate the height of its shadow when Sun’s altitude is
45°. Secti_onB From your pocket money, you save Rs.1 on day 1, Rs. 2 on day 2, Rs. 3 on day 3 and so
on. How much money will you save in the month of March 2008 ? Express sin67°+ Cos75° in terms of trigonometric ratios of angles between 0° and 45°
OR If A,B,C are interior angles of a AABC, then show that 22 13. In the figure given below, DE // BC. lfAD = 2.4 cm, DB = 3.6 cm and AC = 5 cm Find AE. A B C 14. Find the values of x for which the distance between the point P (2,3) and Q (x,5) is 10
units. 15. All cards of ace, jack and queen are removed from a deck of playing cards. One card is
drawn at random from the remaining cards. find the probability that the card drawn is
a) a face card b) not a face card
Section C 16. Find the zeroes of the quadratic polynomial )8 + 5x + 6 and verify the relationship between
the zeroes and the coefficients. 17. Prove that5+«/§ isirrational. 18. For what value or ‘k’ will the following pair of linear equations have infinitely many solutions kx + 3y = k3
12x + ky = k
OR
Solve forxand y ><IO‘I +l:2
y }x¢o,y to ><IO'> _§:1
y 23 19. 20. 21. 22. 23. 24. 25. Determine an A.F? whose 3 '0' term is 16 and when 5th term is subtracted from 7th term,
we get 12. OR
Find the sum of all three digit numbers which leave the remainder 3 when divided by 5.
Prove that
SecA1+ SecA+1= 2CosecA
SecA+1 SecA1 Prove that the points A(—3,0), B(1,3) and C(4,1) are the vertices of an isoscles right triangle.
OR
For what value of ‘K’the points A (1 ,5), B (K1) and C (4,11) are collinear? In what ratio does the point P(2,5) divide the line segment joining A(3,5) and B(4,9)? Construct a triangle similar to given ABC in which AB = 4 cm, BC = 6 cm and 2 ABC =
60°, such that each side of the new triangle is 3A of given AABC. The incircle of A ABC touches the sides BC, CA and AB at D,E, and F respectively. IF
AB = AC, prove that BD=CD. A B D C
PQRS is a square land of side 28m.Two semicircular grass covered portions are to be
made on two of its opposite sides as shown in the figure. How much area will be left uncovered? (Take n=g ) S R
77777777” 7 77777777
77777777 24 26. 27. 28. 29. Section D Solve the following system of linear equations graphically: 3x+y12=0
x3y+6=0 Shade the region bounded by these lines and the xaxis. Also find the ratio of areas of
triangles formed by given lines with xaxis and the yaxis. There are two poles, one each on either bank of a river, just opposite to each other. One
pole is 60m high. From the top of this pole, the angles of depression of the top and the
foot of the other pole are 30° and 60° respectively Find the width of the river and the
height of the other pole. Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of
their corresponding sides.
Use the above theorem, in the following.
The areas of two similar triangles are 81 cm2 and 144 cm2. If the largest side of the smaller
triangle is 27 cm, find the largest side of the larger triangle.
OR
Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the other two sides.
Use the above theorem, in the following.
If ABC is an equilateral triangle with AD J. BC, then AD2 = 3 D02.
An iron pillar has lower part in the form of a right circular cylinder and the upperpart in the form of a right circular cone.The radius of the base of each of the cone and cylinder is 8
cm.The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if 1cm3 of iron weighs 7.5 grams. (Take 7: = g) 7
OR A container (open at the top) made up of a metal sheet is in the form of a frustum of a
cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm
respectively Find (i) the cost of milk when it is completely filled with milk at the rate of Rs 15 per litre. (ii) the cost of metal sheet used, if it costs Rs 5 per 100 cm2 (Take T: = 3.14) 25 30. The median of the following data is 20.75. Find the missing frequencies x and y, if the
total frequency is 100.
Class Interval
0  5
5  1O
1O  15
15  20
20  25
25  3O
3O  35
35  40 Frequency _L _L _L _L 26 Blue Print III
X  Mathematics Form of
Questions Number systems 1 (1) Coordinate 2(1)
Geometry 20(8) 1 2(4) 92
3 8(3) Geometry 2(2) 2(1) 6(2) 6(1) Statistics and 2(2) 2(1)
Probability 10(10) 10(5) 30(10) 30(5) 80(30) 16(6) 3(1) 6(1) 10(3) 6(1) 10(4) 44 Time :Three hours Sample Question Paper Ill Mathematics  Class X Max. Marks : 80 General Instructions : 2. 1. All Questions are compulsory. 2. The question paper consists of thirty questions divided into 4 sections A, B,
C and D. Section A comprises of ten questions of 01 mark each, section B
comprises of five questions of 02 marks each, section C comprises of ten
questions of 03 marks each and section D comprises of five questions of
06 marks each. 3. All questions in Section Aare to be answered in one word, one sentence or as per
the exact requirement of the question. 4. There is no overall choice. However, internal choice has been provided in one
question of 02 marks each, three questions of 03 marks each and two questions
of 06 marks each.\bu have to attempt only one of the alternatives in all such ques tions. 5. In question on construction, drawings should be neat and exactly as per the given
measurements. 6. Use of calculators is not permitted. However, you may ask for mathematical tables. SECTIONA Write 98 as product of its prime factors.
In fig. 1 the graph of a polynomial p(x) is given. Find the zeroes of the polynomial. 45 Fig. 1 For what value of k ,the following pair of linear equations has infinitely many solutions?
10x+5y (k—5) =0
20x + 10y  k = 0 1
Sec 0 What is the maximum value of ? If tan A = g and A+B = 90°, then what is the value of cotB? What is the ratio of the areas of a circle and an equilateral triangle whose diameter and
a side are respectively equal ? Fig. 2 Two tangents TP and T0 are drawn from an external pointT to a circle with centre 0, as
shown in fig. 2. If they are inclined to each other at an angle of 100° then what is the value of 4 P00 ? 46 10. 11.
12. 13. In fig. 3 what are the angles of depression from the observing positions 01 and 02 of the object at A?
oz 0. d \\ A B C
Fig. 3 A die is thrown once. what is the probability of getting a prime number? What is the value of the median of the data using the graph in fig. 4, of less than ogive
and more than ogive? (A)
01 >~n
g 30 more than ogive
3
U 2
g 5 k less than ogive
.“2’ 20
E
g 15
3
0
10
5
x
0 2468101214161820
Marks —>
Fig.4
SECTION : B If the 10‘hterm of an AP. is 47 and its first term is 2, find the sum of its first 15 terms. Justify the statement :“Tossing a coin is a fair way of deciding which team should get
the batting first at the beginning of a cricket game.” Find the solution of the pair of equations: §+§=1, lE=2,x,y=l=0 XY XY 47 14. 15. 16. 17. 18. 19. 20. 21. The coordinates of the vertices of AABC are A(4, 1), B (3, 2) and C (O, k) Given that the
area of ABC is 12 unit2, find the value of k. Write a quadratic polynomial, sum of whose zeroes is 2\/§ and their product is 2. OR What are the quotient and the remainder, when 3x4 + 5x3  7x2 + 2x + 2 is divided by
x2 + 3x + 1? SECTIONC If a student had walked 1km/hr faster, he would have taken 15 minues less to walk 3 km.
Find the rate at which he was walking. Show that 3+5 J2 is an irrational number. Find he value of kso that the following quadratic equation has equal roots:
2x2  (k2) x+1 :0 Construct a circle whose radius is equal to 4cm. Let P be a point whose distance from
its centre is 6cm. Construct two tangents to it from P. Prove that
sin 9 = 2 + sine
cot 6 + cosec 6 cote cosec6 OR
Evalute
0
SL290 + 2 cot 8° cot 17° cot 45° cot 73° cot 82°  3 (sin2 38° + sin2 52°)
Cosec 61
. XP XQ . . . .
In fig. 5, — = — = 3, If the area of XYZ IS 32cm, then find the area of the quadrilateral
PY QZ X
PYZQ. Fig. 5 48 22. 23. 24. 25. OR A circle touches the side BC of a A ABC at a point P and touches AB and AC when
produced at Q and R respeciver Show that A0 = % (Perimeter ofA ABC) Find the ratio in which the line segment joining the points A (3, 6) and B(5,3) is
divided by x  axis.Also find the coordinates of the point of intersection. Find a relation between x and y such that the point P(x,y) is equidistant from the points
A(2, 5) and B(3, 7) If in fig. 6, ABC and AMP are right angled at B and M respectiver prove that
CA x MP = PA x BC C M
A B P
Fig. 6 P
In Fig. 7, OAPB is a sector of a circle of radius
3.5 cm with the centre at O
and AAOB = 120°. Find the length of
OAPBO.
O
120°
B
A Fig. 7 OR Find the area of the shaded region of fig. 8
if the diameter of the circle with centre 0 is 1
28 cm and A0 = 2 AB. Fig. 8 49 [26] [27] [28] [29] [30] SECTIOND Prove that in a triangle, if the square of one side is equal to the sum of the squares of the
other two sides the angle opposite to the first side is a right angle. Using the converse of
above, determine the length of an attitude of an equilateral triangle of side 2 cm. Form a pair of linear equations in two variables using the following information and solve
it graphically. Five years ago, Sagar was twice as old as Tiru. Ten year later Sagar’s age will be ten
years more than Tiru’s age. Find their present ages. What was the age of Sagar when Tim
was born? From the top and foot of a tower 40m high, the angle of elevation of the top of a light house
is found to be 30° and 60° respectively. Find the height of the lighthouse. Also find the
distance of the top of the lighthouse from the foot of the tower. A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid
is 1000m and the diameter of the hemispherical ends is 28cm. find the cost of polishing
the surface of the solid at the rate of 5 paise per sq.cm. OR
An open container made up of a metal sheet is in the form of a frustum of a cone of height
8cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. Find the cost
of oil which can completely fill he container a the rate of Rs. 50 per litre.Also, find the cost of metal used, if it costs Rs. 5 per 100 cm2 (Use Tr: 3.14) The mean of the following frequency table is 53. But the frequencies f1and f2 in the classes
2040 and 6080 are missing. Find the missing frequencies. 2
OR Find the median of the following frequency distribution: Frequency .m_ 400500 N _L _L _L 50 ...
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