ICSE Class 10 Maths Sample Paper 2025 - 2 | Mathematics Class 10 ICSE PDF Download

 Page 1


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
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 work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) 18% b) 15%
c) 9% d) 10%
If the cost of an article is ? 25,000 and CGST paid by the owner is ? 2250, the rate of GST is [1] (a)
a) 629 b) 675
c) 576 d) 567
From a group of Saras birds, one-fourth of the number are moving about in lotus plants, one-ninth
coupled with one-fourth as well as 7 times the square root of the total number are moving on a hill,
while 56 birds are sitting in the Bakula trees. Then, what is the total number of birds?
[1] (b)
a) 14 b) 0
c) 6 d) -6
If x + 1 is a factor of 3x
3
 + kx
2
 + 7x + 4, then the value of k is
[1] (c)
a) 100 b) 75
c) 25 d) 50
If  and , then the value of n is
[1] (d)
A = [ ] [ ] 5 0 5 0 0 5 0 5 = [ ] A n 5 2 0 0 0 5 2 0 0 0 If a, b and c are respectively the pth, qth and rth terms of a GP, then the value of [1] (e)
Mathematics
Page 2


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
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 work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) 18% b) 15%
c) 9% d) 10%
If the cost of an article is ? 25,000 and CGST paid by the owner is ? 2250, the rate of GST is [1] (a)
a) 629 b) 675
c) 576 d) 567
From a group of Saras birds, one-fourth of the number are moving about in lotus plants, one-ninth
coupled with one-fourth as well as 7 times the square root of the total number are moving on a hill,
while 56 birds are sitting in the Bakula trees. Then, what is the total number of birds?
[1] (b)
a) 14 b) 0
c) 6 d) -6
If x + 1 is a factor of 3x
3
 + kx
2
 + 7x + 4, then the value of k is
[1] (c)
a) 100 b) 75
c) 25 d) 50
If  and , then the value of n is
[1] (d)
A = [ ] [ ] 5 0 5 0 0 5 0 5 = [ ] A n 5 2 0 0 0 5 2 0 0 0 If a, b and c are respectively the pth, qth and rth terms of a GP, then the value of [1] (e)
Mathematics
a) log abc b) log bc
c) log ab d) 0
(q - r) log a + (r - p) log P + (p - g) log c is 
a) (-4, -5) b) (-4, 5)
c) (4, 5) d) (4, -5)
A point M is reflected in X-axis to M'(4, -5). M" is the image of M, when reflected in the Y-axis. The
coordinates of M"' when M" is reflected in the origin, is
[1] (f)
a) cm b) 15 cm
c) 13 cm d) cm
Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE = 2 : 1, AB = 8 cm
and BC = 6 m. The length of DE is
[1] (g)
3 1 7 - - v 2 1 9 - - v a)
494.68 cm
2 b)
484.98 cm
2
c)
489.84 cm
2 d)
948.84 cm
2
A hollow cone of radius 6 cm and height 8 cm is vertical standing at the origin, such that the vertex of
the cone is at the origin. Some pipes are hanging around the circular base of the cone, such that they
touch the surface of the graph paper. Then, the total surface area of the formed by the figure will be
[1] (h)
a) b)
c) d)
Find the range of values of x which satisfy the inequation, (x + 1)
2
 - (x - 1)
2
 < 6.
[1] (i)
( - 8 , ) 3 2 ( , 8 ) 3 2 ( - 8 , - ) 3 2 ( - 8 , - ) ? ( , 8 ) 3 2 3 2 a) b)
c) d)
The probability that the minute hand lies from 5 to 15 min in the wall clock, is [1] (j)
1 6 5 6 1 5 1 1 0 a) b) 1
c) d)
If , a > 0, then a
p-q
 is equal to
[1] (k)
[ ] [ ] = [ ] a x a - x 1 2 p q a - 2 2 l o g 2 4 3 2 2 - 3 2 2 3 2 a) 75, 45° b) 45°, 60°
c) 45°, 90 d) 45°, 45°
Suppose PQ be a pole, whose coordinates are P(1, 3) and 0(3, 3) and A be the position of a man
whose coordinates are (1, 1).
i. If a pole makes an angle of elevation to the point A, then the angle  is
ii. Also, if we shift the origin at (1, 1), then the angle  is
[1] (l)
? ? a) 2( + 1)r b)
If P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral
triangle and PS is a diameter of the circle. Then, the perimeter of the quadrilateral PQSR will be
[1] (m)
3 – v 2 + r 3 – v
Page 3


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
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 work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) 18% b) 15%
c) 9% d) 10%
If the cost of an article is ? 25,000 and CGST paid by the owner is ? 2250, the rate of GST is [1] (a)
a) 629 b) 675
c) 576 d) 567
From a group of Saras birds, one-fourth of the number are moving about in lotus plants, one-ninth
coupled with one-fourth as well as 7 times the square root of the total number are moving on a hill,
while 56 birds are sitting in the Bakula trees. Then, what is the total number of birds?
[1] (b)
a) 14 b) 0
c) 6 d) -6
If x + 1 is a factor of 3x
3
 + kx
2
 + 7x + 4, then the value of k is
[1] (c)
a) 100 b) 75
c) 25 d) 50
If  and , then the value of n is
[1] (d)
A = [ ] [ ] 5 0 5 0 0 5 0 5 = [ ] A n 5 2 0 0 0 5 2 0 0 0 If a, b and c are respectively the pth, qth and rth terms of a GP, then the value of [1] (e)
Mathematics
a) log abc b) log bc
c) log ab d) 0
(q - r) log a + (r - p) log P + (p - g) log c is 
a) (-4, -5) b) (-4, 5)
c) (4, 5) d) (4, -5)
A point M is reflected in X-axis to M'(4, -5). M" is the image of M, when reflected in the Y-axis. The
coordinates of M"' when M" is reflected in the origin, is
[1] (f)
a) cm b) 15 cm
c) 13 cm d) cm
Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE = 2 : 1, AB = 8 cm
and BC = 6 m. The length of DE is
[1] (g)
3 1 7 - - v 2 1 9 - - v a)
494.68 cm
2 b)
484.98 cm
2
c)
489.84 cm
2 d)
948.84 cm
2
A hollow cone of radius 6 cm and height 8 cm is vertical standing at the origin, such that the vertex of
the cone is at the origin. Some pipes are hanging around the circular base of the cone, such that they
touch the surface of the graph paper. Then, the total surface area of the formed by the figure will be
[1] (h)
a) b)
c) d)
Find the range of values of x which satisfy the inequation, (x + 1)
2
 - (x - 1)
2
 < 6.
[1] (i)
( - 8 , ) 3 2 ( , 8 ) 3 2 ( - 8 , - ) 3 2 ( - 8 , - ) ? ( , 8 ) 3 2 3 2 a) b)
c) d)
The probability that the minute hand lies from 5 to 15 min in the wall clock, is [1] (j)
1 6 5 6 1 5 1 1 0 a) b) 1
c) d)
If , a > 0, then a
p-q
 is equal to
[1] (k)
[ ] [ ] = [ ] a x a - x 1 2 p q a - 2 2 l o g 2 4 3 2 2 - 3 2 2 3 2 a) 75, 45° b) 45°, 60°
c) 45°, 90 d) 45°, 45°
Suppose PQ be a pole, whose coordinates are P(1, 3) and 0(3, 3) and A be the position of a man
whose coordinates are (1, 1).
i. If a pole makes an angle of elevation to the point A, then the angle  is
ii. Also, if we shift the origin at (1, 1), then the angle  is
[1] (l)
? ? a) 2( + 1)r b)
If P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral
triangle and PS is a diameter of the circle. Then, the perimeter of the quadrilateral PQSR will be
[1] (m)
3 – v 2 + r 3 – v c) 2r d) 2 r 3 – v a) 10 : 9 b) 9 : 10
c) 10 : 8 d) 8 : 10
If the ratio of mode and median of a certain data is 6 : 5, then the ratio of its mean and median is [1] (n)
a) Both A and R are true and R is the
correct explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Assertion (A): a
n
 - a
n - 1
 is not independent of n then the given sequence is an AP. 
Reason (R): Common difference d = a
n
 - a
n - 1
 is constant or independent of n.
[1] (o)
2. Question 2 [12]
Mr. Gupta opened a recurring deposit account in a bank. He deposited ? 2,500 per month for 2 years.
At the time of maturity, he got ?67,500. Find:
i. the total interest earned by Mr. Gupta
ii. the rate of interest per annum.
[4] (a)
Find the third proportional to
i. 16 and 36
ii. (x
2
 + y
2
 + xy)
2
 and (x
3
 - y
3
)
[4] (b)
Prove that:  = sin
2
  cos
2
 
[4] (c)
( 1 + c o t ? + t a n ? ) ( s i n ? - c o s ? ) ? - ? s e c 3 c o s e c 3 ? ? 3. Question 3 [13]
The internal and external diameters of a hollow hemispherical vessel are 7cm and 14 cm, respectively.
The cost of silver plating of 1 sq cm surface is ? 0.60. Find the total cost of silver plating the vessel all
over.
[4] (a)
The side AB of a square ABCD is parallel to the Y-axis as shown in the given figure. 
Calculate
i. the slope of AD.
ii. the slope of BD.
iii. the slope of AC. [Given, tan(90
o
 + 0) = -cot ]
[4] (b)
? Use graph paper to answer this question:
i. The point P(2, - 4) is reflected about the line x = 0 to get the image Q. Find the coordinates of Q.
ii. Point Q is reflected about the line y = 0 to get the image R. Find the coordinates of R.
iii. Name the figure PQR.
iv. Find the area of figure PQR.
[5] (c)
Page 4


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
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 work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) 18% b) 15%
c) 9% d) 10%
If the cost of an article is ? 25,000 and CGST paid by the owner is ? 2250, the rate of GST is [1] (a)
a) 629 b) 675
c) 576 d) 567
From a group of Saras birds, one-fourth of the number are moving about in lotus plants, one-ninth
coupled with one-fourth as well as 7 times the square root of the total number are moving on a hill,
while 56 birds are sitting in the Bakula trees. Then, what is the total number of birds?
[1] (b)
a) 14 b) 0
c) 6 d) -6
If x + 1 is a factor of 3x
3
 + kx
2
 + 7x + 4, then the value of k is
[1] (c)
a) 100 b) 75
c) 25 d) 50
If  and , then the value of n is
[1] (d)
A = [ ] [ ] 5 0 5 0 0 5 0 5 = [ ] A n 5 2 0 0 0 5 2 0 0 0 If a, b and c are respectively the pth, qth and rth terms of a GP, then the value of [1] (e)
Mathematics
a) log abc b) log bc
c) log ab d) 0
(q - r) log a + (r - p) log P + (p - g) log c is 
a) (-4, -5) b) (-4, 5)
c) (4, 5) d) (4, -5)
A point M is reflected in X-axis to M'(4, -5). M" is the image of M, when reflected in the Y-axis. The
coordinates of M"' when M" is reflected in the origin, is
[1] (f)
a) cm b) 15 cm
c) 13 cm d) cm
Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE = 2 : 1, AB = 8 cm
and BC = 6 m. The length of DE is
[1] (g)
3 1 7 - - v 2 1 9 - - v a)
494.68 cm
2 b)
484.98 cm
2
c)
489.84 cm
2 d)
948.84 cm
2
A hollow cone of radius 6 cm and height 8 cm is vertical standing at the origin, such that the vertex of
the cone is at the origin. Some pipes are hanging around the circular base of the cone, such that they
touch the surface of the graph paper. Then, the total surface area of the formed by the figure will be
[1] (h)
a) b)
c) d)
Find the range of values of x which satisfy the inequation, (x + 1)
2
 - (x - 1)
2
 < 6.
[1] (i)
( - 8 , ) 3 2 ( , 8 ) 3 2 ( - 8 , - ) 3 2 ( - 8 , - ) ? ( , 8 ) 3 2 3 2 a) b)
c) d)
The probability that the minute hand lies from 5 to 15 min in the wall clock, is [1] (j)
1 6 5 6 1 5 1 1 0 a) b) 1
c) d)
If , a > 0, then a
p-q
 is equal to
[1] (k)
[ ] [ ] = [ ] a x a - x 1 2 p q a - 2 2 l o g 2 4 3 2 2 - 3 2 2 3 2 a) 75, 45° b) 45°, 60°
c) 45°, 90 d) 45°, 45°
Suppose PQ be a pole, whose coordinates are P(1, 3) and 0(3, 3) and A be the position of a man
whose coordinates are (1, 1).
i. If a pole makes an angle of elevation to the point A, then the angle  is
ii. Also, if we shift the origin at (1, 1), then the angle  is
[1] (l)
? ? a) 2( + 1)r b)
If P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral
triangle and PS is a diameter of the circle. Then, the perimeter of the quadrilateral PQSR will be
[1] (m)
3 – v 2 + r 3 – v c) 2r d) 2 r 3 – v a) 10 : 9 b) 9 : 10
c) 10 : 8 d) 8 : 10
If the ratio of mode and median of a certain data is 6 : 5, then the ratio of its mean and median is [1] (n)
a) Both A and R are true and R is the
correct explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Assertion (A): a
n
 - a
n - 1
 is not independent of n then the given sequence is an AP. 
Reason (R): Common difference d = a
n
 - a
n - 1
 is constant or independent of n.
[1] (o)
2. Question 2 [12]
Mr. Gupta opened a recurring deposit account in a bank. He deposited ? 2,500 per month for 2 years.
At the time of maturity, he got ?67,500. Find:
i. the total interest earned by Mr. Gupta
ii. the rate of interest per annum.
[4] (a)
Find the third proportional to
i. 16 and 36
ii. (x
2
 + y
2
 + xy)
2
 and (x
3
 - y
3
)
[4] (b)
Prove that:  = sin
2
  cos
2
 
[4] (c)
( 1 + c o t ? + t a n ? ) ( s i n ? - c o s ? ) ? - ? s e c 3 c o s e c 3 ? ? 3. Question 3 [13]
The internal and external diameters of a hollow hemispherical vessel are 7cm and 14 cm, respectively.
The cost of silver plating of 1 sq cm surface is ? 0.60. Find the total cost of silver plating the vessel all
over.
[4] (a)
The side AB of a square ABCD is parallel to the Y-axis as shown in the given figure. 
Calculate
i. the slope of AD.
ii. the slope of BD.
iii. the slope of AC. [Given, tan(90
o
 + 0) = -cot ]
[4] (b)
? Use graph paper to answer this question:
i. The point P(2, - 4) is reflected about the line x = 0 to get the image Q. Find the coordinates of Q.
ii. Point Q is reflected about the line y = 0 to get the image R. Find the coordinates of R.
iii. Name the figure PQR.
iv. Find the area of figure PQR.
[5] (c)
Section B
Attempt any 4 questions
4. Question 4 [10]
A shopkeeper bought an article with market price ?1200 from the wholesaler at a discount of 10%.
The shopkeeper sells this article to the customer on the market price printed on it. If the rate of GST is
6%, then find:
i. GST paid by the wholesaler.
ii. Amount paid by the customer to buy the item.
[3] (a)
The sum of the squares of two consecutive odd positive integers is 290. Find them. [3] (b)
Draw a Histogram for the given data, using a graph paper:
Weekly Wages (in ?) No. of People
3000-4000 4
4000-5000 9
5000-6000 18
6000-7000 6
7000-8000 7
8000-9000 2
9000-10000 4
Estimate the mode from the graph.
[4] (c)
5. Question 5 [10]
Evaluate, .
[3] (a)
[ ] 4 s i n 3 0 ° s i n 9 0 ° 2 c o s 6 0 ° 2 c o s 0 ° [ ] 4 5 5 4 O is the circumcentre of the ABC and D is mid-point of the base BC. Prove that BOD = A. [3] (b) ? ? ? Use factor theorem to factorise 6x
3
 + 17x
2
 + 4x - 12 completely.
[4] (c)
6. Question 6 [10]
Calculate the ratio in which the line joining A (-4, 2) and B(3, 6) is divided by P(x, 3). Also, find
i. x
ii. length of AP
[3] (a)
Prove that: 1 -  = sin [3] (b)
? c o s 2 1 + s i n ? ? Sum of the first n terms of an AP is 5n
2
 - 3n. Find the AP and also find its 16th term.
[4] (c)
7. Question 7 [10]
A grassy land is in the shape of a right triangle. The hypotenuse of the land is 1 m more than twice the
shortest side. If the third side is 7 m more than the shortest side, find the sides of the grassy land.
[5] (a)
The marks obtained by 100 students in a Mathematics test are given below
Marks Number of students
0-10 3
10-20 7
20-30 12
[5] (b)
Page 5


Time Allowed: 2 hours and 30 minutes Maximum Marks: 80 
General Instructions:
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 work, including rough work, must be clearly shown and must be done on the same sheet as the rest of the
answers.
Omission of essential work will result in a loss of marks.
The intended marks for questions or parts of questions are given in brackets [ ]
Mathematical tables are provided.
Section A
1. Question 1 Choose the correct answers to the questions from the given options: [15]
a) 18% b) 15%
c) 9% d) 10%
If the cost of an article is ? 25,000 and CGST paid by the owner is ? 2250, the rate of GST is [1] (a)
a) 629 b) 675
c) 576 d) 567
From a group of Saras birds, one-fourth of the number are moving about in lotus plants, one-ninth
coupled with one-fourth as well as 7 times the square root of the total number are moving on a hill,
while 56 birds are sitting in the Bakula trees. Then, what is the total number of birds?
[1] (b)
a) 14 b) 0
c) 6 d) -6
If x + 1 is a factor of 3x
3
 + kx
2
 + 7x + 4, then the value of k is
[1] (c)
a) 100 b) 75
c) 25 d) 50
If  and , then the value of n is
[1] (d)
A = [ ] [ ] 5 0 5 0 0 5 0 5 = [ ] A n 5 2 0 0 0 5 2 0 0 0 If a, b and c are respectively the pth, qth and rth terms of a GP, then the value of [1] (e)
Mathematics
a) log abc b) log bc
c) log ab d) 0
(q - r) log a + (r - p) log P + (p - g) log c is 
a) (-4, -5) b) (-4, 5)
c) (4, 5) d) (4, -5)
A point M is reflected in X-axis to M'(4, -5). M" is the image of M, when reflected in the Y-axis. The
coordinates of M"' when M" is reflected in the origin, is
[1] (f)
a) cm b) 15 cm
c) 13 cm d) cm
Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE = 2 : 1, AB = 8 cm
and BC = 6 m. The length of DE is
[1] (g)
3 1 7 - - v 2 1 9 - - v a)
494.68 cm
2 b)
484.98 cm
2
c)
489.84 cm
2 d)
948.84 cm
2
A hollow cone of radius 6 cm and height 8 cm is vertical standing at the origin, such that the vertex of
the cone is at the origin. Some pipes are hanging around the circular base of the cone, such that they
touch the surface of the graph paper. Then, the total surface area of the formed by the figure will be
[1] (h)
a) b)
c) d)
Find the range of values of x which satisfy the inequation, (x + 1)
2
 - (x - 1)
2
 < 6.
[1] (i)
( - 8 , ) 3 2 ( , 8 ) 3 2 ( - 8 , - ) 3 2 ( - 8 , - ) ? ( , 8 ) 3 2 3 2 a) b)
c) d)
The probability that the minute hand lies from 5 to 15 min in the wall clock, is [1] (j)
1 6 5 6 1 5 1 1 0 a) b) 1
c) d)
If , a > 0, then a
p-q
 is equal to
[1] (k)
[ ] [ ] = [ ] a x a - x 1 2 p q a - 2 2 l o g 2 4 3 2 2 - 3 2 2 3 2 a) 75, 45° b) 45°, 60°
c) 45°, 90 d) 45°, 45°
Suppose PQ be a pole, whose coordinates are P(1, 3) and 0(3, 3) and A be the position of a man
whose coordinates are (1, 1).
i. If a pole makes an angle of elevation to the point A, then the angle  is
ii. Also, if we shift the origin at (1, 1), then the angle  is
[1] (l)
? ? a) 2( + 1)r b)
If P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral
triangle and PS is a diameter of the circle. Then, the perimeter of the quadrilateral PQSR will be
[1] (m)
3 – v 2 + r 3 – v c) 2r d) 2 r 3 – v a) 10 : 9 b) 9 : 10
c) 10 : 8 d) 8 : 10
If the ratio of mode and median of a certain data is 6 : 5, then the ratio of its mean and median is [1] (n)
a) Both A and R are true and R is the
correct explanation of A.
b) Both A and R are true but R is not the
correct explanation of A.
c) A is true but R is false. d) A is false but R is true.
Assertion (A): a
n
 - a
n - 1
 is not independent of n then the given sequence is an AP. 
Reason (R): Common difference d = a
n
 - a
n - 1
 is constant or independent of n.
[1] (o)
2. Question 2 [12]
Mr. Gupta opened a recurring deposit account in a bank. He deposited ? 2,500 per month for 2 years.
At the time of maturity, he got ?67,500. Find:
i. the total interest earned by Mr. Gupta
ii. the rate of interest per annum.
[4] (a)
Find the third proportional to
i. 16 and 36
ii. (x
2
 + y
2
 + xy)
2
 and (x
3
 - y
3
)
[4] (b)
Prove that:  = sin
2
  cos
2
 
[4] (c)
( 1 + c o t ? + t a n ? ) ( s i n ? - c o s ? ) ? - ? s e c 3 c o s e c 3 ? ? 3. Question 3 [13]
The internal and external diameters of a hollow hemispherical vessel are 7cm and 14 cm, respectively.
The cost of silver plating of 1 sq cm surface is ? 0.60. Find the total cost of silver plating the vessel all
over.
[4] (a)
The side AB of a square ABCD is parallel to the Y-axis as shown in the given figure. 
Calculate
i. the slope of AD.
ii. the slope of BD.
iii. the slope of AC. [Given, tan(90
o
 + 0) = -cot ]
[4] (b)
? Use graph paper to answer this question:
i. The point P(2, - 4) is reflected about the line x = 0 to get the image Q. Find the coordinates of Q.
ii. Point Q is reflected about the line y = 0 to get the image R. Find the coordinates of R.
iii. Name the figure PQR.
iv. Find the area of figure PQR.
[5] (c)
Section B
Attempt any 4 questions
4. Question 4 [10]
A shopkeeper bought an article with market price ?1200 from the wholesaler at a discount of 10%.
The shopkeeper sells this article to the customer on the market price printed on it. If the rate of GST is
6%, then find:
i. GST paid by the wholesaler.
ii. Amount paid by the customer to buy the item.
[3] (a)
The sum of the squares of two consecutive odd positive integers is 290. Find them. [3] (b)
Draw a Histogram for the given data, using a graph paper:
Weekly Wages (in ?) No. of People
3000-4000 4
4000-5000 9
5000-6000 18
6000-7000 6
7000-8000 7
8000-9000 2
9000-10000 4
Estimate the mode from the graph.
[4] (c)
5. Question 5 [10]
Evaluate, .
[3] (a)
[ ] 4 s i n 3 0 ° s i n 9 0 ° 2 c o s 6 0 ° 2 c o s 0 ° [ ] 4 5 5 4 O is the circumcentre of the ABC and D is mid-point of the base BC. Prove that BOD = A. [3] (b) ? ? ? Use factor theorem to factorise 6x
3
 + 17x
2
 + 4x - 12 completely.
[4] (c)
6. Question 6 [10]
Calculate the ratio in which the line joining A (-4, 2) and B(3, 6) is divided by P(x, 3). Also, find
i. x
ii. length of AP
[3] (a)
Prove that: 1 -  = sin [3] (b)
? c o s 2 1 + s i n ? ? Sum of the first n terms of an AP is 5n
2
 - 3n. Find the AP and also find its 16th term.
[4] (c)
7. Question 7 [10]
A grassy land is in the shape of a right triangle. The hypotenuse of the land is 1 m more than twice the
shortest side. If the third side is 7 m more than the shortest side, find the sides of the grassy land.
[5] (a)
The marks obtained by 100 students in a Mathematics test are given below
Marks Number of students
0-10 3
10-20 7
20-30 12
[5] (b)
30-40 17
40-50 23
50-60 14
60-70 9
70-80 6
80-90 5
90-100 4
Draw an ogive for the given distribution on a graph sheet, (use a scale of 2 cm = 10 units on both
axes). Use the ogive to estimate the
i. median.
ii. lower quartile.
iii. number of students who obtained more than 85% marks in the test.
iv. number of students who did not pass in the test, if the pass percentage was 35.
8. Question 8 [10]
A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple
of 3 and 4.
[3] (a)
How many solid spheres of diameter 6 cm are required to be melted to form a cylindrical solid of
height 45 cm and diameter 4 cm?
[3] (b)
In the given figure, AC = AE. 
Show that
i. CP = EP
ii. BP = DP
[4] (c)
9. Question 9 [10]
Solve the following inequation and represent the solution set on the number line. 
 + 2 < x + 4   + 5, x  R
[3] (a)
3 x 5 = x 2 ? Mode and mean of a data are 12k and 15k respectively. Find the median of the data. [3] (b)
In the given figure, if DE || BC, find the ratio of ar ( ADE) and ar (DECB). [4] (c) ? 10. Question 10 [10]
Find the fourth proportional to (a
3
 + 8), (a
4
 - 2a
3
 + 4a
2
) and (a
2
 - 4).
[3] (a)