ICSE Class 10 Maths Sample Paper 2025 - 3 | 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) ? 10,000 b) ? 6000
c) ? 2000 d) ? 8000
The marked price of a micro oven is ? 10,000. Dealer offers 20% discount on the marked price. The
selling price of micro oven:
[1] (a)
a) Both k  2 and k  -2 b) k  2
c) k = 2 d) k  -2
The linear factors of the equation x
2
 + kx + 1 = 0 exists, if
[1] (b)
= = = = a) -36 b) 56
c) 44 d) 36
When 6x
3
 + 2x
2
 - x + 2 is divided by (x + 2), then remainder is
[1] (c)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (d)
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) ? 10,000 b) ? 6000
c) ? 2000 d) ? 8000
The marked price of a micro oven is ? 10,000. Dealer offers 20% discount on the marked price. The
selling price of micro oven:
[1] (a)
a) Both k  2 and k  -2 b) k  2
c) k = 2 d) k  -2
The linear factors of the equation x
2
 + kx + 1 = 0 exists, if
[1] (b)
= = = = a) -36 b) 56
c) 44 d) 36
When 6x
3
 + 2x
2
 - x + 2 is divided by (x + 2), then remainder is
[1] (c)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (d)
Mathematics
a) 1470 b) 1610
c) 1370 d) 1540
The sum of series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4 )+ ... + (1 + 2 + 3 + ... + 20) is [1] (e)
a) (2, 3) b) (3, 2)
c) (-2, 3) d) (3, -2)
Which of the following points is invariant with respect to the line y = -2? [1] (f)
a) All of these b) Both (i) and (iii)
c) Both (i) and (ii) d) Both (ii) and (iii)
In a PQR, L and M are two points on base QR, such that LPQ = QRP and RPM = RQP.
Then which of the following is/are true
i. 
ii. QL  RM = PL  PM
iii. PQ
2
 = QR QL
[1] (g) ? ? ? ? ? ? P Q L ~ ? R P M × × · 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) x  b) x  
c) x  d) x  
Solve for . [1] (i) x : | x + 1 | + | x | > 3 ? ( - 2 , 8 ) ? ( - 1 , 8 ) ? ( - 8 , - 2 ] ? [ 1 , 8 ) ? ( - 8 , - 2 ) ? ( 1 , 8 ) ? [ - 2 , 8 ) ? [ - 1 , 8 ) a) at equal distance from the three sides of
the triangle.
b) the point of intersection of the three
altitudes of the triangle
c) the point of intersection of the three
medians.
d) at equal distance from the three vertices
of the triangle.
The circumcentre of a triangle is the point which is : [1] (j)
a) b)
c) d)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (k)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a [ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) (6, - 6); rectangle b) (6, 4); square
Suppose there are four points A(2, 4), B(6, 4), C(6, 6) and D(2, 6), which lie in the first quadrant. 
If we rotate only the axes at an angle of 90
o
 in anti-clockwise direction, then what will be the new
coordinates of the point C and what will be the name of the figure, when we join adjacent points. 
[1] (l)
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) ? 10,000 b) ? 6000
c) ? 2000 d) ? 8000
The marked price of a micro oven is ? 10,000. Dealer offers 20% discount on the marked price. The
selling price of micro oven:
[1] (a)
a) Both k  2 and k  -2 b) k  2
c) k = 2 d) k  -2
The linear factors of the equation x
2
 + kx + 1 = 0 exists, if
[1] (b)
= = = = a) -36 b) 56
c) 44 d) 36
When 6x
3
 + 2x
2
 - x + 2 is divided by (x + 2), then remainder is
[1] (c)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (d)
Mathematics
a) 1470 b) 1610
c) 1370 d) 1540
The sum of series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4 )+ ... + (1 + 2 + 3 + ... + 20) is [1] (e)
a) (2, 3) b) (3, 2)
c) (-2, 3) d) (3, -2)
Which of the following points is invariant with respect to the line y = -2? [1] (f)
a) All of these b) Both (i) and (iii)
c) Both (i) and (ii) d) Both (ii) and (iii)
In a PQR, L and M are two points on base QR, such that LPQ = QRP and RPM = RQP.
Then which of the following is/are true
i. 
ii. QL  RM = PL  PM
iii. PQ
2
 = QR QL
[1] (g) ? ? ? ? ? ? P Q L ~ ? R P M × × · 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) x  b) x  
c) x  d) x  
Solve for . [1] (i) x : | x + 1 | + | x | > 3 ? ( - 2 , 8 ) ? ( - 1 , 8 ) ? ( - 8 , - 2 ] ? [ 1 , 8 ) ? ( - 8 , - 2 ) ? ( 1 , 8 ) ? [ - 2 , 8 ) ? [ - 1 , 8 ) a) at equal distance from the three sides of
the triangle.
b) the point of intersection of the three
altitudes of the triangle
c) the point of intersection of the three
medians.
d) at equal distance from the three vertices
of the triangle.
The circumcentre of a triangle is the point which is : [1] (j)
a) b)
c) d)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (k)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a [ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) (6, - 6); rectangle b) (6, 4); square
Suppose there are four points A(2, 4), B(6, 4), C(6, 6) and D(2, 6), which lie in the first quadrant. 
If we rotate only the axes at an angle of 90
o
 in anti-clockwise direction, then what will be the new
coordinates of the point C and what will be the name of the figure, when we join adjacent points. 
[1] (l)
Section B
Attempt any 4 questions
c) (-6, 6); square d) (2, -6); rectangle
a) 2( + 1)r b)
c) 2r d)
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 2 r 3 – v a) 1 : 1 b) 1 : 2
c) 3 : 2 d) 2 : 1
In a colony, the average age of the boys is 14 yr and the average age of the girls is 17 yr. If the
average age of the children in the colony is 15 yr, then the ratio of number of boys to that of girls 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): Three consecutive terms 2k + 1, 3k + 3 and 5k - 1 form an AP than k is equal to 6. 
Reason (R): In an AP a, a + d, a + 2d, ...the sum of n terms of the AP be S
n
 = 
[1] (o)
( 2 a + ( n - 1 ) d ) n 2 2. Question 2 [12]
Rashmi has a 4 yr Recurring Deposit Account in Bank of Maharashtra and deposits ? 800 per month.
If she gets ? 48200 at the time of maturity, then find
i. the rate of (simple) interest.
ii. the total interest earned by Rashmi.
[4] (a)
Mr. Kamal reduces the number of workers of his factory in the ratio 9 : 7 and increases their wages in
the ratio 13 : 20. In what ratio, the wages bill is increased or decreased?
[4] (b)
Prove that: 
(1 + cot A - cosec A)(1+ tan A + sec A) = 2
[4] (c)
3. Question 3 [13]
Circumference of the base of a cylinder, open at the top, is 132 cm. The sum of radius and height is 41
cm. Find the cost of polishing the outer surface area of cylinder at the rate ? 10 per sq dm (decimetre).
[Take  = ]
[4] (a)
p 2 2 7 Find the equation of the line, which passes through the point (3, 4) and the sum of its intercepts on the
axes is 14.
[4] (b)
Using graph paper and taking 1 cm = 1 unit along with X-axis and Y-axis.
i. Plot the point A (-4, 4) and B(2, 2).
ii. Reflect A and B in the origin to get the images A' and B', respectively.
iii. Write down the coordinates of A' and B'.
iv. Give the geometrical name for the figure ABA'B'.
[5] (c)
4. Question 4 [10]
Let Vinod, Govind and Ankit be three dealers belonging to difference states. Dealer Vinod sells some
products/services to dealer Govind for ?1000 and dealer Govind sells the same products/services to
dealer Ankit at a profit of ?300. Calculate the tax liability of Govind, if the rate of GST is 12%.
[3] (a)
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) ? 10,000 b) ? 6000
c) ? 2000 d) ? 8000
The marked price of a micro oven is ? 10,000. Dealer offers 20% discount on the marked price. The
selling price of micro oven:
[1] (a)
a) Both k  2 and k  -2 b) k  2
c) k = 2 d) k  -2
The linear factors of the equation x
2
 + kx + 1 = 0 exists, if
[1] (b)
= = = = a) -36 b) 56
c) 44 d) 36
When 6x
3
 + 2x
2
 - x + 2 is divided by (x + 2), then remainder is
[1] (c)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (d)
Mathematics
a) 1470 b) 1610
c) 1370 d) 1540
The sum of series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4 )+ ... + (1 + 2 + 3 + ... + 20) is [1] (e)
a) (2, 3) b) (3, 2)
c) (-2, 3) d) (3, -2)
Which of the following points is invariant with respect to the line y = -2? [1] (f)
a) All of these b) Both (i) and (iii)
c) Both (i) and (ii) d) Both (ii) and (iii)
In a PQR, L and M are two points on base QR, such that LPQ = QRP and RPM = RQP.
Then which of the following is/are true
i. 
ii. QL  RM = PL  PM
iii. PQ
2
 = QR QL
[1] (g) ? ? ? ? ? ? P Q L ~ ? R P M × × · 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) x  b) x  
c) x  d) x  
Solve for . [1] (i) x : | x + 1 | + | x | > 3 ? ( - 2 , 8 ) ? ( - 1 , 8 ) ? ( - 8 , - 2 ] ? [ 1 , 8 ) ? ( - 8 , - 2 ) ? ( 1 , 8 ) ? [ - 2 , 8 ) ? [ - 1 , 8 ) a) at equal distance from the three sides of
the triangle.
b) the point of intersection of the three
altitudes of the triangle
c) the point of intersection of the three
medians.
d) at equal distance from the three vertices
of the triangle.
The circumcentre of a triangle is the point which is : [1] (j)
a) b)
c) d)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (k)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a [ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) (6, - 6); rectangle b) (6, 4); square
Suppose there are four points A(2, 4), B(6, 4), C(6, 6) and D(2, 6), which lie in the first quadrant. 
If we rotate only the axes at an angle of 90
o
 in anti-clockwise direction, then what will be the new
coordinates of the point C and what will be the name of the figure, when we join adjacent points. 
[1] (l)
Section B
Attempt any 4 questions
c) (-6, 6); square d) (2, -6); rectangle
a) 2( + 1)r b)
c) 2r d)
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 2 r 3 – v a) 1 : 1 b) 1 : 2
c) 3 : 2 d) 2 : 1
In a colony, the average age of the boys is 14 yr and the average age of the girls is 17 yr. If the
average age of the children in the colony is 15 yr, then the ratio of number of boys to that of girls 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): Three consecutive terms 2k + 1, 3k + 3 and 5k - 1 form an AP than k is equal to 6. 
Reason (R): In an AP a, a + d, a + 2d, ...the sum of n terms of the AP be S
n
 = 
[1] (o)
( 2 a + ( n - 1 ) d ) n 2 2. Question 2 [12]
Rashmi has a 4 yr Recurring Deposit Account in Bank of Maharashtra and deposits ? 800 per month.
If she gets ? 48200 at the time of maturity, then find
i. the rate of (simple) interest.
ii. the total interest earned by Rashmi.
[4] (a)
Mr. Kamal reduces the number of workers of his factory in the ratio 9 : 7 and increases their wages in
the ratio 13 : 20. In what ratio, the wages bill is increased or decreased?
[4] (b)
Prove that: 
(1 + cot A - cosec A)(1+ tan A + sec A) = 2
[4] (c)
3. Question 3 [13]
Circumference of the base of a cylinder, open at the top, is 132 cm. The sum of radius and height is 41
cm. Find the cost of polishing the outer surface area of cylinder at the rate ? 10 per sq dm (decimetre).
[Take  = ]
[4] (a)
p 2 2 7 Find the equation of the line, which passes through the point (3, 4) and the sum of its intercepts on the
axes is 14.
[4] (b)
Using graph paper and taking 1 cm = 1 unit along with X-axis and Y-axis.
i. Plot the point A (-4, 4) and B(2, 2).
ii. Reflect A and B in the origin to get the images A' and B', respectively.
iii. Write down the coordinates of A' and B'.
iv. Give the geometrical name for the figure ABA'B'.
[5] (c)
4. Question 4 [10]
Let Vinod, Govind and Ankit be three dealers belonging to difference states. Dealer Vinod sells some
products/services to dealer Govind for ?1000 and dealer Govind sells the same products/services to
dealer Ankit at a profit of ?300. Calculate the tax liability of Govind, if the rate of GST is 12%.
[3] (a)
If the roots of the equation (b - c)x
2
 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
[3] (b)
The mean of the following distribution is 52 and the frequency of class-interval 30-40 is f. Find f.
Class-interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 5 3 f 7 2 6 13
Find the value of f.
[4] (c)
5. Question 5 [10]
If , then find the values of x, y, z and w.
[3] (a)
[ ] = [ ] x - y 2 x - y 2 x + z 3 z + w - 1 0 5 1 3 In the given figure, O is the centre of circle and AOB = 110
o
. Calculate 
i. ACO
ii. CAO.
[3] (b)
? ? ? If one zero of the polynomial 2x
2
 - 5x - (2k + 1) is twice the other, then find both the zeroes of the
polynomial and the value of k.
[4] (c)
6. Question 6 [10]
Find the value of p , if (p, - 2), (-5, 6) and (1, 2) are collinear. [3] (a)
Find the value of  + sin
2
 63
o
 + cos 63
o
 sin 27
o [3] (b)
+ s i n 2 2 2 ° s i n 2 6 8 ° + c o s 2 2 2 ° c o s 2 6 8 ° If the pth, qth and rth terms of a GP are a, b and c respectively. Prove that  = 1. [4] (c) a q - r b r - p c p - q 7. Question 7 [10]
If - 5 is a root of the quadratic equation 2x
2
 + px -15 = 0 and the quadratic equation p(x
2
 + x) + k = 0
has equal roots, then find the value of k.
[5] (a)
Marks obtained by 200 students in an examination are given below:
Marks Number of students
0 - 10 5
10 - 20 11
20 - 30 10
30 - 40 20
40 - 50 28
50 - 60 37
60 - 70 40
70 - 80 29
80 - 90 14
90 - 100 6
[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) ? 10,000 b) ? 6000
c) ? 2000 d) ? 8000
The marked price of a micro oven is ? 10,000. Dealer offers 20% discount on the marked price. The
selling price of micro oven:
[1] (a)
a) Both k  2 and k  -2 b) k  2
c) k = 2 d) k  -2
The linear factors of the equation x
2
 + kx + 1 = 0 exists, if
[1] (b)
= = = = a) -36 b) 56
c) 44 d) 36
When 6x
3
 + 2x
2
 - x + 2 is divided by (x + 2), then remainder is
[1] (c)
a) A and B are square matrices of same
order
b) A and B are square matrices of different
order
c) A and B are rectangular matrices of
same order
d) A and B are rectangular matrices of
different order
If both A + B and AB are defined, then which one of the following is true? [1] (d)
Mathematics
a) 1470 b) 1610
c) 1370 d) 1540
The sum of series 1 + (1 + 2) + (1 + 2 + 3) + (1 + 2 + 3 + 4 )+ ... + (1 + 2 + 3 + ... + 20) is [1] (e)
a) (2, 3) b) (3, 2)
c) (-2, 3) d) (3, -2)
Which of the following points is invariant with respect to the line y = -2? [1] (f)
a) All of these b) Both (i) and (iii)
c) Both (i) and (ii) d) Both (ii) and (iii)
In a PQR, L and M are two points on base QR, such that LPQ = QRP and RPM = RQP.
Then which of the following is/are true
i. 
ii. QL  RM = PL  PM
iii. PQ
2
 = QR QL
[1] (g) ? ? ? ? ? ? P Q L ~ ? R P M × × · 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) x  b) x  
c) x  d) x  
Solve for . [1] (i) x : | x + 1 | + | x | > 3 ? ( - 2 , 8 ) ? ( - 1 , 8 ) ? ( - 8 , - 2 ] ? [ 1 , 8 ) ? ( - 8 , - 2 ) ? ( 1 , 8 ) ? [ - 2 , 8 ) ? [ - 1 , 8 ) a) at equal distance from the three sides of
the triangle.
b) the point of intersection of the three
altitudes of the triangle
c) the point of intersection of the three
medians.
d) at equal distance from the three vertices
of the triangle.
The circumcentre of a triangle is the point which is : [1] (j)
a) b)
c) d)
If  and  are the roots of the equation x
2
 + x - 6 = 0 such that , then the product of the
matrices  and is
[1] (k)
a ß ß > a [ ] 0 a a ß [ ] ß + 1 - ß 0 a [ ] - 5 - 9 4 - 2 [ ] 6 - 1 3 9 - 6 [ ] 5 9 4 2 [ ] 6 9 1 3 6 a) (6, - 6); rectangle b) (6, 4); square
Suppose there are four points A(2, 4), B(6, 4), C(6, 6) and D(2, 6), which lie in the first quadrant. 
If we rotate only the axes at an angle of 90
o
 in anti-clockwise direction, then what will be the new
coordinates of the point C and what will be the name of the figure, when we join adjacent points. 
[1] (l)
Section B
Attempt any 4 questions
c) (-6, 6); square d) (2, -6); rectangle
a) 2( + 1)r b)
c) 2r d)
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 2 r 3 – v a) 1 : 1 b) 1 : 2
c) 3 : 2 d) 2 : 1
In a colony, the average age of the boys is 14 yr and the average age of the girls is 17 yr. If the
average age of the children in the colony is 15 yr, then the ratio of number of boys to that of girls 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): Three consecutive terms 2k + 1, 3k + 3 and 5k - 1 form an AP than k is equal to 6. 
Reason (R): In an AP a, a + d, a + 2d, ...the sum of n terms of the AP be S
n
 = 
[1] (o)
( 2 a + ( n - 1 ) d ) n 2 2. Question 2 [12]
Rashmi has a 4 yr Recurring Deposit Account in Bank of Maharashtra and deposits ? 800 per month.
If she gets ? 48200 at the time of maturity, then find
i. the rate of (simple) interest.
ii. the total interest earned by Rashmi.
[4] (a)
Mr. Kamal reduces the number of workers of his factory in the ratio 9 : 7 and increases their wages in
the ratio 13 : 20. In what ratio, the wages bill is increased or decreased?
[4] (b)
Prove that: 
(1 + cot A - cosec A)(1+ tan A + sec A) = 2
[4] (c)
3. Question 3 [13]
Circumference of the base of a cylinder, open at the top, is 132 cm. The sum of radius and height is 41
cm. Find the cost of polishing the outer surface area of cylinder at the rate ? 10 per sq dm (decimetre).
[Take  = ]
[4] (a)
p 2 2 7 Find the equation of the line, which passes through the point (3, 4) and the sum of its intercepts on the
axes is 14.
[4] (b)
Using graph paper and taking 1 cm = 1 unit along with X-axis and Y-axis.
i. Plot the point A (-4, 4) and B(2, 2).
ii. Reflect A and B in the origin to get the images A' and B', respectively.
iii. Write down the coordinates of A' and B'.
iv. Give the geometrical name for the figure ABA'B'.
[5] (c)
4. Question 4 [10]
Let Vinod, Govind and Ankit be three dealers belonging to difference states. Dealer Vinod sells some
products/services to dealer Govind for ?1000 and dealer Govind sells the same products/services to
dealer Ankit at a profit of ?300. Calculate the tax liability of Govind, if the rate of GST is 12%.
[3] (a)
If the roots of the equation (b - c)x
2
 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
[3] (b)
The mean of the following distribution is 52 and the frequency of class-interval 30-40 is f. Find f.
Class-interval 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Frequency 5 3 f 7 2 6 13
Find the value of f.
[4] (c)
5. Question 5 [10]
If , then find the values of x, y, z and w.
[3] (a)
[ ] = [ ] x - y 2 x - y 2 x + z 3 z + w - 1 0 5 1 3 In the given figure, O is the centre of circle and AOB = 110
o
. Calculate 
i. ACO
ii. CAO.
[3] (b)
? ? ? If one zero of the polynomial 2x
2
 - 5x - (2k + 1) is twice the other, then find both the zeroes of the
polynomial and the value of k.
[4] (c)
6. Question 6 [10]
Find the value of p , if (p, - 2), (-5, 6) and (1, 2) are collinear. [3] (a)
Find the value of  + sin
2
 63
o
 + cos 63
o
 sin 27
o [3] (b)
+ s i n 2 2 2 ° s i n 2 6 8 ° + c o s 2 2 2 ° c o s 2 6 8 ° If the pth, qth and rth terms of a GP are a, b and c respectively. Prove that  = 1. [4] (c) a q - r b r - p c p - q 7. Question 7 [10]
If - 5 is a root of the quadratic equation 2x
2
 + px -15 = 0 and the quadratic equation p(x
2
 + x) + k = 0
has equal roots, then find the value of k.
[5] (a)
Marks obtained by 200 students in an examination are given below:
Marks Number of students
0 - 10 5
10 - 20 11
20 - 30 10
30 - 40 20
40 - 50 28
50 - 60 37
60 - 70 40
70 - 80 29
80 - 90 14
90 - 100 6
[5] (b)
Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students
on the other axis.
i. the median marks.
ii. the number of students who failed, if minimum marks required to pass is 40.
iii. if scoring 85 and more marks is considered as grade one, find the number of students who secured
grade one in the examination.
8. Question 8 [10]
A number is chosen from 1 to 100. Find the probability that it is a prime number. [3] (a)
The internal and external diameters of steel pipe of length 140 cm are 8 cm and 10 cm, respectively.
Then, find the volume of steel.
[3] (b)
In the figure, AB is parallel to DC, BCE = 80° and BAC = 25°. Find:
i. CAD
ii. CBD
iii. ADC 
[4] (c) ? ? ? ? ? 9. Question 9 [10]
Solve the following inequation and graph the solution set on the number line . [3] (a) x + = , x ? R 2 1 5 - 8 1 5 The following table shows the expenditure of 60 boys on books.
Expenditure (in ?) 20-25 25-30 30-35 35-40 40-45 45-50
No. of students 4 7 23 18 6 2
Find the mode of their expenditure.
[3] (b)
In the following figure, CM and RN are respectively the medians of ABC and PQR. If 
, prove that 
 
i. 
ii. 
[4] (c) ? ? ? A B C ~ ? P Q R ? A M C ~ ? P N R = C M R N A B P Q 10. Question 10 [10]
Two positive numbers are in the ratio 3 : 5 and the difference between their squares is 400. Find the
numbers.
[3] (a)
Draw a circle of radius 4 cm. Mark a point A outside the circle. Draw the tangents to the circle from
point A, without using the centre of the circle.
[3] (b)
An aeroplane at an altitude of 1500 metres finds that two ships are sailing towards it in the same
direction. The angles of depression as observed from the aeroplane are 45
o
 and 30
o
 respectively. Find
[4] (c)