Maths-Question-Paper.pdf - St. Francis High School

DEPARTMENT OF PUBLIC INSTRUCTION, HASSAN

MODEL QUESTION PAPER – 01

SUB: MATHEMATICS Max. Marks : 80

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I Four alternatives are given to each question. Choose the

appropriate answer. Write it along with its alphabet 8* 1 =8

1. If two pair of linear equations are consistent then they

A. intersects each other B. are parallel

C. coincident D. None of these

2. The 11 th term of the A.P -3,2

1 , 2 is

A. 97 B. 77 C. 22 D. 28

3. If the corresponding sides of two similar triangles are

in the ratio 3 : 5, then ratio of their areas

A. 15: 15 B. 3: 8 C. 8: 5 D. 9: 25

4. PT and QT are the tangents drawn to the circle from

an external point T such that 070POQ , then PTQ

A. 1100 B. 550 C. 1400 D. 350

5. If the roots of the equation ( a – b ) x2 + ( b – c ) x + ( c – a ) = 0 are

equal then the value of ( b + c ) is

A. 2a B. 2bc C. 2c D. 2ab

6. In the adjoining graph, number of zeros of the

polynomial p ( x ) is

A. 0 B. 1 C. 2 D. 3

7. Which of the following is not a probability of an event ?

A. 3

2 B. – 1.5 C. 15% D. 0.7

8. The value of 2cos1 is

A. sin B. sin2 C. tan2 D.

2sin

1

II. Solve the following 8* 1 = 8

9. If and are the zeros of the polynomial p (x) = x2 + 7x + 10, then

find the value of .

10. If 2x + 3y = 0 and 4x – 3y = 0 then, find the value of x + y

11. State Thales’ theorem

12. Write the standard form a quadratic equation

13. Express 156 as product of prime factors

14. If P ( x ) = 2x 2 + 3 x + 2,then find the value of p ( 1)

15. If b2 – 4ac > o , then write the nature of roots.

16. Evaluate cot( 90- ) - tan

III. Solve the following 8* 2 = 16

17. Find the 7th term of the A.P 24 ,21,18,,,,,,,,

18. In the adj. fig. if TR

PT

SQ

PS and PRQPST ,then

show that PQR is a isosceles triangle.

19. Find the distance between the points ( - 5 , 7 ) and ( - 1 , 3 )

20. The sum and product of zeros of a polynomial p ( x ) are – 3 and

2 respectively. Find the polynomial.

21. Solve 3x2 – 5x + 2 = 0 by completing square method

OR

Solve 2x2 + x + 4 = 0 by formula method

22. When a dice is thrown once, find the probability of getting

a. A odd number b. A prime number

23. Draw a circle of radius 5 cm construct two tangents from an

external point such that the angle between them is 600

24. A sphere of radius 4.2 cm is melted and recast to form a

cylinder of radius 6 cm, find the height of the cylinder

OR

Find the capacity of frustum of the cone of radius 4 cm and 2

cm with height 14 c.m.

IV. Solve the following 9* 3 = 27

25. Find the mode for the following scores

C- I 0-20 20-40 40-60 60-80 80-100 100-120

Frequency 10 35 52 61 38 29

OR

If the median of the scores is 525, with sum of the frequencies 100

find the value of ‘x’ and ‘y’

C-I 0-100 100-200 200-300 300-400 400-500 500-600 600-700 700-800 800-900 900-1000

F 2 5 X 12 17 20 Y 9 7 4

26. Prove that “length of the tangents drawn to the circle from an

external points are equal”.

27. Prove that 2)cos(cos

cos1

cos1

ec

OR

Prove that

2

2

2

2

cot1

cot

tan1

tan

= 1

28. Draw a triangle of sides 5 cm , 6 cm and 7 cm respectively.

Construct another similar triangles whose sides are 5

7 times of

the corresponding sides

OR

Construct a triangle ABC, BC = 7 cm, 00 105,45 AB , construct

another similar triangle whose sides are 3

4 times the

corresponding sides of the original triangle.

29. Show that ( 4, 5 ) ( 7, 6 ) ( 4, 3 ) and ( 1 ,2 ) forms the vertices

of a quadrilateral

30. Prove that 5 is a irrational number

31. ABC a quadrant of a circle of radius 14 cm and semi circle

drawn on BC as shown in the fig. find the area of the shaded portion.

32. Draw the less than type Ogive for the following data

C – I 100-120 120-140 140-160 160-180 180-200

F 12 14 8 6 14

33. Solve 32

11

xx

OR

If sum to n terms of an A.P is 2

133 2 nn find the 25 th term

V. Solve the following 4* 4 = 16

34. In an A.P if the 3rd term is 32 and 5th term is 40, find the sum

of first 30 terms

35. The angle of elevation of top of a cloud as observed from a 16m

tall building is 600.The angle of depression of foot of the hill is

300.Find the height of the cloud.

36. State and prove Pythagoras theorem.

37. Solve 2x+ y = 4 and 2x – y = 4 graphically.

VI. Solve the following 5*1 = 5

38. A metallic right circular cone 20 cm high and whose vertical

angle is 600 is cut into two parts at the middle of its height by a

plane parallel to its base. If the frustum so obtained be drawn

into a wire of diameter 16

1 cm, find the length of the wire.




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I Four alternatives are given to each question. Choose the appropriate

answer. Write it along with its alphabet 8 x 1 = 8

1. The L.C.M of is

A. 40 B. 560 C. 1120 D. 1680

2. The next term of the A.P , , , . . . . . . is

A. B. C. D.

3. The zeroes of the polynomial x 2 – 2 x – 3 are

A. -3, 2 B. -3, -1 C. 3, -1 D. 3, 1

4. Nature of the roots of the quadratic equation 2x2 – 3x +5 = 0 A.

Real and distinct B. Real and equal

C. No real roots D. None of these

5. If Sin A =5

3 , then tan A = ______

A.5

4 B.4

3 C. 3

4 D.4

5

6. Which of the following cannot be the probability of an event?

A. 3

2 B. -2.5 C. 100 D. 1

7. In the adj. fig , the value of PTQ is

A. 900 B. 1100 C. 700 D. 400

8. If yxyx 22 = 8 , then the value of y is

A. 2

3 B.3

2 C. 0 D.

II Solve the following 8 x 1 = 8

9. Express as the product of prime factors

10. Which type of solution will equation

have?

11. In the quadratic equation ax2 + bx +c =0, if a = 0, then name the

type of equation so obtained.

12. Write the co ordinates of the origin.

13. Find the distance between the points (2,3) and (4, 1)

14. Calculate the average of first ten natural numbers?

15. State Thales theorem

16. Write the formula used to find the volume of frustum of a cone.

III Solve the following 8 x 2 = 16

17. Prove that 2+ is a irrational number

18. Solve 8x+5y=19 and 3x+2y=4

19. Form a quadratic polynomial whose sum and product of the

zeroes are 2 and 3

1 respectively.

20. Prove that SecA(1-SinA)(SecA+tanA)=1

OR

Find the value of 2tan2450 cos2300 Sin2600

21. Calculate mode for the following scores

22. What is the probability of getting doublets, when two dice are

thrown simultaneously?

23. If the volume of a cube is 64cm3, then find the T.S.A of the

cube.

24. Construct two tangents to a circle of radius 5cm such that the

angle between the tangents is 600

OR

Construct two tangents to a circle of radius 3.5 cm , such that

the angle between the radii is 800

I IV. Solve the following 9 x 3=27

25. If two zeroes of the polynomial are3

5 and -3

5 , find other two

zeroes

OR

If the polynomial x3 3x2 x 2 is divided from g(x) , the

remainder and quotient are (x 2) and -2x+4 respectively ,then

find g(x).

26. If 3cot = 4, then show that

2

2

tan1

tan1

=cos2 - sin2

C – I 0-20 20-40 40-60 60-80 80-100 100-120

F 10 35 52 61 38 29

27. The shadow of a tower standing on a level ground is found to be

40m longer when the Sun’s altitude is 300 than when it is 600.

Find the height of the tower

OR

The angle of depression of the top and bottom of an 8 m tall

building from the top of a multi storeyed building are 300 and

450 respectively. Find the height of the multi storeyed building

and the distance between.

28. If A(-5,7), B(-4,-5), C(-1, -6), and D(4, 5) are the vertices of

a quadrilateral ,then find the area of the quadrilateral ABCD.

29. Draw less than type Ogive for the following data

Weight in k. g No. of

students

Less than 38 0

Less than 40 3

Less than 42 5

Less than 44 9

Less than 46 14

Less than 48 28

Less than 50 32

Less than 52 35

30. Construct a triangle of sides 5cm, 6cm and 7 cm. and then another

triangle whose sides are 5

7 of the corresponding sides of the first

triangle.

31. Prove that “length of the tangents drawn to a circle from an

external point are equal”.

32. Two poles of height 9 m and 14 m stands vertically on the

ground level ,such that the distance between them is 12 m. find

the distance between their tops.

OR

In the adj. fig POR=900, OP= 6cm , OR = 8cm ,

PQ = 24 cm and QR=26cm, then show that

PQR is a right angled triangle.

33. Find the area of the shaded regions enclosed by two

concentric circles of radius 7 cm and 14 cm , where AOC= 400

OR

The perimeter of a circle is 45cm more than its diameter, then find

the perimeter of the circle.

V. Solve the following 4 4=16

34. Prove that “ areas of two similar triangles are proportional to the

squares of their corresponding sides”.

35. Solve 0 graphically

36. An express train takes 1 hour less than a passenger train to

travel 132 km between Mysore and Bangalore. If the average

speed of the express train is 11km/h more than that of the

passenger train, find the average speed of the two trains.


angle is 600 is cut into two parts at the middle of its height by a

plane parallel to its base. If the frustum so obtained be drawn

into a wire of diameter 16


OR

A vessel is in the form of a hollow hemisphere mounted by a

hollow cylinder. The diameter of the hemisphere is 14 cm and

the total height of the vessel is 13 cm. find the inner surface

area of the vessel.

VI. Solve the following 5

38. The sum of 3rd and 7th term of an A.P is 6 and their product is

8, find the sum of first 16 terms.




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answer. Write it along with its alphabet 8 x 1 = 8

1. By Euclid’s division algorithm the H.C.F of 135 and 225 is

A) 45 B) 35 C) 50 D)65

2. The 30th term of the A.P 10, 7, 4…….. is

A) 97 B) 77 C)-77 D)-87

3. In the adjoining figure the zeroes of the polynomial p(x) is

A) 4 B)3 C)2 D)5

4. In the adj. fig, if DE‖‖BC then EC

A)3 B)2 C)2.5 D)4

5. The probability of getting a rain is 0.3,then the probability of not

getting a rain is

A) 0.6 B)1.7 C)1 D)0.7

6. If Sin 2A=2sinA , then A

A) 00 B) 300 C)450 D)600

7. In the adj fig if QOR=1000 then QPR=_____

A) 800 B)1800 C)400 D)900

8. The T.S.A of hemisphere of radius 7cm is

A) 616cm2 B) 154cm2 C)308cm2 D) 164cm2

II. Solve the following 8 * 1 = 8

9. Express 3825 as the product of prime factors.

10. Find the 10th term of the A.P 2,7,12……….

11. Form a quadratic polynomial whose sum and product of zeroes are 1

and 1 respectively.

12. Write the positive roots of the equation ax2+bx+c=0

13. Simplify: cos 480-sin 420

14. Find the value of 9sec2A - 9tan2A

15. Write the formula used to calculate the area of sector with

an angle of A0

16. The radius of right circular cone of slant height 14 cm is 6 cm,

find its C.S.A

III Solve the following 8 * 2 =16

17.Prove that 5+ 2 is a irrational number

18. Solve 2x+3y=46 and 3x+5y=74

19. If the roots of the equation 2x2+kx+3=0 are equal, then find the value

of ‘k’

20. If a point P divides the line segment obtained by joining the points

(4,-3), and (8,5) in the ratio 3: 1,then find the co ordinates of the point P.

21. A bag contain 3 red balls and 5 black balls, a ball is drawn randomly,

what is the probability of getting

a. a red ball b. other than a red ball ?

22. In the adj. fig if LM‖CB and LN‖CD then show that =

OR

Δ ABC is an right isosceles triangle with AC=BC , then show that

AB2=2AC2

23. Construct a pair of tangents to a circle of radius 4cm such that the

angle between the radii is 1200

24. If Sin(A-B)=2

1 , cos(A+B)= 2

1 with A>B , A and B are acute angles

then find the value of A and B

OR

If Cos A=5

4 then, find the value of Sin A and tan A

IV Solve the following 9*3 =27

25. Find the zeroes of the polynomial 4s2 - 4s+ 1, and also verify the

relationship between zeroes and its coefficients.

26. The sum of areas of two squares is 468m2 and difference of their

perimeter is 24 m, find the length of sides of the squares.

OR

The difference of squares of two numbers is 180. The square of

smaller number is twice the larger number. Find the two numbers.

27. Find the area of the triangle formed by joining the mid-points of

the sides of the triangle whose vertices are (0, –1), (2, 1) and (0,

3). Find the ratio of this area to the area of the given triangle.

OR

Find a relation between x and y such that the point (x , y) is

equidistant from the points (7, 0) and (1, 2).

28. The following distribution gives the daily income of 50 workers

of a factory. Convert the above distribution to a less than type

cumulative frequency and Draw less than type Ogive

29. The distribution below gives the weights of 30 students of a class.

Find the median weight of the students

OR

The following distribution shows that daily pocket allowance of children

of a locality. The mean pocket allowance is Rs. 18. Find the missing

frequency

X 100-120 120-140 140-160 160-180 180-200

F 12 14 8 6 10

Weight ( in Kg ) 40-45 45-50 50-55 55-60 60-65 65-70 70-75

Number of students 2 3 8 6 6 3 2

Daily pocket

allowance

( in Rs )

11-13 13-15 15-17 17-19 19-21 21-23 23-25

No. of

children 7 6 9 13 f 5 4

30. Prove that the “length of the tangents drawn to a circle from an


31. The cost of 5 pen and 3 pencils is Rs. 35 and the cost of 2 pens and 4

pencils is Rs. 28. Find the cost of each pen and pencil

OR

Solve the pair of equations + 3y = 14, - 4y = 23 by reducing them to a

pair of linear equations

32. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and

ABC = 60°.Then construct a triangle whose sides are4

3 times the

corresponding sides of the triangle ABC.

33. Find the area of the shaded region where a major sector of

radius 6 cm has been drawn with vertex ‘O’ of an equilateral

triangle OAB of side 12 cm as centre

V. Solve the following 4x4=16

34. Solve x + y = 8 and and x – y = 4 graphically

35. Sum of three numbers of an A.P is 27 and sum of their squares is 293.

Find the numbers.

OR

The sum of third and 7th term of an A.P is 6 and their product is 8,

find the A.P.

36. From a point on the ground, the angles of elevation of the bottom and

the top of a transmission tower fixed at the top of a 20 m high building are

45° and 60° respectively. Find the height of the tower.

37. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is

filled with sand. This bucket is emptied on the ground and a conical heap of

sand is formed. If the height of the conical heap is 24 cm, find the radius

and slant height of the heap.

VI Answer the following question 5x1=5

38. State and prove Thale’s theorem.




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appropriate answer. Write it along with its alphabet 8*1 = 8

1. The first three terms of A.P with first term 1 and c.d – 2 is

A. – 1, 1, 3 B. 1. -1, -3 C. 0 , 1 , 3 D. – 3 , 1 , - 1

2. The value of 2cos1 is

A. 1 B. sin C. tan2 D. 2sin

1

3. Which of the following is not probability of an event?

A. 3

2 B. – 1.5 C. 0.7 D. 0.5

4. The formula used to calculate the C.S.A of a cone

A. r l B. r2l C. ( r1 +r2 ) l D. rh

5. In the adjoining figure if 0100AOB , then ACB =

A. 600 B. 700 C. 800 D. 400

6. if tan2A = cot( A - 180) , where 2A is an acute, then A =

A. 180 B. 1800 C. 3600 D. 360

7. In the adjoining graph, number of zeroes of the polynomial p ( x ) is

A. 0 B. 1 C. 2 D. 3

8. The C.S.A of a cylinder of radius 7 cm and height 10 cm is

A. 410 sq. cm B. 420 sq. cm C. 400 sq. cm D. 440 sq. cm


9. Express 3825 as product of prime factors

10. If q

p

is a rational number ( q o), what is the condition of ‘q’ so

that the decimal representation of q

p

is terminating?

11. If and are the zeroes of the polynomial p ( x) = x2 + 5x + 8

, then find the value of + .

12. State Thales theorem

13. If p ( x) = 2x2 + 3x + 2,then find the value of p ( 2 )

14. If b2 – 4ac = 0 then write the nature of the roots

15. If the c.d of an A.P is 4, then find the value of a15 – a10

16. Evaluate tan( 900 - )

III. Solve the following 8 * 2 = 16

17. Prove that 2+ 5 is a irrational number

18. Find the 11 th term from the last of an A.P 10,7,4…….. – 62

19. Solve x + y = 14 and x – y = 4

OR

The difference of two numbers is 26, if one number is thrice the

other, find the number.

20. If p ( x) = x3 – 3 x 2+5x – 3 and g ( x) = x2 – 2, find the

remainder and the quotient

OR

If the polynomial x3 – 3x2 +x+2 is divided by g(x) , the

remainders and quotient were x – 2 and – 2 x + 4, find g ( x).

21. Solve 2x2 – 7x + 3 = 0 by formula method.

22. A dice is thrown once, what is the probability of getting

a. A prime number b. An odd number

23. Draw a circle of radius 5 cm, construct the tangents to the circle

at the ends of radii such that the angle between radii is 600.

24. From each corner of a square of side 4 cm a

quadrant of a circle of radius 1 cm is cut and also

a circle of diameter 2 cm is cut as shown

in the figure. Find the area of the remaining portion of the square.

IV. Solve the following 9 * 3 = 27

25. A fraction becomes 1, if 1 is added to the numerator and 1 is

subtracted from the denominator. It becomes 2

1 , if 1 is added to the

numerator . find the fraction.

OR

Solve x

4 + 3y = 14 and x

3 – 4y = 23 by Elimination method

26. Prove that “the length of the tangents drawn the circle from an


27. Find the area of a quadrilateral whose vertices are ( - 4 , - 2 ) ,

( - 3 , - 3 ), ( 3, - 2 ) and ( 2,3 ).

OR

In what ratio does the point ( - 1 , 6 ) divides the line obtained by

joining the points ( - 3 ,10 ) and ( 6 , 8 )?

28. Find a cubic polynomial with the sum , sum of the product of its

zeroes taken two at a time, and the product of its zeroes are 2 ,-7 and

-14 respectively.

29. Find the area of the shaded region, where ABCD

is a square of side 10 cm and semicircles are drawn

with each side of the square as diameter ( use = 3.14)

OR

Find the area of the shaded where a circular arc of

radius 6 cm has been drawn with vertex O of an

equilateral triangle OAB of side 12 cm as centre

30. Find the median for the following scores

C-I 1-4 4-7 7-10 10-13 13-16 16-19

F 6 30 40 16 4 4

OR

If the median of the following scores is 28.5, then find the value of x

and y

31.A train covers a distance of 360 km with uniform speed , if the speed

had been 5 km / hr more, it would have taken 1 hour less for the same

journey. Find the speed of the train.

C- I 0-10 10-20 20-30 30-40 40-50 50-60

F 5 X 20 15 Y 5

32.Draw more than type Ogive for the following scores

Production

yield 50-55 55-60 60-65 65-70 70-75 75-80

No. of farms 2 8 12 24 38 16

33.Construct a triangle of sides 5cm, 6cm and 7 cm. and then another

triangle whose sides are 5

7 times the corresponding sides of the first

triangle.

V. Solve the following 4* 4 = 16

34.Solve 2x+ y = 4 and 2x – y = 4 graphically.

35.The angle of elevation of top of Hill from the top of a 16 m high

building is 600and the angle of depression of bottom of the hill is 300

. Find the height of the hill.

36.The first and last term of an A.P are 8 and 350 respectively, if the

common difference is 9, find the number of terms and the sum of the

series.

OR

The third term of an A.P is 32 and its fifth term is 40, find the sum

of first thirty terms of the A.P

37.A medicine capsule is in the shape of a cylinder with two hemispheres

stuck to each of its ends. The length of the entire capsule is 14 mm

and the diameter of the capsule is 5 mm. find its surface area.

VI. Solve the following 5 * 1 =5

38.State and Prove A. A. A. criterion of similarity triangles.



SUB: MATHEMATICS Max. Marks: 80

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appropriate answer. Write it along with its alphabet 8 * 1 = 8

1. The nth term of an A. P with first term ‘a’ and c.d. ‘d’ is

A. a +( n +1 ) d B. a + ( n – 1 ) d

C. a – ( n + 1 ) d D. a – ( n – 1 ) d

2. If the H.C.F and L.C.M of two positive numbers are a and b , then

H( a, b ) x L ( a, b ) = --

A. a x b B. b

a C. a – b D. a + b

3. If solution of two lines are consistent then, lines are

A. parallel and coincident B. always intersect each other

C. parallel or intersect each other D. always coincide with each other

4. The distance between origin and ( a, b ) is

A. d = 22 ba B. d = 22 ba C. d = 22 ba D. d = 22 ba

5. The sum of zeroes of the polynomial x2 – 7x +10 is

A. 7 B. – 7 C. 10 D. – 10

6. “The sum of two odd positive numbers is 290”, the algebraic form of

this statement is

A. x2 + ( x+2)2 B. (x+1)+ ( x + 3 ) = 290

C. x2 + ( x + 2 ) = 290 D. x + ( x + 2 ) 2 = 290

7. In the adj. figure if AB = 4 cm and BC = 3 cm, then tan A =

A. 4

3 B. 5

3 C. 3

4 D. 4

5

8. The C.S.A of cone of radius 7 cm and slant height 10 cm is

A. 110 cm2 B. 70 cm2 C. 440 cm2 D. 220 cm2


9. Find the 5th term of an A.P whose nth term is 4n2 – 1 .

10. How many tangents can be drawn to a circle from an external

point?

11. If b2 – 4ac = 0, then comment on nature of the roots .

12. If SinA = 2

1 , then find the value of A

13. Name the solid obtained by rotating a rectangle about one of its

edge.

14. Express 140 as the product of prime factors

15. If P ( E) = 0.05, then find P ( E )

16. Find the distance between the points ( 2 , 3 ) and ( 4, 1 )


17. Prove that 3+ 5 is a irrational number.

18. If the zeroes of the polynomial x 2 -12x+32 are a+ b and

a - b, then find the value of ‘a’ and ‘b’.

19. The sum of the reciprocal of Rehman’s age ( in years ) 3 years

ago and 5 years from now is 3

1 . Find his present age.

20. Solve x +y = 14 and x – y = 4

OR

Half the perimeter of a rectangular garden, whose length us 4 m

more than its width is 36 m. find the dimensions of the garden.

21. Two dice are thrown once, what is the probability of getting

a. Sum of the two numbers is divisible by 4

b. The product of two numbers is a perfect square ?

22. Areas of two similar triangles ABC and DEF, are 64cm2 and

121 cm2 respectively , if EF = 15.4 cm, find the length of BC.

OR

In the adj. fig LM || CB, and LN || CD, then

prove that AD

AN

AB

AM

23. In the adj. fig ABC 090ABC , AD BC

then prove that AC2 = AB2 +BC2 +2BC.BD

24. Draw a pair of tangents to a circle of radius 5 cm which are

inclined to each other at angle of 800.

IV. Solve the following 9* 3 = 27

25. If the roots of the equation 3x2 – 5x + 2 = 0 are real, then find

the roots by using formula

OR

Solve 2x2 – 7x + 3 = 0 by completing square method

26. If 3 cotA = 4, then verify A

A2

2

tan1

tan1

= cos2A – sin2 A

OR

Prove that 1cos

1cos

coscot

coscot

ecA

ecA

AA

AA

27. Draw the less than type Ogive for the following scores

Monthly

consumption

( in units)

65-85 85-105 105-125 125-145 145-165 165-185 185-205

No of

consumers 4 5 13 20 14 8 14

28. Find the median for the following scores

C – I 135-140 140-145 145-150 150-155 155-160 160-165

F 5 4 7 18 11

29. BL and MC are the medians of the right angled triangle

ABC, then prove that 4 ( BL2+MC2 ) = 5BC2

OR

Two poles of height 6 m and 11 m stand vertically on the ground level

such that the distance between them is 12 m, find the distance between

their tops.

30. Prove that “the length of the tangents drawn the circle from an


OR

Two concentric circle of radius 5 cm and 3 cm. find the length of the

chord of the larger circle which touches the smaller circle.

31. Divide 3x2 – x 3 +3x +5 by x – 1 – x 2 and verify division

algorithm.

OR

Find the zeroes of the polynomial x2 +7x +10 and verify the

relationship between the co-coefficients and the zeroes

32. Find the area of a quadrilateral whose vertices are ( - 4 , - 2 )

( - 3 , - 5 ), ( 3, -2 ) and ( 2, 3 ).

33. Construct a triangle of sides 5cm, 6cm and 7 cm. and then

another triangle whose sides are 5

7 of the corresponding sides

of the first triangle.

V. Solve the following 4*4 = 16

34. How many terms of the A.P -10,-7,-4,-1 must be added to make

the sum -104?

OR

Find three numbers in A.P whose sum is 27 and product is 648.

35. If corresponding angles of two triangles are equal, then prove

that corresponding sides are in proportion.

36. Solve x + 3y = 6 and 2x – 3y = 12 graphically

37. From a point on a bridge across a river the angles of depression

of the banks on opposite sides of the river are 300 and 450

respectively, if the bridge is at a height of 3 m from the bank,

find the width of the river.

VI. Solve the following 5 * 1 = 5

38. A cistern internally measuring 150 cm x 120 cm x 110 cm has

129600cm3 of water in it pores bricks are placed in the water

until the cistern is full to the brim each brick observes one

seventeenth of its own volume of its water. How many brick can

be put in without overflowing the water, each brick being

22.5 cm x 7.5cm x 6.5 cm.




====================================================


answer. Write it along with its alphabet 8 * 1 = 8

1. The decimal expansion of 8

3 is

A. 0.375 B. 3.75 C. 37.5 D. 375

2. If 2

1

2

1

2

1

c

c

b

b

a

a , then the lines are

A. coincident B. intersect each other

C. parallel D. none of these

3. The 30th term of the A.P 10 ,7,4,….. is

A. 61 B. 16 C. 79 D. 97

4. The value of cos480 – sin 420 is

A. 300 B. 250 C. 200 D. 0

5. The distance between the points ( 2, 3 ) and ( 4, 1) is

A. 2 units B. 2 units C. 2 2 units D. 22 units

6. The probability of winning a prize in singing competition is 0.62, then

the probability of losing is

A. 0 B. 0.038 C. 3.8 D. 38

7. Number of tangents drawn to a circle

A. 0 B. 1 C. 2 D. Infinity

8. The area of a circle of radius 7 cm is

A. 0.95 B. 0.59 C. 95 D. 15



10. Write the discriminent of the equation px2 + qx + r = 0

11. If sin 5

3 and cos

5

4 , then find the value of tan

12. A man standing on building observes the a car coming towards

the building , name the angle so formed with the line of sight

and the horizontal plane

13. Write the section formula.

14. Calculate the C.S.A of a hemisphere of radius 7 cm.

15. In the adj. fig find the length of OA

16. If S = { 1,2,3,4,5,6} What is the probability of prime number?


17. Prove that 3 is an irrational number

18. Find the quadratic polynomial whose sum and product of the

zeroes are 2 and 3

1 .

19. If P ( x ) = x3 – 3x2 + 5x – 3 is divided from g ( x ) = x – 2

then , find the remainder and the quotient.

20. A circus artist is climbing 20 m long rope which is tightly

stretched and tide from the top of the vertical pole to the ground.

Find the height of the pole, if the angle made by the rope with

the ground level is 300.

OR

The angle of elevation of the top of the tower from a point on the

ground, which is 30 m away from the foot of the tower is 300 , find the

height of the tower.

21. In the adj. fig LM || CB, and LN || CD, then prove that AD

AN

AB

AM

OR

In the adj fig. ABC and AMP are two right triangles,

right angled at B and M respectively prove that

a. ABC ~ AMP b. MP

BC

PA

CA

22. Divide a line segment of length 8 cm in the ratio 3 : 5

23. Find the area of a sector of radius 6 cm with central angle of

600.

24. Find the volume of a hemisphere of diameter 7 cm.


25. Solve the following yx 3

1

2

1 = 2 and

6

13

2

1

3

1

yx

OR

Ritu can row downstream 20 km in 2 hours, and upstream 4 km

in 2 hours. Find the speed of rowing in still water and the speed

of the current.


27. In an A.P, the 2nd and 3rd terms are 14 and 18 respectively, find

the 51st term of the A.P

28. Solve 5x2 – 6x – 2 = 0 using suitable formula and also discuss

the nature of the roots

29. The diagonal of rectangular field is 60m more than the shortest

side. If the longer side is 30 m more than the shorter side, find

the sides of the field.

OR

The sum of the reciprocal of Rehman’s age ( in years ) 3 years

ago and 5 years from now is 3

1 . Find his present age.

30. Prove that the points ( 3, 1 ) ( 6, 4 ) and ( 8 , 6 ) are collinear.

OR

In what ratio does the point ( - 1 , 6 ) divides the line segment

obtained by joining the points ( - 3 , 10 ) and ( 6 , - 8 )?

31. The following shows the ages of the patients admitted in the

hospital during the year.

Ages

( in years) 5-15 15-25 25-35 35-45 45-55 55-65

No. of

patients 6 11 21 23 14 5

Find the mean and the mode for the above data

32. TP and TQ are the tangents drawn to the circle

with centre O from an external point T. Prove

that OPQPTQ 2

33. A drinking glass in the shape of a frustum of a cone of height

14 cm. the diameter of its two circular ends are 4 cm and 2 cm .

find the capacity of glass.


34. Three numbers are in A.P whose sum is 27 and product is 648.

find the numbers

OR

The 2nd and 12th term of an A.P are 14 and 18 respectively, find the

sum of 51st terms of the A.P

35. If cosec2 A = 1+cot2 A , then prove that

1sincos

1sincos

AA

AA = cosecA +cotA

36. Draw more than type Ogive for the following scores

Production

yield 50-55 55-60 60-65 65-70 70-75 75-80

No. of

farms. 2 8 12 24 38 16



7 of the corresponding sides of the

first triangle

VI. Solve the following 5 * 1 = 5

38. State and prove pythagoreas theorem




====================================================



1. The H.C.F of the smallest prime number and the composite number

A. 4 B.3 C. 2 D. 1

2. The sum of first n natural numbers is

A. 2

)1(

nnSn B. Sn = an (n +1 ) C. Sn = n ( n + 1 ) D.

2

)1(

nnSn

3. The zeroes of the polynomial 4x2 – 12x + 9 are

A. 2

3,

2

3 B. 2

3,

2

3 C. 3,-4 D. -3,-4

4. The discriminent of the quadratic equation 2x2 – 4x + 3 = 0 is

A. – 4 B. – 8 C. 4 D. 6

5. If the distance between the points ( 4, p ) and ( 1 , 0 ) is 5 units, then

the value of ‘p’ is

A. 4 B. – 4 C. 1 D. None of these

6. The value of sin300 is

A. 0 B. 2

1 C. 2

3 D. 2

1

7. The coordinates of the origin is

A. ( 0 , 0 ) B. ( 1,1) C. ( 2,2) D. ( 3,3)

8. Total number of possible outcomes, when a coin is tossed thrice

repeatedly is

A. 4 B. 8 C. 5 D. 7

II. Solve the following 8* 1 = 8

9. What is the measure of the angle subtended in a semicircle?

10. Find the distance between the points (2, 3) and the origin.

11. Write the formula used to find the C.S.A of frustum of a cone

12. Simplify A

A2

2

cot1

tan1

13. If the volume of a cube is 64 cm3, then find the length of each

side of the cube

14. If One root of the equation x2 = 3 x – 10 is 5 find the other root


16. Find the 11th term of the A.P 3,2

1 , -2 …………….


17. Prove that 5 - 3 is irrational number

18. Solve 2x+ y = 5 and 3x + 2 y = 8

19. Solve 2x2 – 3x – 5 = 0 by formula method

20. If tan2A = cot ( A – 18) and 2A is an acute angle, then find the

value of A

OR

Prove that AAA

Atansec

sin1

sin1

21. Find the area of a triangle, whose vertices are ( 2, 3 ) , ( - 1 , 0 )

and ( 2 , - 4 )

22. When a dice is thrown once, what is the probability of getting

a. A prime number b. A number between 2 and 6 ?

23. ABCD is a trapezium in which AB || CD, diagonals BD and CD

intersects at O, then show that OD

CO

CO

AO

OR

A ladder 10 m long reaches a window 8 m above the ground.

Find the distance of the foot of the ladder from the base of the wall

24. Construct two tangents to a circle of radius 5 cm from an

external point such that the angle between them is 600.


25. Ritu can row downstream 20 km in 2 hours, and upstream 4 km

in 2 hours. Find the speed of rowing in still water and the speed

of the current.

OR

The ratio of incomes of two persons is 9 : 7 and the ratio of their

expenditures is 4 : 3. if each of them manages to save Rs. 2000

per month, find their monthly incomes.

26. Find the coordinates of the points of trisection of the line

segment joining the points A ( 2, 2) and B ( - 7 , 4 )

OR

Show that the points ( 1, 5 )( 2, 3 ) and ( - 2 , -11) are collinear.

27. Find the remainder and quotient by dividing the polynomial

p ( x ) = 3x4 +5x3- 7x2+2x+2 by x2 +3x+1, and also verify

division algorithm.

28. Prove that “length of the tangents drawn from the external point

to the circle are equal”.



2 of the corresponding sides of

the first triangle

30. A train travels a distance of 480 km at a uniform speed. If the

speed had been 8 km/hr less, then it would have taken 3 hours more to

cover the same distance. Find the speed of the train.

31. Find the mean for the following scores

C – I 10-20 20-30 30-40 40-50

F 1 2 3 4

32. The annual profits earned by 30 shops of a shopping complex in

a locality give rise to the following distribution, Draw the less than

type Ogive

Classes 5-10 10-15 15-20 20-25 25-30 30-35 35-40

No of

shops 2 12 2 4 3 4 3

33. From each corner of a square of side 4 cm a

quadrant of a circle of radius 1 cm is cut and also a

circle of diameter 2 cm is cut as shown in the figure.

Find the area of the remaining portion of the square.

OR

Find the area of the shaded region in the adj. fig

where ABCD is a square of side 14 cm

V. Solve the following 4 * 4= 16

34. Solve x+3y = 6 and 2x – 3y = 12 graphically

35. Sum of first 7 terms of an A.P is 49 and sum of first 17 terms is

289, find the sum of first n terms

36. The angles of depression of top and bottom of an 8 m tall

building from the top of a multi storeyed building are 300 and

450 respectively. Find the height of the multi storeyed building

and the distance between the two buildings.

37. The radii of the ends of a frustum of a cone 45 cm and high are

28 cm and 7 cm . find its volume, the curved surface are and the

total surface area ( use 7

22 )

VI. Solve the following 5*1 = 5

38. State and prove Pythagoras theorem




====================================================



1. The H.C.F of 36 and 18 is

A. 6 B. 2 C. 9 D. 18

2. The ratio of corresponding sides of two similar triangles are 4 : 9 ,

then ratio of their areas is

A. 1 : 2 B. 2 : 3 C. 16 : 81 D. 81 : 16

3. In the adj fig the value of ‘x’ is

A. 600 B. 1200 C. 900 D. 300

4. The 10 the term f the A.P 2,5,8,….. is

A. 30 B. 25 C. 20 D. 29

5. Sum of the zeroes of the polynomial x2 – 2x – 8 is

A. – 2 B. 1 C. 2 D. 0

6. The root of the quadratic equation 6x2 – x – 2 = 0 are

A. 3

2 and 2

1 B. 3

2 and 2

1 C. 3

2 and 2

1 D. 3

2 and 2

1

7. If Sin A = 2

1 , then A =

A. 800 B. 600 C. 300 D. 450

8. If P ( E ) = 0.05, then P ( E ) =

A. 0.95 B. 0.59 C. 95 D. 59


9. Find the common difference of the A.P 3,1,-1,-3,……………

10. State Thale’s theorem


12. Form a quadratic polynomial whose sum and product of zeroes

are - 3 and 2 respectively.

13. Evaluate sin600 +cos300

14. In the adj. figure find the value of ‘x’

15. Write the formula used to calculate the C.S.A of frustum of a

cone

16. Calculate the C.S.A of a hemisphere of radius 3 cm.


17. Areas of two similar triangles ABC and DEF, are 64cm2 and

121 cm2 , if EF = 15.4 cm, find the length of BC.

OR

ABCD is a trapezium in which AB || CD, diagonals BD and CD

intersects at O, then show that OD

CO

CO

AO

18. Solve 2x + y = 6 and 4x – 2y – 4 = 0

19. Construct two tangents to a circle of radius 5 cm, such that the

angle between the tangents is 600.

20. Find the distance between the points ( – 5 , 7 ) and ( - 3 , 3 )

21. Prove that 2 + 3 is irrational number

22. Solve 2x2 – 7x + 3 = 0 using formula method

23. If tan 2A = cot ( A – 180), where 2A is an acute angle, find ‘A’.

OR

Prove that A

A

A

A

cos

sin1

sin1

cos

= 2 secA

24. When a dice is thrown twice, what is the probability of getting a

number whose product is 12 ?


25. A fraction becomes 11

9 , if 2 is added to both the numerator and

the denominator if 3 is added to both the numerator and the

denominator it becomes 6

5 . Find the fraction.

OR

If we add 1 to the numerator and subtract 1 from the denominator a

fraction reduces to 1. it becomes 2

1 if we only add 1 to the denominator.

What is the fraction?

26. Divide 3x3 – x 2 + 2x + 5 by 1 +2x + x2

27. Sum of two numbers is 27 and their product is 182. Find the

numbers.

OR

The height of a right angled triangle is 11 cm longer than its shortest

sides. If the area of the triangle is 13 cm2. find the sides of the triangle

28. Find the area of a triangle whose vertices are ( 5, 2 ), ( 4, 7 ) and

( 7 , - 4 )

OR

If A ( - 5 , 7 ) , B ( - 4 , - 5 ) , c ( -1 , - 6 ) and D (4, 5 ) are the vertices

of a quadrilateral, find the area of the quadrilateral ABCD.

29. A survey conducted on 20 households on a locality by a group of

students resulted in the following frequency table for the number of

family members in a household, find the mode of this data

Family

Size 1-3 3-5 5-7 7-9 9-11

Number of

families 7 8 2 2 1

30. The following distribution gives the daily income of 50 workers

of a factory

Daily

income

( in Rs. )

100-120 120-140 140-160 160-180 180-200

Number of

workers 12 14 8 6 10

Convert the above distribution to a less than type cumulative frequency

distribution and draw its Ogive.

31. Prove that the “length of the tangents drawn to a circle from an


32. Construct a triangle similar to a given triangle ABC with its sides

equal to 4

3 of the corresponding sides of the triangle ABC.

33. Find the area of the shaded region in the adj. fig

where ABCD is a square of side 14 cm

OR

Find the area of the shaded region in the adj fig.

if ABCD is a square of side 14 cm and APD and

BPC are semicircles.

V. Solve the following 4 * 4 = 16

34. The pth , qth and rth term of an A.P are a, b, and c respectively,

then show that a ( q- r ) +b ( r – p ) +c ( p – q ) = 0

OR

The sum of 3rd and 7th term of an A.P is 6 and their product is 8, find

the sum of first 16 terms.


36. Prove that area of similar triangles are proportional to squares of

their corresponding sides.

37. From the top of a 7 m high building, the angle of elevation of top

of a cable tower is 600 and the angle of depression of its foot is 450.

determine the height of the tower.

VI. Solve the following 5* 1 = 5


angle is 600 is cut into two parts at the middle of its height by a plane

parallel to its base. If the frustum so obtained be drawn into a wire of

diameter 16





====================================================



1. If the H.C.F of 6 and 20 is 2, then their L.C.M is

A. 40 B. 120 C. 60 D. 240

2. The pair of linear equations 2x + 3y – 9 = 0 and 4x + 6y – 18 = 0 has

A. No solution B one solution C.

Only two solutions D. Many solutions

3. The common difference of the A.P 2

3 , 2

1 ,2

1 ,……. Is

A. -1 B. 2

1 C. 2

1 D. 3

2

4. The degree of the polynomial 4x3 – 2x2 + 3x5 – 4 is

A. 2 B. 3 C. 4 D. 5

5. The discriminent of the quadratic equation ax2 + bx + c = 0 is

A. b2 – ac B. b2 – 4ac C. acb 42 D. b2 +4ac

6. In the adj. fig. A quadrilateral ABCD is circumscribe a circle with AB

= 3 cm, and CD= 8 cm , then AD+BC= ---- cm

A. 11 B. 8 C. 3 D. 5

7. Area of a sector of angle ‘p’ of a circle of radius p is

A. 360

2pR B. 270

2pR C. 360

2Rp D. 270

2Rp

8. Formula used to calculate the C.S.A of frustum of a cone is

A. ( r1 +r2) l B. ( r1 +r2) h C. ( r1 - r2) l D. ( r1 - r2) h


9. State fundamental theorem of Arithmetic

10. If the nth term of an A.P is 3 + 2n, then find its fourth term

11. If SinA = 5

4 , then find cosecA

12. What is the probability of a sure event?

13. State Thale’s theorem

14. What is the sum of angles between tangent and radii of a

circle?

15. The angle subtended by the arc of a circle of radius ‘r’ units

is 900. Find the area of a sector.

16. Name the combination of solids of a petrol tanker.


17. Prove that 6 - 3 is a irrational number

18. Solve x – y = 26 and x – 3y = 0

19. Solve 3x2 – 5x +2 = 0 using suitable formula

20. Find he distance between the point ( 8 , 3 ) and ( 6 , - 2 )

21. A lot of 20 bulbs contain 4 defective ones. One bulb is drawn

at random from the lot. What is the probability that this bulb is

a. Defective b. Non defective?

22. In the adj fig, DE || BC, find AD .

OR

In the adj. fig , altitudes AD and CE of ABC

intersect each other at the point P . Show that AEP ~ CDP

23. Construct tangents to a circle of radius 3.5 cm such that the angle

between the tangents is 700.

24. From each corner of a square of side 4 cm a quadrant

of a circle of radius 1 cm is cut and also a circle of

diameter 2 cm is cut as shown in the figure. Find the area of the

remaining portion of the square.

OR

In the adj. fig OACB is a quadrant of a circle with centre O and

radius 3.5 cm. if OD = 2 cm find the area of the shaded region


25. Find the zeroes of the polynomial 6x2 – 3 – 7x and verify the

relationship between the co-coefficients and the zeroes

26. If the polynomial p ( x) = x2 – 3x2 +5x -3 is divided from

g ( x) = x 2 – 2, find the remainder and quotient and hence verify

Euclid’s division algorithm.

27. A train covers a distance of 360 km with uniform speed , if the

speed had been 5 km / hr more, it would have taken 1 hour less for the

same journey. Find the speed of the train.

OR

The perimeter of a rectangular field is 24 m and its area is 400 m2,

find length and breadth of the rectangular field.

28. Prove that

2

2

2

2

cot1

cot

tan1

tan

= 1

29. If A ( 6, 1 ) , B ( 8 , 2 ) , C ( 9 , 4 ) and D ( p , 3 ) are the vertices

of a parallelogram taken in an order, then find the value of ‘p’.

OR

Show that the points ( - 3 , 1 2 ) , ( 7 , 6 ) and ( 8 , 9 ) are collinear.

30. Draw the less than type Ogive for the following scores

Class

interval 0-3 3-6 6-9 9-12 12-15

Frequency 9 3 5 3 1

31. A class teacher has the following absentee record of 40 students

of a class for the whole term. Find the mean number of days a student

was absent.

Number

of days 0-5 5-10 10-15 15-20 20-25 25-30

Number

of

students

11 10 7 4 5 3

OR

Calculate mode for the following scores

Class

interval 1-3 3-5 5-7 7-9 9-11

Frequency 7 8 2 2 1

32. Prove that “the length of the tangents drawn from the external

point to the circle are equal”.

OR

In the adj fig TP and TQ are the tangents

drawn to the circle with centre O from an external point T.

Prove that OPQPTQ 2



2 of the corresponding sides of the

first triangle.

V. Solve the following 4 * 4 = 16

34. Solve x – 2y = 0 and x + y = 6 graphically

35. The first term and last term of an A.P are 17 and 350

respectively with the common difference 9. How many terms

are there in the A.P ? and also find the sum of the series.

36. Three numbers are in A.P whose sum is 27 and product is 648.

find the numbers

37. A vessel is in the form of a hollow hemisphere mounted by a

hollow cylinder. The diameter of the hemisphere is 14 cm and

the total height of the vessel is 13 cm. find the inner surface

area of he vessel

VI. Solve the following 5* 1 = 5

38. A tower stands vertically on a bank of a canal. From a point on

the other bank directly opposite to the tower, the angle of elevation of

the top of the tower is 600. from another point 20 m away from this

point on the line joining this point the foot of the tower is 300. find the

height to the tower and the width of this canal.

( use tan 580 = 1.6003)

Maths-Question-Paper.pdf - St. Francis High School

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