ICSE Class 10 Maths Sample Paper 2025 - 4 | 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) ad  bc b) ac  2bd
c) 2ac  bd d) ac  bd
The equation x
2
(a
2
 + b
2
) + 2x(ac + bd) + (c
2 
+ d
2
) = 0 has no real roots, if
[1] (b)
? ? ? ? a) -2 b) -3
c) 2 d) 3
If on dividing 2x
3
 + 6x
2
 - (2k - 7)x + 5 by x + 3, the remainder is k - 1 then the value of k is
[1] (c)
a) b)
c) d)
The matrices A and B, such that AB = O, but A  O and B  O, are [1] (d) ? ? A = [ ] , B = [ ] - 2 2 - 2 2 1 1 1 1 A = [ ] , B = [ ] 2 2 2 2 1 1 1 1 A = [ ] , B = [ ] - 2 - 2 - 2 - 2 - 1 - 1 - 1 - 1 A = [ ] B = [ ] 2 2 2 2 1 - 1 1 - 1 Five distinct positive integers are in arithmetic progression with a positive common difference. If their
sum is 10020, then the smallest possible value of the last term is
[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) ad  bc b) ac  2bd
c) 2ac  bd d) ac  bd
The equation x
2
(a
2
 + b
2
) + 2x(ac + bd) + (c
2 
+ d
2
) = 0 has no real roots, if
[1] (b)
? ? ? ? a) -2 b) -3
c) 2 d) 3
If on dividing 2x
3
 + 6x
2
 - (2k - 7)x + 5 by x + 3, the remainder is k - 1 then the value of k is
[1] (c)
a) b)
c) d)
The matrices A and B, such that AB = O, but A  O and B  O, are [1] (d) ? ? A = [ ] , B = [ ] - 2 2 - 2 2 1 1 1 1 A = [ ] , B = [ ] 2 2 2 2 1 1 1 1 A = [ ] , B = [ ] - 2 - 2 - 2 - 2 - 1 - 1 - 1 - 1 A = [ ] B = [ ] 2 2 2 2 1 - 1 1 - 1 Five distinct positive integers are in arithmetic progression with a positive common difference. If their
sum is 10020, then the smallest possible value of the last term is
[1] (e)
Mathematics
a) 2007 b) 2004
c) 2006 d) 2002
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[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)
The solution set of the inequation  is [1] (i) = 0 1 5 + 3 x ( - 8 , ) - 5 3 ( - 8 , ) 5 3 ( - , 8 ) 5 3 ( , 8 ) 5 3 a) 1 b) 3/4
c) 1/4 d) 2/4
Two coins are tossed together. The probability of getting at most one head is: [1] (j)
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) (0, 1) b) (0, 3 - 4 )
c) (1, 0) d) (1, 3 - 4 )
If (-4, 3) and (4, 3) are two vertices of an equilateral triangle and the origin lies in the interior of the
triangle, then the coordinates of the third vertex will be
[1] (l)
3 – v 3 – v 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 In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each.
Remaining students brought atleast one book each and no two students brought the same number of
[1] (n)
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) ad  bc b) ac  2bd
c) 2ac  bd d) ac  bd
The equation x
2
(a
2
 + b
2
) + 2x(ac + bd) + (c
2 
+ d
2
) = 0 has no real roots, if
[1] (b)
? ? ? ? a) -2 b) -3
c) 2 d) 3
If on dividing 2x
3
 + 6x
2
 - (2k - 7)x + 5 by x + 3, the remainder is k - 1 then the value of k is
[1] (c)
a) b)
c) d)
The matrices A and B, such that AB = O, but A  O and B  O, are [1] (d) ? ? A = [ ] , B = [ ] - 2 2 - 2 2 1 1 1 1 A = [ ] , B = [ ] 2 2 2 2 1 1 1 1 A = [ ] , B = [ ] - 2 - 2 - 2 - 2 - 1 - 1 - 1 - 1 A = [ ] B = [ ] 2 2 2 2 1 - 1 1 - 1 Five distinct positive integers are in arithmetic progression with a positive common difference. If their
sum is 10020, then the smallest possible value of the last term is
[1] (e)
Mathematics
a) 2007 b) 2004
c) 2006 d) 2002
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[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)
The solution set of the inequation  is [1] (i) = 0 1 5 + 3 x ( - 8 , ) - 5 3 ( - 8 , ) 5 3 ( - , 8 ) 5 3 ( , 8 ) 5 3 a) 1 b) 3/4
c) 1/4 d) 2/4
Two coins are tossed together. The probability of getting at most one head is: [1] (j)
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) (0, 1) b) (0, 3 - 4 )
c) (1, 0) d) (1, 3 - 4 )
If (-4, 3) and (4, 3) are two vertices of an equilateral triangle and the origin lies in the interior of the
triangle, then the coordinates of the third vertex will be
[1] (l)
3 – v 3 – v 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 In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each.
Remaining students brought atleast one book each and no two students brought the same number of
[1] (n)
a) 16 b) 14
c) 12 d) 18
books. If the average number of books brought in the class is a positive integer, then the minimum
number of books brought by the remaining students is
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): Let the positive numbers a, b, c be in A.P., then , , are also in A.P. 
Reason (R): If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P. 
[1] (o)
1 b c 1 a c 1 a b 2. Question 2 [12]
Mr. Aarav has a Recurring Deposit Account for 2 yr at 6% interest per annum. He receives ? 975 as
interest on maturity. Find
i. the monthly instalment amount.
ii. the maturity amount
[4] (a)
If x, y, z and u are in proportion, then prove that (lx + my) : (lz + mu) :: (lx - my) : (lz - mu) [4] (b)
Prove that: 2sec
2
  - sec
4
  - 2 cosec
2
  + cosec
4
  = cot
4
  - tan
4
 
[4] (c)
? ? ? ? ? ? 3. Question 3 [13]
A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the
remaining solid where the measurements are as follows: 
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm.
Height of cone is 3 cm. Give your answer correct to the nearest whole number.  
[4] (a)
[ Take p = ] 2 2 7 In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis
at P and Q respectively. 
i. Write the coordinates of A.
ii. Find the ratio in which Q divides AC.
[4] (b)
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) ad  bc b) ac  2bd
c) 2ac  bd d) ac  bd
The equation x
2
(a
2
 + b
2
) + 2x(ac + bd) + (c
2 
+ d
2
) = 0 has no real roots, if
[1] (b)
? ? ? ? a) -2 b) -3
c) 2 d) 3
If on dividing 2x
3
 + 6x
2
 - (2k - 7)x + 5 by x + 3, the remainder is k - 1 then the value of k is
[1] (c)
a) b)
c) d)
The matrices A and B, such that AB = O, but A  O and B  O, are [1] (d) ? ? A = [ ] , B = [ ] - 2 2 - 2 2 1 1 1 1 A = [ ] , B = [ ] 2 2 2 2 1 1 1 1 A = [ ] , B = [ ] - 2 - 2 - 2 - 2 - 1 - 1 - 1 - 1 A = [ ] B = [ ] 2 2 2 2 1 - 1 1 - 1 Five distinct positive integers are in arithmetic progression with a positive common difference. If their
sum is 10020, then the smallest possible value of the last term is
[1] (e)
Mathematics
a) 2007 b) 2004
c) 2006 d) 2002
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[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)
The solution set of the inequation  is [1] (i) = 0 1 5 + 3 x ( - 8 , ) - 5 3 ( - 8 , ) 5 3 ( - , 8 ) 5 3 ( , 8 ) 5 3 a) 1 b) 3/4
c) 1/4 d) 2/4
Two coins are tossed together. The probability of getting at most one head is: [1] (j)
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) (0, 1) b) (0, 3 - 4 )
c) (1, 0) d) (1, 3 - 4 )
If (-4, 3) and (4, 3) are two vertices of an equilateral triangle and the origin lies in the interior of the
triangle, then the coordinates of the third vertex will be
[1] (l)
3 – v 3 – v 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 In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each.
Remaining students brought atleast one book each and no two students brought the same number of
[1] (n)
a) 16 b) 14
c) 12 d) 18
books. If the average number of books brought in the class is a positive integer, then the minimum
number of books brought by the remaining students is
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): Let the positive numbers a, b, c be in A.P., then , , are also in A.P. 
Reason (R): If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P. 
[1] (o)
1 b c 1 a c 1 a b 2. Question 2 [12]
Mr. Aarav has a Recurring Deposit Account for 2 yr at 6% interest per annum. He receives ? 975 as
interest on maturity. Find
i. the monthly instalment amount.
ii. the maturity amount
[4] (a)
If x, y, z and u are in proportion, then prove that (lx + my) : (lz + mu) :: (lx - my) : (lz - mu) [4] (b)
Prove that: 2sec
2
  - sec
4
  - 2 cosec
2
  + cosec
4
  = cot
4
  - tan
4
 
[4] (c)
? ? ? ? ? ? 3. Question 3 [13]
A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the
remaining solid where the measurements are as follows: 
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm.
Height of cone is 3 cm. Give your answer correct to the nearest whole number.  
[4] (a)
[ Take p = ] 2 2 7 In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis
at P and Q respectively. 
i. Write the coordinates of A.
ii. Find the ratio in which Q divides AC.
[4] (b)
Section B
Attempt any 4 questions
iii. Find the equation of the line AC.
Find the reflection of the following points in the line x = 0.
i. (-2.5, 3.5)
ii. (0, 7)
iii. (3, -1.5)
iv. (-1, 0)
[5] (c)
4. Question 4 [10]
Find the amount for the following intra-state transaction.
Cost of per item (in ?) 100 200 250 150 300
No. of items 25 30 40 50 60
GST (Rate %) 12 12 18 28 18
[3] (a)
The product of two successive multiples of 4 is 28 more than the first multiple. Find them. [3] (b)
Using a graph paper draw a histogram for the given distribution showing the number of runs scored
by 50 batsmen. Estimate the mode of the data:
Runs scored
3000-
4000
4000-
5000
5000-
6000
6000-
7000
7000-
8000
8000-
9000
9000-
10000
No. of
batsmen
4 18 9 6 7 2 4
[4] (c)
5. Question 5 [10]
Find x and y. If, 
 = 
[3] (a)
3 [ ] - [ ] 5 4 - 6 x 6 0 y 6 3 [ ] 3 4 - 2 0 In the given figure, O is the centre of a circle. Find the value of b. [3] (b)
If (y - p) is a common factor of the polynomials, f(y) = y
2 
+ ay + b and g(y) = y
2 
+ my + n then show
that .
[4] (c)
p = n - b a - m 6. Question 6 [10]
The centroid of a triangle is the point (6, -1). If two vertices are (3, 4) and (-2, 5), then find third
vertex.
[3] (a)
Prove that:  = cos A + sin A [3] (b) + c o s A 1 - t a n A s i n A 1 - c o t A If the 2nd term of an AP is 13 and 5th term is 25, then what is its 7th term? [4] (c)
7. Question 7 [10]
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip
was reduced by 200 km/h and the time of flight increased by 30 min. Find the duration of flight.
[5] (a)
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) ad  bc b) ac  2bd
c) 2ac  bd d) ac  bd
The equation x
2
(a
2
 + b
2
) + 2x(ac + bd) + (c
2 
+ d
2
) = 0 has no real roots, if
[1] (b)
? ? ? ? a) -2 b) -3
c) 2 d) 3
If on dividing 2x
3
 + 6x
2
 - (2k - 7)x + 5 by x + 3, the remainder is k - 1 then the value of k is
[1] (c)
a) b)
c) d)
The matrices A and B, such that AB = O, but A  O and B  O, are [1] (d) ? ? A = [ ] , B = [ ] - 2 2 - 2 2 1 1 1 1 A = [ ] , B = [ ] 2 2 2 2 1 1 1 1 A = [ ] , B = [ ] - 2 - 2 - 2 - 2 - 1 - 1 - 1 - 1 A = [ ] B = [ ] 2 2 2 2 1 - 1 1 - 1 Five distinct positive integers are in arithmetic progression with a positive common difference. If their
sum is 10020, then the smallest possible value of the last term is
[1] (e)
Mathematics
a) 2007 b) 2004
c) 2006 d) 2002
a) (-3, -2) b) (3, 2)
c) (-3, 0) d) (3, -2)
If the image of the point P under the reflection in the X-axis is (-3, 2), then the coordinates of the
point P are
[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)
The solution set of the inequation  is [1] (i) = 0 1 5 + 3 x ( - 8 , ) - 5 3 ( - 8 , ) 5 3 ( - , 8 ) 5 3 ( , 8 ) 5 3 a) 1 b) 3/4
c) 1/4 d) 2/4
Two coins are tossed together. The probability of getting at most one head is: [1] (j)
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) (0, 1) b) (0, 3 - 4 )
c) (1, 0) d) (1, 3 - 4 )
If (-4, 3) and (4, 3) are two vertices of an equilateral triangle and the origin lies in the interior of the
triangle, then the coordinates of the third vertex will be
[1] (l)
3 – v 3 – v 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 In a class of 20 students, 10 boys brought 11 books each and 6 girls brought 13 books each.
Remaining students brought atleast one book each and no two students brought the same number of
[1] (n)
a) 16 b) 14
c) 12 d) 18
books. If the average number of books brought in the class is a positive integer, then the minimum
number of books brought by the remaining students is
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): Let the positive numbers a, b, c be in A.P., then , , are also in A.P. 
Reason (R): If each term of an A.P. is divided by abc, then the resulting sequence is also in A.P. 
[1] (o)
1 b c 1 a c 1 a b 2. Question 2 [12]
Mr. Aarav has a Recurring Deposit Account for 2 yr at 6% interest per annum. He receives ? 975 as
interest on maturity. Find
i. the monthly instalment amount.
ii. the maturity amount
[4] (a)
If x, y, z and u are in proportion, then prove that (lx + my) : (lz + mu) :: (lx - my) : (lz - mu) [4] (b)
Prove that: 2sec
2
  - sec
4
  - 2 cosec
2
  + cosec
4
  = cot
4
  - tan
4
 
[4] (c)
? ? ? ? ? ? 3. Question 3 [13]
A hemispherical and a conical hole is scooped out of a solid wooden cylinder. Find the volume of the
remaining solid where the measurements are as follows: 
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm.
Height of cone is 3 cm. Give your answer correct to the nearest whole number.  
[4] (a)
[ Take p = ] 2 2 7 In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis
at P and Q respectively. 
i. Write the coordinates of A.
ii. Find the ratio in which Q divides AC.
[4] (b)
Section B
Attempt any 4 questions
iii. Find the equation of the line AC.
Find the reflection of the following points in the line x = 0.
i. (-2.5, 3.5)
ii. (0, 7)
iii. (3, -1.5)
iv. (-1, 0)
[5] (c)
4. Question 4 [10]
Find the amount for the following intra-state transaction.
Cost of per item (in ?) 100 200 250 150 300
No. of items 25 30 40 50 60
GST (Rate %) 12 12 18 28 18
[3] (a)
The product of two successive multiples of 4 is 28 more than the first multiple. Find them. [3] (b)
Using a graph paper draw a histogram for the given distribution showing the number of runs scored
by 50 batsmen. Estimate the mode of the data:
Runs scored
3000-
4000
4000-
5000
5000-
6000
6000-
7000
7000-
8000
8000-
9000
9000-
10000
No. of
batsmen
4 18 9 6 7 2 4
[4] (c)
5. Question 5 [10]
Find x and y. If, 
 = 
[3] (a)
3 [ ] - [ ] 5 4 - 6 x 6 0 y 6 3 [ ] 3 4 - 2 0 In the given figure, O is the centre of a circle. Find the value of b. [3] (b)
If (y - p) is a common factor of the polynomials, f(y) = y
2 
+ ay + b and g(y) = y
2 
+ my + n then show
that .
[4] (c)
p = n - b a - m 6. Question 6 [10]
The centroid of a triangle is the point (6, -1). If two vertices are (3, 4) and (-2, 5), then find third
vertex.
[3] (a)
Prove that:  = cos A + sin A [3] (b) + c o s A 1 - t a n A s i n A 1 - c o t A If the 2nd term of an AP is 13 and 5th term is 25, then what is its 7th term? [4] (c)
7. Question 7 [10]
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip
was reduced by 200 km/h and the time of flight increased by 30 min. Find the duration of flight.
[5] (a)
Use graph paper for this question. 
The marks obtained by 120 students in an English test are given below:
Marks
0 -
10
10 -
20
20 -
30
30 -
40
40 -
50
50 - 60 60 - 70 70 - 80 80 - 90 90 - 100
No. of
students
5 9 16 22 26 18 11 6 4 3
Draw the ogive and hence, estimate:
i. the median marks.
ii. the number of students who did not pass the test if the pass percentage was 50.
iii. the upper quartile marks.
[5] (b)
8. Question 8 [10]
A die is thrown once. Find the probability of getting
i. a prime number.
ii. a number lying between 2 and 6.
iii. an odd number.
[3] (a)
The diameter of the roller 120 cm long is 84 cm. If it takes 500 complete revolutions to level a
playground, then find the cost of levelling at the rate of 30 paise per m
2
.
[3] (b)
In the given figure PQRS is a cyclic quadrilateral where PQ and SR produced to meet at T.
i. Prove TPS  TRQ.
ii. Find SP if TP = 18 cm, RQ = 4 cm and TR = 6 cm.
iii. Find area of quadrilateral PQRS if area of PTS = 27 cm
2
. 
[4] (c)
? ~ ? ? 9. Question 9 [10]
Let A = {x : 11x - 5 > 7x + 3, x  R} and B = {x : 18x - 9  15 + 12x, x  R}, then find the solution
set of A  B.
[3] (a) ? = ? n If the mean of the distribution is 33.2 and the sum of all frequencies is 100, then find the missing
frequencies f
1
 and f
2
.
Class 6-14 14-22 22-30 30-38 38-46 46-54 54-62 62-70
Frequency 11 21
f
1 15 14 8
f
2 6
[3] (b)
The dimensions of the model of a multistoried building are 1 m  60 cm  1.25 m. If the model is
drawn to a scale 1 : 60, then find the actual dimension of the building in metres.
[4] (c) × × 10. Question 10 [10]
A labourer earns ? 9000 per month and spends ? 6500 per month on his family and the rest he saves
for the future needs. Find the ratio of his
i. income to his expenditure.
ii. income to his savings.
[3] (a)