10th maths Test paper Co-Ordinate Geometry

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 point on the y-axis whose ordinate is 5 and B is the point (-3, 1). Calculate the length of AB.

3. The distance between A(1, 3) and B(x, 7) is 5. Find the possible values of x.

4. P and Q have co-ordinates (-1, 2) and (6, 3) respectively. Reflect P in the x-axis to P'. Find the length

of the segment P'Q.

5. Point A(2, -4) is reflected in the origin as A'. Point B(-3, 2) is reflected in x-axis at B'. Write the co-ordinates of A' and B'. Calculate the distance A'B' correct to one decimal place.

6. The center of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

7. A and B have co-ordinates (4, 3) and (0, 1) respectively. Find (i) the image A' of A under reflection in the y-axis.

(ii) the image B' of B under reflection in the line AA'.

(iii) the length of A'B'.

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CBSE ADDA: CBSE TEST PAPER 10TH MATHEMATICS ...

Assignments class 10 Chapter 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)

Q6. Show that following points are vertices of a rectangle:
(a) (2 , –2) , ( 8, 4) , ( 5, 7 ) , (– 1, 1)
b)(–4 , –1) , (–2 , 4) , ( 4, 0 ) , ( 2, 3 )

Q7. Show that following points are vertices of a square:
a) ( 0 , –1) , ( 2, 1) , ( 0, 3) , (–2, 1)
(b)( 0, 1) , ( 1, 4) , ( 4,3) , ( 3, 0)

Q8. Show that following points are vertices of rhombus:

(a) ( 0, 5 ) , (–2, –2 ) , ( 5 , 0 ) , ( 7, 7 ) (b ) ( 2, –1) , ( 3, 4) , (–-2, 3) , (–3 , –2)

Q9. Show that the points ( a, a ) , (–a, –a ) and (–√3 a , √3 a) form an equilateral triangle.

Q10. Find the co-ordinates of circumcenter of a ∆ ABC where A( 1, 2) ,B ( 3, –4) and C ( 5, –6 ).

Q11. Find radius of the circle, the co-ordinates of the ends of whose diameter are (–1, 2) and (3, –4 ).

Q12. (a) Find the point on x-axis, which is equidistant from points ( 7, 6 ) and ( 9 , 4 ).

(b)Find the point on y-axis, which is equidistant from points ( 5, 2 ) and (–4 , 3 ).

Q13. A point P is at a distance of√10 from the point ( 4, 3). Find the co-ordinates of P, if its ordinate is twice its abscissa.

Q14. A line of length 10 units has (–-2, 3) as one of its end points. If the ordinate of the other end be 9, Show that its abscissa is 6 or–10.

Q15. The opposite angular points of a square be ( 3, 4 ) and ( 1, –1). Find the co-ordinates of the remaining angular points.

Answers

Ans 1 . (a) 13, (b) 2 √a² + b²

Ans 2. 6 or – 10

Ans 10. (11, 2)

Ans11.√13

Ans12. (a) (3, 0)(b ) (0, 15)

Ans13. (3, 6)

Ans15. (9/2, 1/2) and (–1/2 , 5/2 )

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?

Q6. A bag contains 100 identical tokens, on which numbers 1 to 100 are marked. A token is drawn at random. What is the probability that the number on the token is:
(a) an even number
(b) an odd number
(c) a multiple of 3
(d) a multiple of 5
(f) a multiple of 3 and 5
(g) a multiple of 3 or 5
(h) a number less than 20
(i) a number greater than 70(j) a perfect square number(k) a prime number less than 20.

Q7. A card is drawn from a well-shuffled pack of cards. Find the probability that the card drawn is:
(a) a queen
(b) a king bearing diamond sign
(c) a black card
(d) a jack
(e) black and a queen
(f) either black or a queen
(g) a red card
(h) a face card
(i) a diamond or a club
(j) neither heart nor a jack
(k) a 2 of diamond
(l) an ace of hearts
(m) a face card of red color
(n) 10 of a black “suit”

Q8. In a simultaneous toss of two coins, find:
(a) P(2 tails)
(b) P(exactly one tail)
(c) P(no tails)
(d) P(at most one head)
(e) P(one head)

Q9. A coin is tossed successively three times. Find probability of getting exactly one head or two heads.

Q10. Three coins are tossed once. Find probability of: 

(a) 3 heads
(b) exactly 2 heads
(c) atleast 2 heads
(d) atmost 2 heads
(e) no tails
(f) head and tail appear alternatively
(g) atleast one head and one tail

Q11. A dice is thrown once. Find:
(a) P(number 5)
(b) P(number 7)
(c) P(an even number)
(d) P( a number greater than 4)
(e) P( a number less than or equal to 4)
(f) P(a prime number)

Q12. A bag contains 10 white, 6 black and 4 red balls. Find probability of getting:
(a) a white ball
(b) a black ball
(c) not a red ball
(d) a white or a red ball

Q13. Two dice are thrown simultaneously. Find:
(a) P(an odd number as a sum)
(b) P(sum as a prime number)
(c) P(a doublet of odd numbers)
(d) P(a total of atleast 9)
(e) P( a multiple of 2 on one die and a multiple of 3 on other die)
(f) P(a doublet)
(g) P(a multiple of 2 as sum)
(h) P(getting the sum 9)
(i) P(getting a sum greater than 12)
(j) P( a prime number on each die)
(k) P( a multiple of 5 as a sum)

Q14. Find the probability that a leap year at random contains 53 Sundays.

Q15. Two black kings and two black jacks are removed from a pack of 52 cards. Find the probability of getting:
(a) a card of hearts
(b) a black card
(c) either a red card or a king
(d) a red king
(e) neither an ace nor a king
(f) a jack, queen or a king 

Ans
(1)1/2	(2)1/6	(3)0.6	(4)1/4	(5)2
(6) (a)1/2	(b)1/2	(c)33/100	(d)1 /5	(e) 3/50	( f) 47/100
( g) 19/100	(h ) 3/10	(7) (a) 1/13	(b) 1/52	( c) ½	( d) 1/13
( e) 1/26	( f) 7/13	( g)1/2	(h) 4/13	(i) ½	(j) 9/13
( k) 1/52	(l) 1/52	(m) 3/26	(n) 1/26	(8) (a) ¼	(b) ½
( c) ¼	(d)3/5	(e) ½	(9) ¾	(10) (a) 1/8	(b) 3/8
( c) ½	(d ) 7/8	( e) 1/8	( f) ¼	( g) ¾	(11) (a)1/6
(b) 0	( c) ½	(d) 1/3	( e)2/3	( f) 1/2	(12) (a) ½
(b) 3/10	( c) 4/5	( d) 7/10	(13) (a) ½	( b)5/12	( c) 1/12
( d) 5/18	( e) 11/36	( f) 1/6	( g) ½	(h ) 1/9	( i) 0
( j) 1/12	( k) 7/36	(14) 2/7	( 15)