Mathematics Holiday Homework

(Do 4-5 questions daily)

Chapter 7: Coordinate Geometry
Distance formula
Q1. The coordinate of a general point on x-axis is of the form:
(a) (x, 0) (b) (0, x) (c) (x, y) (d) None of these

Q2. The distance between the points (3, 7) and (8, 9) is:
(a) 11 units (b) 12 units (c) 29 units (d) Can’t be found

Q3. The point on the x-axis which is equidistant from (2, –5) and (–2, 9) is:
(a) (–7, 0) (b) (–5, 0) (c) (–6, 0) (d) (–7, 1)

Q4. If ‘a’ is any positive integer such that the distance between the points P(a, 2) and Q(3, –6) is 10 units, then
the value of ‘a’ is:
(a) –3 (b) 6 (c) 9 (d) 3

Q5. The distance between ( tan , 0) and (0, 1) is:

(a) 2 sec  (b) 2 cot  (c) sec (d) cot 

Q6. The distance of the point (2, 3) from the x-axis is:
(a) 2 units (b) 3 units (c) 4 units (d) 5 units

Q7. The distance of (–6, 8) from the origin is:

(a) 8 units (b) 27 units (c) 10 units (d) 6 units

Q8. The values of y for which the distance between the points P(2, –3) and Q(10, y) is 10 units, is:
(a) –9, 5 (b) –9, 3 (c) –9, 2 (d) –9, 6

Q9. The distance between the points A(b, 0) and B(0, a) is:
(a) a 2 + b2 (b) a 2 − b2 (c) a+b (d) a −b

Application of distance formula

Q10. The perimeter of the triangle formed by the points (0, 0), (2, 0), and (0, 2) is:
(a) 4 units (b) 6 units (c) 6 2 units (d) 4 + 2 2 units

Q11. What type of triangle do the points (3, 2), (–2, –3), and (2, 3) form?
(a) right triangle (b) equilateral triangle (c) isosceles triangle (d) None of these

Q12. Name the quadrilateral formed by the following points:

a) (4,5),(7,6), (4,3), (1,2)
b) (-1,-4), (0,3), (3,1), (-3,5)
c) (-1,2), (-3,0), )-1,-2), (1,0)

Q13. AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). Square of the length of its diagonal
is:
(a) 5 (b) 3 (c) 34 (d) 4

Q14. The points (–4, 0), (4, 0), and (0, 3) are the vertices of a/an:
(a) Right triangle (b) Isosceles triangle (c) Equilateral triangle (d) Scalene triangle

Q15. The endpoints of the diameter of the circle are (2, 4) and (–3, –1). Find its radius.
Section formula
Finding the coordinates:
Q1. Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3 internally.
Q2. Find the coordinates of the point which divides the join of (8,5) and (4,-3) in the ratio 3:1 internally.
Q3. Find the coordinates of the points of trisection of the line segment joining (-2,3) and (4,-1).
Q4. Find the coordinates of the points of trisection of the line segment joining (2,-2) and (-7,4).
Q5. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1:2 internally lies in the:
(a) I quadrant (b) II quadrant (c) III quadrant (d) IV quadrant
Finding the ratio:
Q6. Find the ratio in which the point (-1,6) divides the line segment joining the points (-3,10) and (6,-8).
Q7. In what ratio is the segment joining the points A(6, 3) and B(–2, –5) divided by the x-axis?
(a) 3:2 (b) 3:5 (c) 2:3 (d) 2:5
Q8. The ratio in which the line joining the points (5, 3) and (–1, 6) is divided by the y-axis is:
(a) 5:3 (b) 2:3 (c) 4:5 (d) 5:1
Also, find the coordinates of points of division.
Q9. The ratio in which the x-axis divides the line segment joining the points (5, 4) and (2, –3) is:
(a) 5:2 (b) 3:4 (c) 2:5 (d) 4:3
Also, find the coordinates of points of division.
Application of Mid-point formula
Q10. Find the mid-point of the line segment joining the points (2,7) and (-2,7).
Q11. Find the coordinates of a point A, where AB is the diameter of a circle whose center is (4,-3) and (2,4).
Q12. The fourth vertex D of a parallelogram ABCD whose three vertices are A(–2, 3), B(6, 7) and C(8, 3) is:
(a) (0, 1) (b) (0, –1) (c) (–1, 0) (d) (1, 0)
Q13. If the points A(6, 1), B(8, 2), C(9, 4), and D(p, 3) are vertices of a parallelogram, taken in order, then the value of p
is:
(a) 7 (b) 9 (c) 5 (d) 8
Q14. If A and B are (-2,-2) and (2,-4) respectively, find the coordinates of P such that 7AP = 3AB and P lies on the line
segment AB.
15. Case study-based question:

Q1. Taking A as the origin, write the coordinates of the vertices of triangle PQR.

Q2. Find the mid-point of the side PQ.

Q3. Taking C as the origin, write the coordinates of the vertices of triangle PQR.
 Chapter-14: Statistics

Q1. The median and mode respectively of a frequency

distribution are 26 and 29, Then its mean is
(a) 27.5 (b) 24.5
(c) 28.4 (d) 25.8
Q2. Find the median of the data, using an empirical
relation when it is given that Mode = 12.4 and Mean = Q10. Find the mean, median, and mode of the following
10.5. frequency distribution:
Q3. Find the mode of the following data :

Q4. Find the median for the given frequency distribution Q11. Find the mean of the following distribution by step
: deviation method.

Q5. Find the mean of the following data :

Q12. Find the mean, mode, and median for the following
data :

Q6. The arithmetic mean of the following frequency

distribution is 53. Find the value of k. Q 13. Find the mean, median, and mode of the following
data:

Q7. The mean of the following distribution is 18. Find the

frequency of the class 19-21. Q14. Find the median of the following data:

Q8. The median of the following data is 525. Find the Q 15. If the median of the following frequency distribution
values of x and y if the total frequency is 100. is 32.5. Find the values of f1 and f2.

Q9. The mode of the following frequency distribution is

36. Find the missing frequency f.
 Chapter 15: Probability
Q1. If an event cannot occur, then its probability is Q12. The sum of the probabilities of all the elementary
(a) 1 (b) 4/3 (c) 2/1 (d) 0 events of an experiment is ______________.
Q2. Which of the following cannot be the probability
of an event? Q13. One card is drawn from a well-shuffled deck of 52
cards. Find the probability of getting
(a) 1/3 (b) 0.1 (c) 3% (d) 17/16
(a) an ace card (b) a jack, queen, or a king
(c) neither a red card nor a queen card
Q3. If the probability of an event is p, then the
(d) a face card
probability of its complementary event will be
(e) a black suit card
1
(a) p - 1 (b) p (c) 1 - p (d) 1 −
p Q13. Two dice are thrown simultaneously. Find the
probability of getting:
Q4. The P(A) denotes the probability of an event A, (a) Sum of outcome 9
then (b) Sum of outcome 11
(a) P(A) < 0 (b) P(A) > 1 (c) Difference of outcome 5
(c) 0  P ( A)  1 (d) −1  P ( A)  1 (d) Difference of outcome zero
(e) Multiplication of outcome 5
Q5. Two coins are tossed simultaneously. Find the
Q14. Three coins are tossed simultaneously. Find the
probability of getting:
probability of getting:
a) Atleast one head c) 1 head and 1 tail
b) Atmost 1 head d) Both head a) Two tails and one head
b) Same outcome in all three coins
Q6. Out of one-digit prime numbers, one number is c) Atmost one head
selected at random. Find the probability of selecting d) Atleast two tails
an even number. e) Atmost two tails

Q7. When a die is thrown, the probability of getting an Q15. Cards marked with numbers 1, 2, 3…….50 are
odd number less than 3 is ______. placed in the box and mixed thoroughly. One card is
drawn at random from the box. What is the probability of
getting?
Q8. If P(E) = 0.06, then what is the probability of ‘not E’? (a) a perfect square number
(a) 0.94 (b) 0.95 (c) 0.89 (b) a number divisible by 2 and 3.
(d) 0.90 (c ) a number divisible by 7.
(d) a two-digit number divisible by 4
Q9. If two dice are thrown in the air, the probability of (e) a perfect cube number.
getting a sum of 12 will be:
(a) 2/18 (b) 3/18 (c) 3/18 (d) 1/36

Q10. The probability of getting a fused bulb in a lot of 400

is 0.035. The number of fuse bulbs in the lot is:
(a) 7 (b) 14 (c) 21 (d) 28

Q11. Two players, Ravi and Sanjay, play a tennis match. It

is known that the probability of Ravi winning the match is
0.62. The probability of Sanjay winning the match is
__________.
 Chapter 1: Real Numbers
Q1. Prove that the following are irrational numbers:
1
a) 2 b) 3 c) 5 d) 2 −3 e) 10 − 3 3 f) g) 3 7
5
Q2. Find the HCF and LCM of the following and verify that HCF x LCM= Product of the two numbers.
a) 26 and 91 b) 100 and 190 c) 15, 18 and 45

Q3. What is the H.C.F. of the smallest composite number and smallest prime number?
Q4. Three bells ring at intervals of 4, 7, and 14 minutes. All three rang at 6 AM. When will they ring together
again?
Q5. If LCM (x, 18) = 36 and HCF(x, 18) =2. Find x.
Q6. Given that L.C.M (26, 169) =338, find H.C.F (26,169).

Each of the following examples contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has the
following four choices (a), (b), (c), and (d), only one of which is the correct answer. Mark the correct answer.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.

Q7. Statement-1 (Assertion): If HCF (90, 144) = 18, then LCM (90, 144) = 720.
Statement-2 (Reason): HCF (a, b) x LCM (a, b) = a x b.
Q8.Statement-1 (Assertion): If LCM (60, 72) = 360, then HCF (60, 72) = 12.
Statement-2 (Reason): HCF (a, b) x LCM (a, b) = a + b.

Q9. Justify whether 5× 3 × 11+ 11 and 5 × 7 +7 × 3 + 3 are composite numbers.

Q10. Explain why 7x11x13+13 and 7x6x5x4x3x2x1+5 are composite numbers.
Q11.Four different electronic devices make a beep after every 30 minutes, 1 hour, 1 hour 30 min, and 1 hour 45
min respectively. All the devices beeped together at 12 pm. At what time will they beep again together?
Q12.Check whether 6n can end with the digit 0 for any natural number n.
Q13. Show that any natural number n,12𝑛 can not end with the digit 0 or 5.
Q14. A sweet seller has 420 kaju barfi and 130 badam barfis. She wants to stack them in such a way that each
stack has the same number and takes up the least area of the tray. What is the number of barfis that can be placed
in each stack for this purpose?

Q15. Three bells toll at intervals of 9, 12, and 15 minutes respectively. If they start tolling together, what time
will they next toll together?

Trigonometry
3
Q1. If sin A = , find tan A, cos A, cot A,sec A, cot A .
5
Q2. If 12cos = 13 , find 2tan A − 3cot A .
Do questions 1,2 and 3 of Exercise 8.2.
Do questions 4 and 5 of Exercise 8.4