MOCK 3 EXAMINATION – 2025

MATHEMATICS

Grade: 10 Time: 3 hours

Date: 01/03/2025 Maximum Marks: 80
• Answers to this paper must be written on the paper provided separately.
• You will NOT be allowed to write during the first 15 minutes. This time is to be spent
reading the question paper.
• The time given at the head of this paper is the time allowed for writing the answers.

• Attempt all questions from Section A and any four questions from Section B.
• All working, including rough work, must be clearly shown and should be done on the
same sheet as the rest of the answer.
• Omission of essential working will result in loss of marks.
• Intended marks for questions or parts of questions are given in brackets [ ].
• Mathematical tables will be provided.

SECTION A
(Attempt all questions from this Section)

Question 1

Choose the correct answers to the questions from the given options. [15]

(Do not copy the question, write the correct answers only.)

(i) The sum of money required to buy 50, ₹40 shares at a discount of 10% is :
(a) ₹2000.00 (b) ₹1800.00 (c) ₹1700.00 (d) ₹1000.00

(ii) If ‘x’ is a negative integer, then the solution set of -12 x > 30 is:
(a) {2, - 1} (b) {..., -5, - 4, - 3} (c) {..., -5, - 4, - 3, - 2} (d) {-2, -1, 0, 1, 2, ....}

(iii) The angle between the lines x - 3y = 0 and 3x + y = 0 is:

(a) 0° (b) 90° (c) 45° (d) none of these

(iv) Madhu deposits a certain amount of money per month in a Recurring Deposit
account such that after 2 years, the interest accumulated is equal to her monthly
deposit. Find the rate of interest per annum that the bank is paying.
(a) 4% (b) 8% (c) 10% (d) 12%

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(v) In the adjoining figure, AC is a diameter of the circle with centre O, AC = 8cm
and OP perpendicular to AB. If the area of ∆APO is 12 cm², then area of
quadrilateral BCOP is:
(a) 12 cm2
(b) 24cm2
(c) 36 cm²
(d) 48cm²

(vi) At a certain time of the day, the ratio of the length of its shadow to the height
of the pole is 1: 3 , then the angle of elevation of the sun at that time of the day is:
(a) 30° (b) 45° (c) 60° (d) 90°

(vii) If a dice is rolled, the ratio of the probability of getting a prime number to the
probability of getting a multiple of 3 is:
(a) 1 : 2 (b) 1 : 3 (c) 2 : 3 (d) 3 : 2

(viii) The ratio of the volumes of a sphere, a cone and a cylinder each of same diameter
and same height is:
(a) 4 : 1 : 3 (b) 1 : 3 : 2 (c) 1 : 2 : 3 (d) 3 : 2 : 1

x 
(ix) If M =   and N =  p q 
 y
Assertion (A): Product MN and NM are both possible.
Reason (R): Matrix multiplication is commutative.
(a) A is true, R is false.
(b) A is false, R is true.
(c) Both A and R are true, and R is the correct reason for A.
(d) Both A and R are true, but R is the incorrect reason for A.

(x) In the adjoining figure, PT and QT are tangents to a circle such that  TPS =45° and
 TQS =300. Then, the value of  PSQ is:

(a) 300
(b) 450
(c) 75°
(d) 105°

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 x 2 + y 2 17
(xi) If = , then x : y is equal to:
x2 − y 2 8
25
(a)
9
9
(b)
25
5
(c)
3
3
(d)
5

(xii) A retailer buys an article at its listed price from a wholesaler and sells it to the
consumer in the same state after marking up the price by 20%. The list price of the
article is ₹2500, and the GST is 12%. What is the tax liability of the retailer to the
central government?
(a) 10
(b) 15
(c) 30
(d) 60

(xiii) If the equation x² - x + k = 0 has real roots, then

(a) k = ¼
(b) k = 0
(c) k > ¼
(d) k ≤ ¼

(xiv) The locus of a point which is equidistant from a given circle consists of:
(a) a pair of circles, inside and out, concentric with the given circle.
(b) a circle concentric with the given circle and inside it.
(c) a circle concentric with the given circle and outside it.
(d) a pair of lines parallel to each other on either side of the centre.

(xv) The scale factor of a picture and actual height of Sonia is 20 cm : 1.6 m. If her height
in the picture is 18 cm, then her actual height is:
(a) 14.4 m
(b) 2.25 m
(c) 1.78 m
(d) 1.44 m

Question 2

(i) Using the Remainder and Factor theorem, factorize the given 3x3 + 2x2 -19x + 6
completely. [4]

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(ii) A (a, b), B (- 4, 3) and C (8, -6) are the vertices of a triangle ABC. Point D is on BC
such that BD: DC is 2 :1 and M (6, 0) is mid-point of AD. Find: [4]
(a) Coordinates of point D.
(b) Coordinates of point A.
(c) Equation of a line passing through M and parallel to line BC.

(iii) The tangents TA and TB are drawn to the circle with centre O,  AOQ = 150 0 and
 ATB = 50°. Calculate  TAB,  QAC and  OAB. [4]

Question 3

(i) If the sum of the first 7 terms of an AP is 119, and that of the first 17 terms is 714.
Find the sum of first n terms & hence the 10th term. [4]

(ii) The total surface area of a right circular cone of slant height 17 cm is 200  cm2.
Calculate its radius. If this cone is melted and formed into solid spheres of radius
2 cm, find the number of spheres formed. [4]

(iii) For this question, use a graph paper. Take scale: 2 cm = 1 unit along both x and y
axis. Plot points A (2, 2) and B (6,-2) in the graph paper and answer the following: [5]
(a) Reflect point A in the origin to get D and write the coordinates of point D.
(b) Reflect point A in the line y = - 2 to point C and write the coordinates of point C.
(c) Find a point P on CD which is invariant under reflection in x = 0, write its coordinates.
(d) Write the geometric name of the figure ABCD.
(e) Write the coordinates of the point of intersection of the diagonals of ABCD.

SECTION B

(Attempt any four complete questions from this Section.)

Question 4

(i) Hetal invests ₹4500 in 8%, ₹10 shares at ₹15, She sells the shares when the price rises
to ₹30 and invests the proceeds in 12%, ₹100 shares at ₹125. Calculate: [3]
(a) the sale proceeds.
(b) the number of ₹100 shares she buys.
(c) the change in her annual income from the dividend.

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(ii) Solve the following in-equation, write the solution set and represent it on the real
number line.
x 3x
+5  x + 4  2+ , xR [3]
2 5

(iii) Prove the following trigonometric identity: [4]

(cos A − sin A)(1 + tan A)
= sec A
2cos 2 A − 1

Question 5

(i) Sanjay deposits a certain sum of money every month in a recurring deposit scheme
for 5 years at 6% p.a. If the amount he receives at the time of maturity is ₹55,320,
find his monthly deposit. [3]

(ii) In the figure, chord AD and tangent at B meet at C. [3]

(a) Prove ∆ABC ⁓ ∆BDC.

(b) If CD = 4 cm and BC = 6 cm, then
find AC.
(c) Find Area (∆BDC) : Area (∆ABC)

(iii) Using Assumed Mean method, find the Mean for the following frequency
Distribution: [4]
Class 0 - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90

Frequency 3 4 7 6 8 2

Question 6

(i) Find the ratio in which the line y = 2 + 3x divides the line segment AB joining the
points A (-3, 9) and B (4, 2). [3]

(ii) In the adjoining figure, [3]

 ABC= 1400,  AED= 100° and

AE parallel to BD.
Find  DBC,  BAE and  BCD.

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(iii) The bill shows the GST rate and the marked price of the articles: [4]

S.no. Item Quantity Marked Price Rate of GST

per kg (₹)
1. Wheat 5 kg 35.00 x%
2. Rice 5 kg 180.00 5%
3. Detergent y kg 220.00 18%
Find:
(a) the value of ‘x’ if the GST on wheat and rice is ₹53.75.
(b) the value of ‘y’, if CGST paid for detergent powder is ₹39.60.
(c) the total amount to be paid including GST for the above bill.

Question 7

(i) The angles of depression of the top and the bottom of an 8 m tall building from the
top of a multi-storied building are 30° and 45° respectively. Find the height of the
multi-storied building and the distance between the two buildings. Give the answer
correct to the nearest metre. [5]

(ii) The table shows scores obtained by 200 shooters in a shooting competition.
Scores 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100
Shooters 5 11 14 26 29 25 25 33 22 10

Use your graph to estimate the following: [5]

(a) The median
(b) The lower quartile.
(c) The number of shooters who obtained a score of more than 75%.

Question 8

(i) There are 25 cards numbered l to 25. What is the probability that a card picked up
randomly: [3]
(a) is a square number?
(b) is a multiple of 3 and 5?
(c) is a multiple of 3 or 5

(ii) Find two numbers whose mean proportion is 12 and the third proportion is 96. [3]

(iii) In a class test, the sum of Vikram's marks in Mathematics and Science is 25. Had he
got 5 marks more in Mathematics and 3 marks less in Science, the product of their
marks would have been 140. Find his marks in the two subjects. [4]

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Question 9

(i) Draw a Histogram from the following frequency distribution and find the Mode
from the graph: [3]
Class 0-5 5 - 10 10 - 15 15 - 20 20 - 25 25 – 30
Frequency 2 5 18 14 8 5

(ii) The fifth term of a G.P. is 81 and its second term is 24. Find the geometric
progression. [3]

(iii) The ratio of the radius and the height of a solid metallic right circular cylinder is
7:27. This is melted and made into a cone with a diameter of 14 cm and slant
height 25cm. Find the height of the cylinder. [4]

Question 10

(i) Find the value of ‘m’ for which the given quadratic equation has real and equal
roots: [3]
x2 + 2(m – 1) + (m + 5) = 0

 −6 0  1 0 
(ii) Given matrix, A =   and B =  
 4 2  1 3
Find matrix M, if M = A2 - 2B + 5I, where I is the identity matrix. [3]

(iii) Construct a triangle ABC in which AB = 6 cm, BC=5 cm and BC = 5 cm and

 ABC= 1200. [4]
(a) Construct a circle circumscribing the triangle ABC.
(b) Draw a cyclic quadrilateral ABCD so that D is equidistant from B and C.

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