Cuboid Cube Cylinder Cone Sphere( surface area and volume) for class 9

Questions Bank Related to 

Surface Area of a Cuboid and a Cube
Surface Area of a Right Circular Cylinder
Surface Area of a Right Circular Cone
Surface Area of a Sphere
Volume of a Cuboid Volume of a Cylinder
Volume of a Right Circular Cone Volume of a Sphere

1. An underground water tank is in the shape of cube of side 7 m. What will be its volume?
2. What will be volume of a box whose length 16 m, breadth 8 m and height is 5 m?
3. The length, breadth and height of a room are 12 m, 10 m, and 9m respectively. Find the area of our walls of room?
4. The volume of a cube is 27a3 . Find the length of its edge?
5. How much Aluminium sheet will be required to make a container with lid whose length is 13 m, breadth is 8 m and height is 4 m?
6. The volume of a cube is 1331 cm3 . Find the length of its edge?
7. The length of diagonal of a cube is 17.32 cm. Find the volume of that cube?
8. Three cubes whose sides are 6 cm, 8 cm and 10 cm. They are melted and form a cube. Find the volume of that cube?
9. Two cubes have edge 10 m. Their edges have been joined and form a cuboid. What will be the surface area of cuboid thus formed?
10. The total volume of a cube is 512 cubic cm. Find the side of a cube?
11. A rectangular box 14 cm long, 10 cm wide and 5 cm high is to be made with card-board. Find the area of card-board to make that box?
12. What will be the volume of a cylindrical tank whose radius is 7 cm and height is 5 cm?
13. How many solid spheres of 2/3 cm radius can be made from a solid sphere of 2 cm radius?
14. If the volume and surface area of a sphere is numerically same then what will be its radius?
15. The volume of a right circular cylinder is 392 π cm3 and its height is 8 cm. Find the radius?
16. The surface area of a sphere is 448 p cm2 . Find its radius?
17. What will be the edge of a cube? If its surface area is 324 sq cm .
18. The volume of a hemisphere is 144 π cm³. What will be its radius?
19. The curved surface area of a cone is 140 π cm². What will be the radius of cone whose slant height is 5 cm.
20. The radius of a solid sphere is 12 cm. How many sphere can be made from it of 6cm radius?
21. The volume of a cuboid is 840 cm³. If its length is 14 cm and breadth is 5 cm. Find the height of cuboid?
22. Four equal cubes have side 5 cm each. They are joined together edge to edge. What will be the surface area of cuboid thus formed?
23. The area of a rhombus is 56 cm2 and its diagonal is 7 cm. Find the length of other diagonal of the rhombus?
24. Find the maximum length of the rod that can be kept in cyboidal box of sides 30cm, 24cm and 18cm.
25. The curved surface area of a cylinder is 216 π . If its height is 18 cm then what will be its radius?
26. 60 circular plates of equal radius are placed on each other to form a cylinder. Find height of cylinder if thickness of each plate if 3/4 cm.
27. Curved surface area of a cone is thrice and curved surface area of the other. Slant height of
second cone is thrice the slant height of first. Find ratio of their radii.
28. A well of 2m diameter is dug 14m deep on the ground. Find the volume of earth taken out.
29. Volume of a solid sphere is 36πcm³ . Find its radius.
30. A boy recasted a cone of 4cm height and 27cm radius into a solid sphere. Find the radiusof the sphere.
Surface Area And Volume (Chapter-11) Answers
1. 343m³ 2. 640m³ 3. 396m² 4. 3a 5. 376m² 6. 11cm 7. 1000cm³ 8. 1728cm³ 9. 1000m² 10. 8cm 11. 520cm² 12. 770cm²1 3. 2714. 3 units 15. 7cm 16. 112cm or 4 7cm 17. 9cm 18. 6cm1 9. 28cm 20. 8
21. 12cm 22. 450cm² 23. 16cm 24. √1800cm or 30 √2cm
25. 6cm 26. 45cm 27. 9:1 28. 44m³ 29. 3cm 30. 9cm

9th surface area and volume I Cuboid and a Cube I Cylinder I Cone

1. The curved surface area of a right circular cylinder of height 14 cm is 88cm2. Find the diameter of the base of the cylinder. 
2. Curved surface area of a right circular cylinder is 4.4m2. If the radius of the base of the cylinder is 0.7m, find its height. 
3. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.Find (i) the curved surface area and (ii) the total surface area of a hemisphere of radius 21 cm. 
4. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas. 
5. Find the radius of a sphere whose surface area is 154cm2. 
6. A matchbox measures 4cm x 2.5cm x 1.5cm. What will be the volume of a packet containing 12 such boxes? 
7. A cubical water tank is 6m long, 5m wide and 4.5m deep. How many liters of water can it hold? 
8. The capacity of a cubical tank is 50000 liters of water. Find the breadth of the tank, if its length and depth are respectively 2.3m and 10m. 
9. The height and the slant height of a cone are 21cm and 28 cm respectively. Find the volume of the cone. 
10. If the volume of a right circular cone of height 9cm is 48π cm3, find the radius of the base. (Use π=3.14)
11. A triangle ABC with sides 5cm, 12cm and 13cm cm is revolved about the side 12 cm. Find the volume of the solid so obtained. 
12. Find the volume of a sphere whose surface area is 154cm2. 
13. How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold? 
14. Find the amount of the water displaced by a solid spherical ball of diameter (i) 28cm (ii) 0.21m 
15. Find the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel wad actually used, if 1/12 th of the steel actually used was wasted in making the tank. Section B
16. A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine (in mm3) is needed to fill this capsule? 
17. A hemispherical tank is made up of an iron sheet 1cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank. 
18. The diameter of a metallic ball is 4.2cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm3? 
19. A conical pit of top diameter 3.5m is 12m deep. What is its capacity in kilolitres? 
20. The volume of a right circular cone is 9856 cm3. If the diameter of the base is 28cm, find (i) height of the cone (ii) Slant height of the cone. (iii) Curved surface area of the cone. 
21. A heap of the wheat is the form of a cone whose diameter is 10.5m and height is 3m. Find its volume. The heap is to be covered by congas to protect it from rain. Find the area of the canvas required. 
22. The circumference of the base of a cylindrical vessel is 132 cm and height is 25 cm. How many liters of water can it hold? 
23. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.\ 
24. A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute? 
25. A hemispherical bowl is made of steel, 0.25cm thick. The inner radius of the bowl is 5cm. Find the ratio of their surface areas. 
26. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of Rs. 12.50per m2. 
27. The floor of a rectangular hall has a perimeter 250m If the cost of painting the four walls at the rate of Rs 10per m2 is Rs 15000, find the height of the hall. Section C
28. Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much he would spend for the tiles, if the cost of the titles is Rs 360 per dozen. 
29. A plastics box 1.5 m long wide and 65 cm deep is to made. It is opened at the top. Ignoring the thickness of the plastics sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of the sheet for it, if a sheet measuring the box. 
30. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm, wide and 25 cm high. (i) What is the area of the glass? (ii) How much of tape is needed for all 12 edges? 
31. Savitri had to make a model of cylindrical kaleidoscope for her science project. She wanted to use chart paper to make the curved surface of the kaleidoscope. What would be the area of chart paper required by her, if she wanted to make a kaleidoscope of length 25cm with a 2.5 cm radius? (Use π=22/7) 
32. A metal pipe is 77 cm long. The inner diameter of a cross section is 4cm, the outer diameter being 4.4 cm. Find its (i) inner curved surface area. (ii) Outer curved surface area. (iii) Total surface area. 
33. In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system. 
34. The hollow sphere, in which the circus motorcyclist performs his stunts, has a diameter of 7m. Find the area available to the motorcyclist for riding. 
35. A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6m, find the cost of painting it, given the cost of painting is Rs 5 per 100cm2. 
36. A village, having a population of 4000, requires 150liters of water per head per day. It has measuring 20m x 15 x 6m. For how many days will the water of this tank last? 
37. It cost Rs. 2200 to paint the inner curved surface of a cylinder of a cylinder vessel 10 deep. If the cost of painting is at the rate of Rs 20per m2, find (i) inner curved surface area of the vessel. (ii) Radius of the base, (iii) Capacity of the vessel.

ASSIGNMENT AREAS RELATED TO CIRCLES CLASS X

ASSIGNMENT AREAS RELATED TO CIRCLES CLASS X AREAS RELATED TO CIRCLES CLASS X
1. The radius of the circle is 3 m. What is the circumference of another circle, whose area is 49 times that of the first?

2. Two circles touch externally. The sum of their areas is 130 p sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.

3. A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm² . If the same wire is bent in the form of a circle, find the area of the circle.

4. The area enclosed between the two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

5. A wheel of diameter 42 cm, makes 240 revolutions per minute. Find :

(i) the total distance covered by the wheel in one minute. (ii) the speed of the wheel in km/hr.

6. An arc of length 20pcm subtends an angle of 144° at the centre of the circle. Find radius of circle.

7. The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

8. In the given figure, the length of the minor arc is 7/24 of the circumference of the circle. Find : (i) <AOB

(ii) If it is given that the circumference of the circle is 132 cm, find the length of the minor arc AB and the radius of the circle.

9. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find :

(i) Area of the minor sector (ii) Area of the minor segment

(iii) Area of major sector (iv) Area of major segment ( use p = 3.14 )

10. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. [use p = 3.14, √3 = 1.73]

11. In the given figure, ABC is an equilateral triangle inscribed in a circle of radius 4 cm. Find the area of the shaded region.

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10th Mathematics test paper for Quadrilateral

1. Find the value of k for      kx² + 2x - 1 = 0, so that it has two equal roots

2. Find the value of k for    k x²   - 2√ 5 x + 4 = 0, so that it has two equal roots.

3. If the roots of the equation (b - c) x² + (c - c) x + (a - b) = 0 are equal, accordingly prove that 2b = a + c.

4. Find the discriminant of the quadratic equation 3x²– 4 √3 x + 4 = 0, and hence find the nature of its roots.

5. Find the value of k for       2 x² + k x + 3 = 0, so that it has two equal roots.

6. Find the value of k for     k x (x – 2) + 6 = 0, so that it has two equal roots.

7. Find the value of k for which the equation x² + 5kx + 16 = 0 has no real roots.

8 Find the discriminant of the quadratic equation 2x²– 6x + 3 = 0, and hence find the nature of its roots.

CBSE/NCERT 1Oth Maths Comprehensive Test chapter Probability

Q1. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it? (ii) She will not buy it?

Q2. An unbiased die is thrown. What is the probability of getting:
(i) an even number or a multiple of 3
(ii) an even number and multiple of 3
(iii) a number 3 or 4.

Q3. Two unbiased coins are tossed simultaneously. Find the probability of getting
(i) at least one head. (ii) at most one head. (iii) No head.

Q4. Three unbiased coins are tossed together. Find the probability of getting:
(i) all heads (ii) at least two heads

Q5. Two dice are thrown simultaneously. Find the probability of getting :
(i) the sum as a prime number
(ii) a total of at least 10
(iii) a doublet of even number
(iv) a multiple of 2 on one dice and a multiple of 3 on the other.

Q6. Find the probability that a leap year selected at random will contain 53 Sundays.

Q7. What is the probability that a number selected from the numbers 1,2,3…,25 is a prime number, when 
each of the given numbers is equally likely to be selected?

Q8. One card drawn from a pack of 52 cards, each of the 52 cards being equally likely to be to drawn. Find the probability that the card drawn is:
(i) an once (ii) red (iii) either red or king (iv) red and a king
(v) a face card (vi) a red face card (vii) ‘2’ of spades (viii) ‘10’ of a black suit

Q9. The king, queen and jack of clubs are removed from a deck of 52 playing cards and the well shuffled. One card is selected from the remaining cards. Find the probability of getting:
(i) a heart (ii) a king (iii) a club (iv) the ‘10’ of hearts.

Q10. A bag contains 5 red balls and some blue balls. If the probability of drawing blue ball is double that of a red ball, find the number of blue balls in the bag.

Q11. A contains 12 balls out of which x are white.
(i) If one ball is drawn at random, what is the probability that it will be a white ball?
(ii) If 6 more white balls are put in the bag, the probability of drawing a white ball will be double than that in (i). Find x.

Q12. Cards marked with the numbers 2 to 101 are placed in box and mixed thoroughly. One Card is drawn from this box. Find the probability that the number on the card is:
(i) an even number (ii) a number less than 14
(iii) a number which is a perfect square (iv) a prime number less than 20.

Q13. A letter is chosen at random from the letters of the word ‘ASSASSINATION’. Find the probability that the letter chosen is a (i) vowel (ii) consonant.

Q14. A jar contains 54 marbles each of which is blue, green or white. The probability of selecting a blue marble at random from the jar is 2/3, and the probability of selecting a green marble at random is . How many white marbles does the jar contain?

Q15. A number x is selected from the numbers 1,2,3 and then a second number randomly selected from the numbers 1,4,9. What is the probability that the product xy of the two numbers will beless than 9?

Q16. Tickets numbered from 1 to 20 are mixed up together and then a ticket is drown at random. What is the probability that the ticket has a number which is a multiple of 3 or 7.

Q17. It is known that a box of 600 electric bulbs contains 12 defective bulbs. One bulb is taken out at random from this box. What is the probability that it is a non-defective bulb?

Q18. 17 cards numbered 1,2,3…,17 are put in a box and mixed thoroughly. One person draws a card from the box. Find the probability that the number on the card is:
(i) odd ii) a prime (iii) divisible by 3 (iv) divisible by 3 and 2 both

Q19. A bag contains 5 red balls, 8 white balls, 4 green balls and 7 black balls. If one ball is drawn at
random, find the probability that it is:
(i) black (ii) red (iii) not green.

Q20. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e. three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Q21. If a number x is chosen at random from the numbers –2,-1,0,1,2. What is the probability that 2x<2?

Q22. A jar contains 24 marbles some are green are others are blue. If a marble is drawn at random from the jar, the probability that it is green is 2/3. Find the number of blue marbles in the jar.

Q23. A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is
(i) black king (ii) either a black card or a king
(iii) black and a king (iv) a jack, queen or a king
(v) neither a heart nor a king (vi) spade or an ace
(vii) neither an ace nor a king (viii) neither a red cad nor a queen
(ix) other than an ace (x) a ten
(xi) a spade (xii) a black card
(xiii) the seven of clubs (xiv) jack
(xv) the ace of spades (xvi) a queen
(xvii) a heart (xviii) a red card

Q24. In a lottery of 50 tickets numbered 1 to 50, one ticket is drawn. Find the probability that the drawn ticket bears a prime number.

Q25. In a lottery there are 10 prizes and 25 blanks. What is the probability of getting a prize?

CBSE/NCERT TEST PAPER MATHEMATICS (Class-10) Circle

I. Fill in the blanks. 

a. The word ‘tangent’ comes from the Latin word ------------ 

b. A tangent to a circle intersects it in ----------- point (s).

c. A line intersecting a circle in two points is called a --------

d. A circle can have -----------parallel tangents at the most.

e. The common point of a tangent to a circle and the circle is called ----------

2. Solve these questions (any five) 4X5=20

1. Prove that The tangent at any point of a circle is perpendicular to the radius through the point of contact

2. Prove that the lengths of tangents drawn from an external point to a circle are equal. 

3. Two tangents TP and TQ are drawn to a circle with centre O from an external point T.(see fig. 1) Prove that < PTQ = 2 < OPQ. 

4. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig. 2) Find the length TP. 

5. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. 

6. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre. 

7. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

8. A triangle PQR is drawn to circumscribe a circle of radius 4cm. The circle touches QR at D such that   QD = 6 cm and RD = 8 cm. Find PQ and PR.

9. The tangent at a point C of a circle and a diameter AB when extended intersect at P. If <PCA = 110⁰ , find < CBA.

10. In the figure. X.Y. are two parallel tangents to a circle with Center O and another tangent AB with point of contact C intersecting XY at A and X.Y. at B. Prove that <AOB = 90⁰.

CBSE TEST PAPER 10TH MATHEMATICS Distance and Sect...

CBSE TEST PAPER 10TH MATHEMATICS Distance and Sect...: 1. Calculate the distance between the points P(2, 2), Q(5, 4) correct to three significant figures. (Do not consult tables). 2. A is a ...

Cbse maths test paper class 10 Chap. Co-ordinate

ASSIGNMENT CLASS X Chap. Co-ordinate

Q1. Find the distance between the following points:

(a) A(3 , 5) and B(8 , – 7) (b)P( a + b , a – b ) and Q ( a– b , –a – b )
Q2. Find the value of x for which the distance between points A(x, 7) and B (–2, 3) is 4√5 units.
Q3. If the points (3, 2) and (2, –3) are equidistant from points (x, y) show that x + 5y = 0.
Q4. Show that the following points are collinear:

(a) (–5, 6), (–1, 2) and (2, –1)

(b) (4, 3) , (5,1 ) and (1, 9)

Q5. Show that following points are vertices of right triangle. Also, name the right angle.

(a)(4, 4) , ( 3 , 5) , (–1 ,1)

(b)(–2, 3) , ( 8, 3) , ( 6, 7)

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CBSE Class 10th maths ASSIGNMENT PROBABILITY

ASSIGNMENT PROBABILITYCLASS X

Q1. A coin is tossed. Find the probability that a head is obtained.

Q2. Find probability of throwing 5 with an ordinary dice.
Q3. Probability of winning a game is 0.4. What is the probability of loosing the game?
Q4. A person is known to hit the target in 3 shots out of 4 shots. Find the probability that the target is not hit.
Q5. Tickets numbered from 1 to 20 are mixed together and a ticket is drawn at random. What is the
probability that the ticket has a number which is multiple of 3 or 7?

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APPLICATION OF TRIGONOMETRY(Height and Distance) 1...

APPLICATION OF TRIGONOMETRY(Height and Distance) 10th Maths Test Papers

Q1 A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60°with the wall, find the height of the wall. (7.5 √3 )

Q 2 A pole 12 m high casts a shadow 4 √3 m long on the ground. Find the angle of elevation (60°)

Q 3 The angle of elevation of the top of a tower from a point on the ground is 30° if on walking 30m towards the tower, the angle of elevation becomes 60°.Find the height of the tower.(15√3 )

Q 4 An observer 1.5m tall is 20.5m away from a tower 22m high. Determine the angle of elevation of the top of the tower from the eye of the observer. (45°)

Q 5 An aero plane when flying at a height of 5000m from the ground passes vertically above another aero plane at an instant when the angles of the elevation of the two planes from the same point on the ground are 60° and 45° respectively. Find the vertical distance between the aero planes at the instant. (2116.5m)

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CBSE_NCERT Maths Test Paper-10th - Probability

1) The probability of a leap year selected at random contain 53 Sunday is:

(a) 53/ 366 (b) 1/7 (c) 2/7 (d) 53/365

2) A bag contains 3 red and 2 blue marbles. A marble is drawn at random. The probability of drawing a black ball is : (a) 3/5 (b) 2/5 (c) 0/5 (d) 1/5

3) The probability that it will rain tomorrow is 0.85. What is the probability that it will not rain

tomorrow

(a) 0.25 (b) 0.145 (c) 3/20 (d) none of these

4) What is the probability that a number selected from the numbers (1, 2, 3,..........,15) is a multiple of 4?

(a) 1/5 (b) 4/5 (c) 2/15 (d) 1/3

5) What are the total outcomes when we throw three coins?

(a) 4 (b) 5 (c) 8 (d) 7

6) The probability that a prime number selected at random from the numbers (1,2,3,..........35) is :

(a) 12/35 (b) 11/35 (c) 13/35 (d) none of these

7) The sum of the probability of an event and non event is :

(a) 2 (b) 1 (c) 0 (d) none of these.

8) The following probabilities are given; choose the correct answer for that which is not possible.

(a) 0.15 (b) 2/7 (c) 7/5 (d) none of these.

9) If three coins are tossed simultaneously, than the probability of getting at least two heads, is

(a) 1/4 (b) 3/8 (c) 1/2 (d) 1/8

10) A letter is chosen at random from the letters of the word “ASSASSINATION". The probability that the letter chosen has:

(a) 6/13 (b) 7/13 (c) 1 (d) none of these.

Answer Key: 1. a 2. c 3. c 4. a 5. c 6. b 7. b 8. c 9. c 10. b

11. A game of chance of a spnning wheel has number 1 to 10. What is the probability of getting a number less than to 5 when wheel comes to rest?

12. Two dice are rolled once what is the probability of getting a doublet?

13. A die is rolled once. What is the probability of getting a prime number?

14. A bank A.T.M. has notes of denomination 100, 500 and 1000 in equal numbers. What is the probability of getting a note of Rs. 1000.

15. What is the probability of getting a number greater than 6 in a single throw of a die.

16. A selection committee interviewed 50 people for the post of sales manager. Out of which 35 are
males and 15 are females. What is the probability of a female candidate being Selected.

17. A bag contains cards numbering from 5 to 25. One card is drawn fro the bag. Find the probability
that the card has numbers from 10 to 15.

18. In 1000 lottery tickets thre are 5 prize winning tickets. Find the probability of winning a prize. if a person buys one tickets.

19. It is known that in a box of 600 screws, 42 screws are defective. One screw is taken out at random from this box. Find the probability that it is not defective.

20. Write all the possible outcomes when a coin is tossed twice.

21. Two dice are rolled simultaneously. Find the probability that the sum is more than and equal to 10.

22. From the well shuffled pack of 52 cards. Two Black king and Two Red Aces are removed. What is the probability of getting a face card.

23. In a leap year what is the probability of 53 Sundays.

24. A box contains card numbered from 2 to 101. One card is drawn at random. What is the probability of getting a numer which is a perfect square.

25. A bag contains 5 red balls and ‘n’ green balls. If the P(green ball) = 3 × P (red ball) then what is the value of n.

10th Maths SA-2 Chapter wise Test Papers Links
Quadratic Equations	Circles	Co-ordinate Geometry
Arithmetic Progressions	Area Related to Circles	Probability
Height and Distance	Surface Areas and Volumes	Sample papers

CBSE Test Paper Ch -04 ( Co-Ordinate Geometry)

                                   CBSE TEST PAPER UNIT: 4 (coordinate geometry)                                                                                                            Section-A
Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2                            (B) 3                (C) 1                           (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                            (B) 8                (C) 4                           (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8                            (B) 2 √7          (C) 10                         (D) 6

4. The distance between the points (0, 5) and (–5, 0) is

(A) 5                           (B) 5√ 2          (C) 2 √5                      (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                            (B) 3                (C) √ 34                   (D) 4  

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the 
ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7) is equal, show that 3x = 2y.

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by  [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that   x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q. 

10th Maths SA-2 Chapter Links

Quadratic Equations

Arithmetic Progressions

Height and Distance

Co-ordinate Geometry

Circles

Area Related to Circles

Surface Areas and Volumes

Probability

CBSE TEST  PAPER UNIT: 4 (coordinate geometry)

Section-A

Choose the correct answer from the given four options:

1. The distance of the point P (2, 3) from the x-axis is

(A) 2                            (B) 3                (C) 1                           (D) 5

2. The distance between the points A (0, 6) and B (0, –2) is

(A) 6                            (B) 8                (C) 4                           (D) 2

3. The distance of the point P (–6, 8) from the origin is

(A) 8                            (B) 2 √7          (C)20         (C) 2 √5                      (D) 10

5. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is

(A) 5                            (B) 3                (C) √ 34                                  (D) 4

Section-B

1. Find the coordinates of the mid point of the line segment joining the points (4, 3) and (2, 1).

2. Find the coordinates of the point which divides the line segment joining the points (1, 3) and (2, 7) in the ratio 3: 4.

3. Show that the points (1, 1), (3, - 2) and (- 1, 4) are collinear.

4. Find the centroid of the triangle whose vertices are (3, - 5); (- 7, 4) and (10, - 2).

5. If the distance of the point P(x, y) from the points A (5, 1) and B (- 1, 5) is equal, show that 3x = 2y.

CBSE TEST   PAPER UNIT: 4 (coordinate geometry)

6. Find the area of a triangle whose vertices are A (1, 2); B (3, 5) and C (- 4, - 7)

7. In what ratio does the point P (- 4, 6) divide the line segment joining the points A (- 6, 10) and B (3, - 8).

8. For what value of m, the points (4, 3), (m, 1) and (1, 9) are collinear.

9. Prove that the coordinates of the centroid of a triangle ABC with vertices A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are given by  [(x₁+x₂+x₃)/3] , [ )y₁+y₂+y₃)/3]

10. Prove that the diagonals of a rectangle bisect each other and are of equal length

11. Find the coordinates of the points Q and R on medians BE and CF respectively such that BQ: QE = 2: 1 and CR: RF = 2: 1.

12. In what ratio does the line 4x + y = 11 divide the line segment joining the points (1, 3) and (2, 7).

13. PQRS is a square of side .b. units. If P lies at the origin, sides PQ and PS lie along x - axis and y - axis respectively, find the coordinates of the vertices of the square PQRS.

14. If the points (5, 4) and (x, y) are equidistant from the point (4, 5); then show that   x² + y² - 8x -10y + 39 = 0

15. The line segment joining the points (3, - 4) and (1, 2) is trisected at the points P and Q. If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, Find the value of p and q.

CBSE Test Paper Chapter 4 : Quadratic Equations

CBSE TEST PAPER MATHEMATICS (Class-10)Chapter 4 : Quadratic Equations

1. Find the value of k for  kx² + 2x - 1 = 0, so that it has two equal roots

2. Find the value of k for  k x²   - 2√ 5 x + 4 = 0, so that it has two equal roots.

3. If the roots of the equation (b - c) x² + (c - c) x + (a - b) = 0 are equal, accordingly prove that
2b = a + c.

4. Find the discriminant of the quadratic equation 3x²– 4 √3 x + 4 = 0, and hence find the nature of its roots.

5. Find the value of k for  2 x² + k x + 3 = 0, so that it has two equal roots.

6. Find the value of k for     k x (x – 2) + 6 = 0, so that it has two equal roots.

7. Find the value of k for which the equation x² + 5kx + 16 = 0 has no real roots.

8 Find the discriminant of the quadratic equation 2x²– 6x + 3 = 0, and hence find the nature of its roots.

9. Find the value of k for   k² x² –  2 (2 k - 1) x + 4 = 0, so that it has two equal roots.

10. Find the value of k for (k + 1) x²  – 2 ( k - 1) x + 1= 0, so that it has two equal roots.

11. Determine the positive value of k for which the equation x² + k x + 64 + 0 and x² – 8x + k = 0 will both have real roots.

12. Find the discriminant of the quadratic equation 2x² – 3 x + 5 = 0, and hence find the nature of its roots.

13. Find the value of k for x² – 2(k + 10x + k² ) = 0, so that it has two equal roots.
14. If - 4 is a root of the quadratic equation x² + px–4=0 and the quadratic equation x²+ px +k=0 has equal roots, find the value of k.

15. Find the discriminant of the quadratic equation 2x² – 4x + 3 = 0, and hence find the nature of its roots.

16. The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.


17. In a class test, the sum of Amit’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 Marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

18. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

19. A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

20. Two water taps together can fill a tank in 9 ³/₈  hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.