10th maths Assignments 2011-12 term-II-DPS -Bokaro

Class: X Subject : Mathematics Assignments
QUADRATIC EQUATIONS,ARITHMETIC PROGRESSION,CIRCLES,CONSTRUCTIONS
AREAS RELATED TO CIRCLES,TOPIC- SURFACE AREA AND VOLUME,TOPIC : COORDINATE GEOMETRY,HEIGHTS AND DISTANCES,TOPIC – PROBABILITY

1. A circular wheel make 420 rounds per minute with a speed of 55.44 km/hr. Find the radius of the
wheel.
2. Find the radius of a circle, if an arc of angle 1200 has length of 24 cm. Also, find the area of the
sector formed by this arc.
3. A wire is bent in the form of a circle of area 3850 sq cm. If the same wire is bent in the form of a
rectangle of length 65cm, find the area of the rectangle formed.
4. A chord of a circle subtends an angle of 1200 at the centre. Find the area of the corresponding
segment of the circle whose radius is 12cm. ( use p  = 3.14, Ö3 = 1.73 )
5. The minute hand of a clock is 10cm long. Find the area on the face of the clock described by the
minute hand between 9a.m and 9.35a.m.
6. A car has two wipers which do not overlap. Each wiper has a blade of length 25cm sweeping
through an angle of 1150. Find the total area cleaned at each sweep of the blades.
X Science Assignments 2011-12_term-II_DPS-Bokaro_steel_city
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10th_maths Assignments 2011-12_  term-II-DPS -Bokaro_steel_city
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CBSE ADDA: X Arithmetic progression assignment

Q. 1 How many terms of A.P. 22, 20, 18, . . . . . . . . should be taken so that their sum is zero?
Q. 2 Find the sum of odd positive integers less than 199. 
Q. 3 How many two digits numbers between 3 and 102 are divisible by 6? 
Q. 4 If 7 times the 7th term is equal to 11 times the 11th term of an A.P. Find its 18th term. 
Q. 5 Which term of A.P. 13, 21, 29, . . . . . . will be 48 less than its 19th term? 
Q. 6 Find the A.P. whose 3rd term is –13 and 6th term is +2. 
Q. 7 Find the A.P., whose 5th term is 23 and 9th term is 43. 
Q. 8 The angles of a triangle are in A.P. If the smallest angle is one fifth the sum of other two angles. Find the angles. 
Q. 9 Aditi saved Rs. 500 in the first month of a year and then increased her monthly savings by Rs. 50. If in the nth month, her monthly savings become Rs 1000. Find the value of 'n'. 
Q. 10 The sum of first n terms of an A.P. is 2n2 + n . Find nth term and common deference of the A.P. 
Q. 11 The sum of 3rd and 7th terms of an A.P. is 14 and the sum of 5th and 9th terms is 34. Find the first term and common difference of the A.P. 
Q. 12. Find the sum of the first 30 terms of an A.P., whose nth term is 2–3n. If mth and nth terms of an A.P. are 1/n and1/m respectively, then find the sum of mn terms 
Q. 13 If mth , nth and rth terms of an A.P. are x, y and z respectively, then prove that :- m( y – z) + n(z – x) + r (x – y) = 0 
Q. 14. If the roots of the equation a(b – c) x2 + b(c – a) x + c (a – b) = 0 are equal, then show that 1/a , 1/b , 1/c are in A.P. 
Q. 15. If the sum of m terms of an A.P. is n and the sum of n terms is m, then show that sum of (m +n) terms is – ( m + n).

CBSE MATH STUDY: X Arithmetic progression assignment:(For next set of 20 Questions)

CBSE X Maths Constructions

Construction of a tangent to a circle (using the centre)
We remember that: In a circle, the radius drawn at the point of contact is perpendicular to the tangent at
that point.
Q. Draw a circle of radius 3.2 cm. Take a point P on this circle and draw a tangent at P.(using the centre)   Given: Radius of the circle = 3.2 cm.

Steps of construction

(i) With O as the centre draw a circle of radius 3.2 cm.
(ii) Take a point P on the circle and join OP.
(iii) Draw an arc of a circle with centre at P cutting OP at L.
(iv) Mark M and N on the arc such that m(arc L M ) = m(arcMN)
(v) Draw the bisector PT of the angle <MPN
(vi) Produce TP to Tlto get the required tangent T'PT.
Construction of pair of tangents to a circle from an external point

We remember that:

(i) Two tangents can be drawn to a circle from an external point.
(ii) Diameters subtend 90 degree on the circumference of a circle.

Q. Draw a circle of radius 3 cm. From an external point 7 cm away from its centre, construct
the pair of tangents to the circle and measure their lengths.
Given: Radius of the circle = 3 cm. OP = 7 cm.
Construction Steps:
(i) With O as the centre draw a circle of radius 3 cm.
(ii) Mark a point P at a distance of 7 cm from O and join OP.
(iii) Draw the perpendicular bisector of OP. Let it meet OP at M.
(iv) With M as centre and MO as radius, draw another circle.
(v) Let the two circles intersect at T and Tl.
(vi) Join PT and PT'. They are the required tangents.
Length of the tangent, PT = 6.3 cm
Q. Draw a line segment of length 7 cm and divide it in the ratio 2 : 3.
Solution. Step of constructions :
1. Draw AB = 7 cm
2. Draw ray AX making a suitable acute angle with AB.
3. Cut 2 + 3 = 5 equal segments AA1, A1A2, A2A3, A3A4 and A4A5 on AX.
4. Join A5 with B.

5. Through A2 ,Draw A2P parallel to A5B by making corresponding angles AA2P and AA5B
equal.
6. The line through A2 and parallel to A5B will meet the given line segment at point P.
Then P is the required point which divides AB in the ratio 2 : 3 i.e. AP : PB = 2 : 3
Q. Construct a triangle similar to a given triangle with sides 7 cm, 9 cm and 10 cm and whose sides are 5/7 th of the corresponding sides of the given triangle.
Solution.
Steps of Constructions :
1. With the given measurements construct the triangle ABC in which AB = 7 cm, BC = 9 cm andAC = 10 cm
2. Draw a ray AP, making any suitable angle with AB and on opposite side of vertex C
3. Starting from A, cut off seven equal line-segments AX1, X1X2, X2X3, X3X4, X4X5, X5X6 and X6X7 on AP.
4. Join BX1 and draw a line X5B' parallel to X7B which meets AB at B'.
5. Through B', draw B'C' || BC which meets AC at point C'.

The DAB'C', so obtained, is similar to the given D ABC and each side of DAB'C' is 5/7 times the corresponding side of D ABC.

Q. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given
triangle.
Solution.
 Step of Constructions :
1. Draw BC = 4 cm
2. At B, draw a ray BP making angle 90° with BC i.e. <PBC = 90°
3. From BP, cut BA = 3 cm
4. Join A and C to get the given DABC
5. Through vertex B, draw ray BX making any suitable angle with BC.
6. On BX cut 5 equal line segments BB1 = B1B2 = B2B3 = B3B4 = B4B5.
7. Join B3 to C. 

8. Through B5, draw a line parallel to B3C to meet BC produced at point C'.
9. Through C', draw a line parallel to side CA to meet BA produced to A'.

D A'BC' is the required triangle

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CBSE Ch:Probability X Mathematics Assignments

 X Mathematics Assignments Chapter: probability

Directions for 1 – 4: State true or false

1. If the probability of a candidate winning an election is 80%, then the probability of the opponent winning the election is also 80%.

2. If two dice are thrown simultaneously then the total number of outcomes is 12.

3. A throws a coin twice and ‘B’ throws a similar coin thrice, the possibility of getting ‘all heads’ is more for ‘B’ than ‘A’.

4. The sum of the probability of an event happening and the same not happening is always the same.

1. F                2. F                3. F                            4. F

5. An unbiased die is thrown. What is the probability of getting?

(i) an even number?  (ii) a multiple of 5? (iii) an even number or a multiple of 3? (iv) a multiple of 2 and 3?

6. Two unbiased coins are tossed simultaneously. What is the probability of getting(i) all heads? (ii) at least one head?  (iii) at the most one tail? (iv) at least one head and one tail?

7. Two dice are thrown simultaneously. What is the probability of getting?

(i) an odd number as the sum? (ii) a total of at least 10? (iii) the same number on both dice? (iv) a sum greater then 10?

8. Find that the probability of a leap year selected at random will contain 53 Mondays.

9. One card is drawn from a pack of 52 cards. What is the probability of getting

(i) an ace or a king? (ii) a red card and a king? (iii) a face card? (iv) a king or a queen or a jack?

10. All the face cards are removed from a pack of 52 cards and are then shuffled well. One card is selected from the remaining cards. What is the probability of

(i) getting an ace? (ii) getting a red card? (iii) getting 10 of spade? (iv) getting a number less than 5?

11. A bag contains five red balls and some white balls. If the probability of drawing a white ball is double that of a red ball, find the number of white balls in the bag.

12. A bag contains 20 balls out of which ‘x’ are red.

(i) If one ball is drawn at random, what is the probability that it will not be a white ball?

(ii) If five more red balls are added, the probability of drawing a red ball will become 40%. Find the number of balls which are not red.

13. 1000 tickets of a lottery were sold and there are three prizes in the lottery. If Sachin has purchased one ticket, what is the probability of his winning a prize?

14. 26 cards marked with English letters A to Z (one letter on each card) are shuffled well. If one card is selected at random, what is the probability of getting?

(i) a vowel?    (ii) a letter in the word PROBABILITY?

50 Mohan and Salim are friends. What is the probability that both will have

(i) the same birthday?     (ii) different birthdays?

(iii) their birthday on the same weekday?

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

52. What is the probability that a number selected at random from the numbers 10, 20, 20, 30, 30, 30, 40, 40, 40, 40 will be their mean?

16. A game consists of tossing a coin three times and noting the outcome each time. If one gets the same outcome in all the three tosses, then he wins. What is the probability of a participant winning the game?

16. While shuffling a pack of 52 cards, Khushi dropped one card by mistake. What is the probability of the dropped card being a red queen?

17. A die is numbered in such a way that its faces show the numbers 1,2,2, 3, 3, 6. It is thrown twice and the total score in two throws is noted. Find the sample space of the experiment. What is the probability that the total score  (i) is even?  (ii) is odd? (iii) is at least 5?

18. A circle of diameter 7 cm is drawn inside A rectangle of dimensions 15 cm × 7 cm . If a coin is dropped randomly inside the rectangle, what is the probability that the coin lands inside the  circle?

19. A piggy bank contains one hundred 50 p coins, fifty Re 1 coins, twenty Re 2 coins and ten Re 5 coins. If it is turned upside down one coin will fall. When Gautam turned it up side down for the first time, he got a Rs 2 coin. If he turns it upside down for a second time, what is the probability of getting

(i) an amount more than Re 1? (ii) a Rs 5 coin?(iii) a 50 p coin or Re 1 coin? (iv) at least one rupee?

20. In a game, Raju asks his friend Karan to write down a two-digit number secretly. What is the probability that Karan will write a doublet? What is the probability that Karan’s number is divisible by 2, 3 and 5?

21. Two customers, Mohan and Nishu are visiting a shop in the same week (Sunday to Saturday). Each is likely to visit the shop on any day as on any other day. What is the probability that both will visit the shop on (i) the same day? (ii) Consecutive days?