Maths EM 1

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2023-24
X– MATHEMATICS
MODEL PAPER-1, E/M
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CLASS-X MAX, MARKS: 80 TIME: 3.15 Hrs
Instructions:
1. Read the question paper carefully and understand.
2. Answer the questions under Part-A in the answer sheet provided.
3. Write the answer to the questions under Part-B in the space provided and attach it
to the answer book let of Part -A.
4. Part-A contains 3 sections . Write the answers following the instructions given in
each section.
PART – A
Time: 2.45 hrs. Marks:60
----------------------------------------------------------------------------------------------------------------
SECTIONS: I 6 x 2 = 12
Instructions.
1) Answer ALL the following questions.

3. Each question carries 2 marks
1. Find the value of log 125

2. Give one example each for a finite set and an infinite set.
3. Srikar says that the order of the polynomial ( – 5)( +1) is 6. Do you agree
With him?
4. Is (x + 2) 2 = x2 + 3 a Quadratic Equation? Justify.
5. Find the centroid of a ∆ABC, when vertices are A(1, 3), B(2, 6), C(–3, –9).
6. Write the formula to find total surface area of a cone and explain each
term in it.
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SECTION – II
6 x 4 = 16
Instructions:
i. Answer ALL the following questions.

ii. Each question carries 4 marks
marks.
7. Find value of .
8. From the Deck of 52 cards, if a what is randomly chosen, find the
probability of getting a card with ((i) a even number on it, ( ii ) ace on it.
9. Find the value of fi xi for the below data, where xi is the mid value of
each class.
Class Interval 10 – 20 20 - 30 - 40 – 50 50 - 60
30 40
Frequency (fi) 5 8 10 5 2
10. If the present ages of Hari and Balu are in ratio of 9 : 4 and after
7 years the ratio of the ages will be 5 : 3 then find their present ages.
11. A manufacturer of TV sets produced 500 sets in the third year and 700 sets
in The seventh year. Assuming that the production increase uniformly by
a fixed number every year. Find the production of TV sets in the 15th year.
12. In ABC, D and E are points on AB and AC respectively. If AB =
14cm; AD = 3.5 cm, AE = 2.5 cm and AC = 10 cm, show that DE ǁ BC.
SECTION – III
4 × 6 = 24
Instructions:
i. Answer any FOUR of the questions
ii. Each question carries 6 marks.
13. Prove that 3 + 2√3 is an irrational number.

14. Draw the graph of the polynomial p (x) = x2 + 4x – 2 on the graph paper. Find
Its zeroes from the graph.
15. The sum of the radius of base and height of a solid right circular cylinder is 37 if its
total surface area is 1628 cm2, then find the volume of the cylinder. (Use = )
16. The angle of elevation of top of the tower from two points at a distance of 4 m
and 9 m from the base of the tower and in the same to straight line with it, are
Complementary. Prove that the height of the tower is 6 m
17. The following table gives production yield per hectare of wheat of 100 farms of
a village.
Production 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80
Yields(Quintals/Hect.)
No. of farmers 2 24 16 8 38 12
Draw both O gives for the above data. Hence obtain the median production
yield
18.A = {x : x ∈ N and x is a multiple of 4}; B = {x : x ∈ N and x is a multiple of 6};
C = {x : x ∈ N and x is a multiple LCM of 4 and 6} . Find A∩B. How can you
relate the sets A∩B and C.
----0----
PART – B
Instructions:
i) Write answers to all the questions.
ii) 1 mark for each question.
iii) All the answers should be written in the question paper itself.
iv) Marks will not be awarded for corrected, deleted answers.
1.The exponential form of log √ = y is . . . . . . . . ( )

A. ya = x1/2 B. xa = y1/2 C. ay= x1/2 D. x = a2
y
2. Which one of the following is the example of null set? ( )

2
A. {x / x∈ N and x = 9}
B. Set of rational Integers between 2 and 3.
C. Set of all multiples of even prime numbers.
D. Set of all odd prime numbers.
3. If p(x) = x3 – 4x2 + 5, then the value of p(-1) is . . . . ( )
A. 0 B. -1 C. 1 D. 2
4. If 2x + 6y = 4 and 3x + py = 6 has infinite solutions then p = . . . . . ( )
A. 8 B. 6 C. 10 D. 9
5. Which of the following geometric progressions has the common
ratio as √5 ( )
A.√10 , √20,√30 B. √5 , √10 , √15 C. √5 , √15 ,√45 D. √5 , √25 ,√125
6. Sum of the distances from A(3, 5) to X – axis and from B(9, 7) to Y – axis
is ……… ( )
A. 14 B. 10 C. 11 D. 9
7. In the adjacent figure, AB = 5 cm, BC = 3 cm, BE = 2 cm, then
CD = . . . . D ( )
A. 1.5 cm E
B. 2.5 cm
C. 1.6 cm C B A
D. 1.2 cm
8. At a point ‘P’ on a circle, PQ is a tangent and ‘O’ is the centre of the circle.
If △OPQ is an isosceles triangle, then △OQP is equal to . . . . . . . . ( )
0 0 0 0
A. 90 B. 30 C. 45 D. 60
9. The volume of a cone with base radius 7 cm is 462 cc., its height is . ( )
A. 9 cm B. 18 cm C. 3 cm D. 27 cm
10. In the formula of volume of right circular cone C = π r l, the

letter ‘l’ represents . . . ( )
A. Diameter B. Height C. Volume D. Slant height
11. If θ is acute, angle, then cos θ x sec θ = . . . . . . . . ( )
A. tan θ B. cot θ C. 1 D. Cosec θ
12. If the angle of elevation of sun decreases from 900 to 00 , then the length
of shadow of the tower..……… ( )
A. No change B. increases C. decreases D. Can’t be decided
13. A ladder touches a wall at a height of 7 m. The angle made by the ladder with
the ground, if its length is 14 m, will be . . . . . ( )
0 0 0 0
A. 30 B. 60 C. 45 D. 90
14. There are 10 red balls, 15 blue balls and 5 white balls in a box. When a
Ball is drawn at random from the box, what is the probability of getting
a red ball? ( )
A. 1/3 B. 2/5 C. 1/2 D. 1/6
15. For the terms x + 1, x + 2, x – 1, x + 3 and x – 2 (x∈ Average of mid values of
the data N), the median of the data is 12 then x = . . . . . . . ( )
A. 9 B. 10 C. 11 D. 13
16. Find the median of first 7 composite numbers. ( )
A. 7 B. 8 C. 9 D. 10
17.A pole and its shadow have same length, find the angle of the ray made
with the earth at that time. ( )
0 0 0 0
A. 30 B. 60 C. 45 D. 90
18. Express cosθ in terms of sinθ . ( )
A. 1+sinθ B. C. D. 1- sin2 θ .
19. For a right circular cone with radius = r, height = h and slant height = l,
which of the following is true? ( )
A. Always l > h B. Always l < r C. Always r = π D. l = r + h 2 2 2
20. ∆ABC ∼ ∆DEF, if ∠A = 300 and ∠E = 450 , then ∠C is . . . . ( )

0 0
A. 90 B. 105 C. 120o D. 60o
---- 0 ---

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www.sakshieducation.

CLASS-X MAX, MARKS: 80 TIME: 3.15 Hrs

1) Answer ALL the following questions.

1. Find the value of log 125

i. Answer ALL the following questions.

13. Prove that 3 + 2√3 is an irrational number.

1.The exponential form of log √ = y is . . . . . . . . ( )

2. Which one of the following is the example of null set? ( )

10. In the formula of volume of right circular cone C = π r l, the

20. ∆ABC ∼ ∆DEF, if ∠A = 300 and ∠E = 450 , then ∠C is . . . . ( )

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