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2023

PYQ’S 2023
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GYAANI KEEDA

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GYAANI KEEDA bhattdeepak454 https://t.me/gyannikeedamaths
 GYAANI KEEDA
MAYUR VIHAR PH-1 EAST DELHI-110091
CLASS X Math - Previous Year Question Paper
2023 (Basic)
GENERAL INSTRUCTIONS
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) This Question Paper is divided into FIVE Sections - Section A, B, C, D and E.
(iii) In Section-A question number 1 to 18 are Multiple Choice Questions (MCQs) and
question number 19 & 20 are Assertion-Reason based questions of 1 mark each.
(iv) In Section-B question number 21 to 25 are Very Short-Answer-I (SA-I) type question
of 2 marks each.
(v) In Section-C question number 26 to 31 are Short Answer-II (SA-II) type questions
carrying 3 marks each.
(vi) In Section-D question number 32 to 35 are Long Answer (LA) type questions
carrying 5 marks each.
(vii) In Section-E question number 36 to 38 are Case Study / Passage based integrated
units of assessment questions carrying 4 marks each. Internal choice is provided in 2
marks question in each case-study.
(viii) There is no overall choice. However, an internal choice has been provided in 2
questions in Section-B, 2 questions in Section-C, 2 questions in Section-D and 3
question in Section-E.
22
(ix) Draw neat figures wherever required. Take 𝜋 = wherever required if not stated.
7

(x) Use of calculator is NOT allowed

SECTION-A
Each question is of 1 mark.
Q1. The prime factorisation of natural number 288 is
(a) 24 × 33 (b) 24 × 32 (c) 25 × 32 (a) 25 × 31
Q2. If 2 cos 𝜃 = 1, then the value of 𝜃 is
(a) 45° (b) 60° (c) 30° (a) 90°
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Q3. A card is drawn at random from a well-shuffled deck of 52 cards. The
probability of getting a red card is:
1 1 1 1
(a) (b) (c) (a)
26 13 4 2

Q4. The discriminant of the quadratic equation 2𝑥 2 − 5𝑥 − 3 = 0 is

(a) 1 (b) 49 (c) 7 (a) 19
Q5. The distance between the points (3,0) and (0, −3) is
(a) 2√3 𝑢𝑛𝑖𝑡𝑠 (b) 6 𝑢𝑛𝑖𝑡𝑠 (c) 3 𝑢𝑛𝑖𝑡𝑠 (a) 3√2𝑢𝑛𝑖𝑡𝑠
Q6. The seventh term of an A.P. whose first term is 28 and common difference
−4, is
(a) 0 (b) 4 (c) 52 (a) 56
Q7. The graph of 𝑦 = 𝑝(𝑥) is shown in the figure for some polynomial 𝑝(𝑥 ). The
number of zeroes of 𝑝(𝑥) is/are:

(a) 0 (b) 1 (c) 2 (a) 3

Q8. The sides of two similar triangles are in the ratio 4: 7. The ratio of their
perimeters is
(a) 4: 7 (b) 12: 21 (c) 16: 49 (a) 7: 4
Q9. In the given figure, 𝐴𝐵 ∥ 𝐶𝐷. If 𝐴𝐵 = 5 𝑐𝑚, 𝐶𝐷 = 2 𝑐𝑚 and 𝑂𝐵 = 3 𝑐𝑚,
then the length of 𝑂𝐶 is

15 10 6 3
(a) 𝑐𝑚 (b) 𝑐𝑚 (c) 𝑐𝑚 (a) 𝑐𝑚
2 3 5 5

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Q10. The sum and the product of zeroes of the polynomial 𝑝(𝑥 ) = 𝑥 2 + 5𝑥 + 6
are respectively
(a) 5, −6 (b) −5,6 (c) 2,3 (a) −2, −3
Q11. A die is thrown once. Find the probability of getting a number less than 7
5 1
(a) (b) 1 (c) (a) 0
6 6

Q12. The angle subtended by a vertical pole of height 100 m at a point on the
ground 100 √3 m from the base is, has measure of

(a) 90° (b) 60° (c) 45° (a) 30°

Q13. The volume of a cone of radius 'r' and height '3r' is:
1
(a) 𝜋𝑟 3 (b) 3𝜋𝑟 3 (c) 9𝜋𝑟 3 (a) 𝜋𝑟 3
3

Q14. The distance between two parallel tangents of a circle of diameter 7 cm is

7
(a) 7 𝑐𝑚 (b) 14 𝑐𝑚 (c) 𝑐𝑚 (a) 28 𝑐𝑚
2

Q15.

In the above figure, the criterion of similarity by which ∆𝐴𝐵𝐶~ ∆𝑃𝑄𝑅 is:
(a) SSA (Side - Side - Angle) Similarity (b) ASA (Angle - Side-Angle) Similarity
(c) SAS (Side-Angle-Side) Similarity (d) AA (Angle - Angle) Similarity
Q16. The larger of two supplementary angles exceeds the smaller by 18
degrees. What is the measure of larger angle?
(a) 81° (b) 99° (c) 36° (a) 54°
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Q17. In the given figure, the perimeter of ∆𝐴𝐵𝐶 is

(a) 30 𝑐𝑚 (b) 15 𝑐𝑚 (c) 45 𝑐𝑚 (a) 60 𝑐𝑚

Q18. In the given figure, BC and BD are tangents to the circle with centre O and
radius 9 cm. If OB = 15 cm, then the length (BC + BD) is:

(a) 18 𝑐𝑚 (b) 12 𝑐𝑚 (c) 24 𝑐𝑚 (a) 36 𝑐𝑚

(Assertion - Reason based questions)
Directions for Q.19 & Q.20 In question numbers 19 and 20, a statement of
Assertion (A) is followed by a statement of Reason (R).
Choose the correct option:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but
Reason (R) is true.
Q19. Assertion (A): A tangent to a circle is perpendicular to the radius through
the point of contact.
Reason (R): The lengths of tangents drawn from the external point to a circle
are equal.

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Q20. Assertion (A): The system of linear equations 3𝑥 + 5𝑦 − 4 = 0 and
15𝑥 + 25𝑦 − 25 = 0 is inconsistent.
Reason (R): The pair of linear equations 𝑎1 𝑥 + 𝑏1 𝑦 + 𝑐1 = 0 and 𝑎2 𝑥 + 𝑏2 𝑦 +
𝑎1 𝑏1 𝑐1
𝑐2 = 0 is inconsistent if = ≠ .
𝑎2 𝑏2 𝑐2

SECTION-B

Every question is of 2 marks

Q21. (a) Find the coordinates of the point which divides the line segment joining
the points (7, -1) and (-3, 4) internally in the ratio 2:3.
OR
(b) Find the value(s) of 𝑦 for which the distance between the points A(3,-1) and
B(11, y) is 10 units.
Q22. Evaluate: 𝑡𝑎𝑛2 60° − 2 𝑐𝑜𝑠𝑒𝑐 2 30° − 2𝑡𝑎𝑛2 30°.
Q23. Find the LCM and HCF of 92 and 510, using prime factorisation.
Q24. (a) Solve for 𝑥 and 𝑦: 𝑥 + 𝑦 = 6,2𝑥 − 3𝑦 = 4
OR
(b) Find out whether the following pair of linear equations are consistent or
inconsistent: 5𝑥 − 3𝑦 = 11, −10𝑥 + 6𝑦 = 22
Q25. In the given figure, ABC and AMP are two right triangles, right angled at B
and M, respectively. Prove that ∆𝐴𝐵𝐶 − ∆𝐴𝑀𝑃.

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 SECTION-C

Every question is of 3 marks

Q26. (a) Prove that
sec 𝜃 (1 − sin 𝜃 )(sec 𝜃 + tan 𝜃 ) = 1
OR
(a) Prove that
1+sec 𝜃 𝑠𝑖𝑛2
=
sec 𝜃 1−cos 𝜃

Q27. Show that the points A(1, 7), B(4, 2) C(-1,-1) and D(-4, 4) are vertices of the
square ABCD.
Q28. Prove that the tangents drawn from an external point to a circle are equal
in length.
Q29. If 𝑎, 𝛽 are zeroes of the quadratic polynomial 𝑥 2 + 3𝑥 + 2. find a
quadratic polynomial whose zeroes are 𝛼 + 1, 𝛽 + 1.
Q30. Prove that 3 + 7√2 is an irrational number, given that √2 is an irrational
number.
Q31. (a) In the given figure, DE || AC and DF || AE

Prove that
𝐵𝐹 𝐵𝐸
=
𝐹𝐸 𝐸𝐶

OR

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The diagonals of a quadrilateral ABCD intersect each other at the point 𝑂 such
𝐴𝑂 𝐶𝑂
that =
𝐵𝑂 𝑂𝐷

Show that quadrilateral ABCD is a trapezium

SECTION-D

Every question is of 5 marks

Q32. (a) The diagonal of a rectangular field is 60 m more than the shorter side.
If the longer side is 80 m more than the shorter side, find the length of the sides
of the field.
OR
(b) The sum of the ages of a father and his son is 45 years. Five years ago, the
product of their ages (in years) was 124. Determine their present age.
33. A vessel is in the form of a hemispherical bowl surmounted by a hollow
cylinder of same diameter. The diameter of the hemispherical bowl is 14. cm
and the total height of the vessel is 13 cm. Find the inner surface area of the
vessel. Also, find the volume of the vessel.
Q34. The table given below shows the daily expenditure on food of 25
households in a locality:

Find the mean daily expenditure on food. Also, find the mode of the data.

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Q35. (a) A TV tower stands vertically on the bank of a canal. From a point on the
other bank directly opposite the tower, the angle of elevation of the top of the
tower is 60°. From another point 20 m away from the point on the line joining
this point to the foot of the tower, the angle of elevation of the top of the tower
is 30°. Find the height of the tower
OR
(b) An aeroplane when flying at a height of 4000 m from the ground passes
vertically above another aeroplane at an instant when the angles of elevation of
the two planes from the same point on the ground are 60° and 45° respectively.
Find the vertical distance between the aeroplanes at that instant. √3 = 1.73

SECTION-E

Every question is of 4 marks

Q36. Aahana being a plant lover decides to convert her balcony into beautiful
garden full of plants. She bought few plants with pots for her balcony. She
placed the pots in such a way that number of pots in the first row is 2, second
row is 5, third row is 8 and so on.

Based on the above information, answer the following questions:

(i) Find the number of pots placed in the 10th row.
(ii) Find the difference in the number of pots placed in 5th row and 2nd row.
(iii) If Aahana wants to place 100 pots in total, then find the total number of
rows formed in the arrangement.
OR
(iii) If Aahana has sufficient space for 12 rows, then how many total number of
pots are placed by her with the same arrangement?

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Q37. Interschool Rangoli Competition was organized by one of the reputed
schools of Odissa. The theme of the Rangoli Competition was Diwali
celebrations where students were supposed to make mathematical designs.
Students from various schools participated and made beautiful Rangoli designs.
One such design is given below.

Rangoli is in the shape of square marked as ABCD, side of square being 40 cm.
At each corner of a square, a quadrant of circle of radius 10 cm is drawn (in
which diyas are kept). Also a circle of diameter 20 cm is drawn inside the
square.
(i) What is the area of square ABCD?
(ii) Find the area of the circle.
(iii) If the circle and the four quadrants are cut off from the square ABCD and
removed, then find the area of remaining portion of square ABCD.
OR
(iii) Find the combined area of 4 quadrants and the circle, removed.
Q38. Blood group describes the type of blood a person has. It is a classification
of blood based on the presence or absence of inherited antigenic substances on
the surface of red blood cells. Blood types predict whether a serious reaction
will occur in a blood transfusion.
In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and
rest had type AB blood group.

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Based on the above, answer the following questions:
(i) What is the probability that a person chosen at random had type O blood?
(ii) What is the probability that a person chosen at random had type AB blood
group?
(iii) What is the probability that a person chosen at random had neither type A
nor type B blood group?
OR
(iii) What is the probability that person chosen at random had either type A or
type B or type O blood group?
Answers
Q1. C Q19. B
Q2. B Q20. A
Q3. D Q21. (3, 1) OR y = 5, – 7
Q4. B 17
Q22. −
3
Q5. D Q23. HCF = 2, LCM= 23460
Q6. B 22 8
Q24. 𝑥 = ,𝑦 =
Q7. A 5 5

Q8. A Q29. k(x2 + x) or x2 + x

Q9. C Q32. OR Father’s age = 36 years,
Q10. B son’s age = 9 years
Q11. B Q33. 572 cm2, 1642.67 cm3
Q12. D Q34. Mean=211, mode=220·59
Q13. D Q35. 17·3 m OR 1693.33 m (approx.)
Q14. A Q36. (i) 29, (ii) 9, (iii) 8 OR 222
Q15. C Q37. (i) 1600 cm2 (ii) 314.28 cm2 (iii)
Q16. B 971.43 cm2 OR 628.57 cm2
21 1 23 24
Q17. A Q38. (i) (ii) (iii) OR
50 25 50 25
Q18. C

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 GYAANI KEEDA
MAYUR VIHAR PH-1 EAST DELHI-110091
CLASS X Math - Previous Year Question Paper
2023 (Standard)
GENERAL INSTRUCTIONS
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) This Question Paper is divided into FIVE Sections - Section A, B, C, D and E.
(iii) In Section-A question number 1 to 18 are Multiple Choice Questions (MCQs)
and question number 19 & 20 are Assertion-Reason based questions of 1 mark
each.
(iv) In Section-B question number 21 to 25 are Very Short-Answer-I (SA-I) type
question of 2 marks each.
(v) In Section-C question number 26 to 31 are Short Answer-II (SA-II) type
questions carrying 3 marks each.
(vi) In Section-D question number 32 to 35 are Long Answer (LA) type questions
carrying 5 marks each.
(vii) In Section-E question number 36 to 38 are Case Study / Passage based
integrated units of assessment questions carrying 4 marks each. Internal choice
is provided in 2 marks question in each case-study.
(viii) There is no overall choice. However, an internal choice has been provided in
2 questions in Section-B, 2 questions in Section-C, 2 questions in Section-D and 3
question in Section-E.
22
(ix) Draw neat figures wherever required. Take 𝜋 = wherever required if not
7
stated.
(x) Use of calculator is NOT allowed.

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 SECTION-A

Every question is of 1 marks

Q1. The graph of 𝑦 = 𝑝(𝑥) is given, for a polynomial 𝑝(𝑥). The number of
zeroes of 𝑝(𝑥) from the graph is

(a) 3 (b) 1 (c) 2 (d) 0

Q2. The value of k for which the pair of equations 𝑘𝑥 = 𝑦 + 2 and
6𝑥 = 2𝑦 + 3 has infinitely many solutions,
(a) 𝑘 = 3 (b) 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑒𝑥𝑖𝑠𝑡 (c) 𝑘 = −3 (d) 𝑘 = 4
Q3. If 𝑝 − 1, 𝑝 + 1 and 2𝑝 + 3 are in A.P., then the value of 𝑝 is
(a) −2 (b) 4 (c) 0 (d) 2
Q4. In what ratio, does x-axis divide the line segment joining the points A(3, 6)
and B(-12.-3)?
(a) 1: 2 (b) 1: 4 (c) 4: 1 (d) 2: 1
Q5. In the given figure, PQ is tangent to the circle centred at O. If ∠𝐴𝑂𝐵 = 95°,
then the measure of ∠𝐴𝐵𝑄 will be

(a) 47.5° (b) 42.5° (c) 85° (d) 95°

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 4 sin 𝐴+3 cos 𝐴
Q6. If 2 tan 𝐴 = 3, then the value of is
4 sin 𝐴−3 cos 𝐴
7 1
(a) (b) (c) 3 (d) 𝑑𝑜𝑒𝑠 𝑛𝑜𝑡 𝑒𝑥𝑖𝑠𝑡
√13 √13
1 1
Q7. If 𝛼, 𝛽 are the zeroes of a polynomial 𝑝(𝑥 ) = 𝑥 2 + 𝑥 − 1, then + equals
𝛼 𝛽
to
−1
(a) 1 (b) 2 (c) −1 (d)
2

Q8. The least positive value of 𝑘, for which the quadratic equation
2𝑥² + 𝑘𝑥 − 4 = 0 has rational roots, is
(a) ±2√2 (b) 2 (c) ±2 (d) √2
3
Q9. [ 𝑡𝑎𝑛2 30° − 𝑠𝑒𝑐 2 45° + 𝑠𝑖𝑛2 60°] is equal to
4
5 3 1
(a) −1 (b) (c) − (d)
6 2 6

Q10. Curved surface area of a cylinder of height 5 cm is 94.2 cm2. Radius of the
cylinder is (Take л = 3.14)
(a) 2 𝑐𝑚 (b) 3 𝑐𝑚 (c) 2.9 𝑐𝑚 (d) 6 𝑐𝑚
Q11. The distribution below gives the marks obtained by 80 students on a test:-

The modal class of this distribution is:

(a) 10 − 20 (b) 20 − 30 (c) 30 − 40 (d) 50 − 60
Q12. The curved surface area of a cone having height 24 cm and radius 7 cm, is
(a) 528 𝑐𝑚2 (b) 1056 𝑐𝑚2 (c) 550 𝑐𝑚2 (d) 500 𝑐𝑚2
Q13. The distance between the points (0,2√5) and (−2√5, 0) is
(a) 2√10 𝑢𝑛𝑖𝑡𝑠 (b) 4√10 𝑢𝑛𝑖𝑡𝑠
(c) 2√20 𝑢𝑛𝑖𝑡𝑠 (d) 0

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 −2 2
Q14. Which of the following is a quadratic polynomial having zeroes and ?
3 3
4 9
(a) 4𝑥 2 − 9 (b) (9𝑥 2 + 4) (c) 𝑥 2 + (d) 5(9𝑥 2 − 4)
9 4

Q15. If the value of each observation of a statistical data is increased by 3, then

the mean of the data
(A) Remains unchanged (B) increases by 3
(C) Increases by 6 (D) increases by 3n
Q16. Probability of happening of an event is denoted by p and probability of
non-happening of the event is denoted by q. Relation between p and q is
(A) 𝑝 + 𝑞 = 1 (B) 𝑝 = 1, 𝑞 = 1
(C) 𝑝 = 𝑞 − 1 (D) 𝑝 + 𝑞 + 1 = 0
Q17. A girl calculates that the probability of her winning the first prize in a
lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought?
(a) 40 (b) 240 (c) 480 (d) 750
Q18. In a group of 20 people, 5 can't swim. If one person is selected at random,
then the probability that he/she can swim, is
3 1 1
(a) (b) (c) 1 (d)
4 3 4

(Assertion - Reason based questions)

Directions for Q.19 & Q.20 In question numbers 19 and 20, a statement of
Assertion (A) is followed by a statement of Reason (R).
Choose the correct option:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct
explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct
explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false. (d) Assertion (A) is false, but
Reason (R) is true.

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Q19. Assertion (A): Point P(0, 2) is the point of intersection of y-axis with the
line 3𝑥 + 2𝑦 = 4.
Reason (R): The distance of point P(0, 2) from x-axis is 2 units.
Q20. Assertion (A): The perimeter of ∆𝐴𝐵𝐶 is a rational number. Reason (R):
The sum of the squares of two rational numbers is always rational.

SECTION-B

Every question is of 2 marks

Q21. (a) Solve the pair of equations 𝑥 = 3 and 𝑦 = −4 graphically.
OR
(b) Using graphical method, find whether following system of linear equations is
consistent or not: x=0 and y=-7
Q22. In the given figure, XZ is parallel to BC. AZ = 3 cm, ZC=2 cm, BM= 3 cm and
MC=5 cm. Find the length of XY

Q23. (a) If sin 𝜃 + cos 𝜃 = √3, then find the value of sin 𝜃 . cos 𝜃.
OR
1
(b) If sin 𝛼 = and cot 𝛽 = √3, then find the value of 𝑐𝑜𝑠𝑒𝑐 𝛼 + 𝑐𝑜𝑠𝑒𝑐 𝛽
√2

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Q24. Find the greatest number which divides 85 and 72 leaving remainders 1
and 2 respectively.
Q25. A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at
random from the bag. Find the probability that drawn ball is (i) red (ii) yellow.

SECTION-C

Every question is of 3 marks

Q26. Half of the difference between two numbers is 2. The sum of the greater
number and twice the smaller number is 13. Find the numbers.
Q27. Prove that √5 is an irrational number.
Q28. If (-5, 3) and (5, 3) are two vertices of an equilateral triangle, then find co-
ordinates of the third vertex, given that origin lies inside the triangle. √3 = 1.7
Q29. (a) Two tangents TP and TQ are drawn to a circle with centre O from an
external point T. prove that ∠𝑃𝑇𝑄 = 2∠𝑂𝑃𝑄.

OR
(b) In the given figure, a circle is inscribed in a quadrilateral ABCD in which
∠𝐵 90°. If AD= 17 cm, AB = 20 cm and DS 3 cm, then find the radius of the
circle.

tan 𝜃+sec 𝜃−1 1+sin 𝜃

Q30. Prove that: =
tan 𝜃−sec 𝜃+1 cos 𝜃

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Q31. (a) A room is in the form of cylinder surmounted by a hemi-spherical
dome. The base radius of hemisphere is one-half the height of cylindrical part.
1408 22
Find total height of the room if it contains ( ) 𝑚3 of air. (𝜋 = ).
21 7

OR
(b) An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so
1 𝑡ℎ
that lower part of the cone which is ( ) of the volume of the cone is unfilled
6
but hemisphere is formed on the top. Find volume of the ice-cream.
(𝜋 = 3.14).

SECTION-D

Every question is of 5 marks

Q32. If a line is drawn parallel to one side of a triangle to intersect the other
two sides at distinct points, prove that the other two sides are divided in the
same ratio.
Q33. (a) The angle of elevation of the top of a tower 24 m high from the foot of
another tower in the same plane is 60°. The angle of elevation of the top of
second tower from the foot of the first tower is 30°. Find the distance between
two towers and the height of the other tower. Also, find the length of the wire
attached to the tops of both the towers.
OR
(b) A spherical balloon of radius r subtends an angle of 60° at the eye of an
observer. If the angle of elevation of its centre is 45° from the same point, then
prove that height of the centre of the balloon is √2 times its radius.

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Q34. A chord of a circle of radius 14 cm subtends an angle of 60° at the centre.
Find the area of the corresponding minor segment of the circle. Also find the
area of the major segment of the circle.
Q35. (a) The ratio of the 11th term to 17th term of an A.P. is 3: 4. Find the ratio of
5th term to 21st term of the same A.P. Also, find the ratio of the sum of first 5
terms to that of first 21 terms.
OR
(b) 250 logs are stacked in the following manner:
22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on
(as shown by an example). In how many rows, are the 250 logs placed and how
many logs are there in the top row?

SECTION-E
Every question is of 4 marks
Q36. While designing the school year book, a teacher asked the student that the
length and width of a particular photo is increased by x units each to double the
area of the photo. The original photo is 18 cm long and 12 cm wide.
Based on the above information, answer the following questions:
(I) write an algebraic equation depicting the above information.
(II) Write the corresponding quadratic equation in standard form.
(III) What should be the new dimensions of the enlarged photo?

OR
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Can any rational value of x make the new area equal to 220 cm²?
Q37. India meteorological department observes seasonal and annual rainfall
every year in different sub-divisions of our country.

It helps them to compare and analyse the results. The table given below shows
sub-division wise seasonal (monsoon) rainfall (mm) in 2018:

Based on the above information, answer the following questions:

(I) Write the modal class.
(II) Find the median of the given data.
OR
Find the mean rainfall in this season.
(III) If sub-division having at least 1000 mm rainfall during monsoon season, is
considered good rainfall sub-division, then how many sub- divisions had good
rainfall?

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Q38. The discus throw is an event in which an athlete attempts to throw a
discus. The athlete spins anti-clockwise around one and a half times. Through a
circle, then releases the throw. When released, the discus travels along tangent
to the circular spin orbit.

In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is
centre of the circle and ∠𝐴𝐵𝑂 = 30°. PQ is parallel to OA.
Based on above information:
(a) Find the length of AB.
(b) Find the length of OB.
(c) Find the length of AP.
OR
Find the length of PQ

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Answers
Q1. B Q21. OR equations is consistent
Q2. B Q22. 1.8 cm
Q3. C Q23. 1 OR √2 (√2 + 1)
Q4. D Q24. 14
Q5. A 4 2
Q25. (i) (ii)
9 9
Q6. C
Q26. 7, 3
Q7. A
Q28. (0,-5.5)
Q8. B
Q29. OR 6 cm
Q9. A
Q31. 6 cm OR 150.72cm3
Q10. B
Q33. H= 8, L=8√7m
Q11. C
Q34. Minor =17.9cm2, major=598.1cm2
Q12. C
Q35. 3:7, 25:189 OR 3
Q13. A
Q36. (i) 2(18 ×12), (ii) 0 (iii) 24 cm × 18 cm
Q14. D
OR can’t have any such rational value of x.
Q15. B
Q37. (i) Modal Class is 600-800 (ii) 771·4
Q16. A
OR (ii) mean= 850 (iii) 7
Q17. C
75√3
Q18. A Q38. (i) 75√3 𝑐𝑚 (ii) 150 cm (iii) 𝑐𝑚
2
Q19. B 75
OR (iii) 𝑐𝑚
2
Q20. D

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