01.Show that the diagonals of a square are equal and bisect each other at right angles.
02. Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side
is 18 cm
03. An edge of a cube is increased by 10%. Find the percentage by which the surface area of
the cube has increased.
04.Find the mode of the following data:
5, 7, 6, 5, 9, 8, 6, 7, 11, 10, 5, 7, 6, 8, 6, 9, 10.
05. In a cricket match, a batsman hits a boundary 4 times out of 30 balls, he plays. Find the
probability that he did not hit a boundary.
06. If the arithmetic mean of 25, 30, 32, x, 43 is 34, then find the value of x.
07. Find three different solutions for the equation
3x – 8y = 27
08 A coin is tossed 15 times and observed that 11 times head comes up. Find the
probability that a tail comes up.
09 Construct the angles of the following measurements:
(i) 30° (ii) 15°
10.A heap of wheat is in the form of a cone, the diameter of whose base is 14m and height is
3m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the
area of the canvas required.
19. Find mean of the following data:
Marks: 10 11 12 13 14 15
Number of students: 6 3 4 5 7 5
20.The points scored by a basket-ball team in a series of matches are as follows:
17, 2, 7, 27, 25, 5, 14, 18 , 10, 24, 10, 8, 7, 10
Find mean, median and mode for the data.
21. Give the geometrical representation of x = -3 as an equation
(i) in one variable (ii) in two variables.
22.Solve the equation 2x+1 = x–3 and represent the solution(s) (i) on the number line
(ii) in the Cartesian plane.
23. The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the
quadrilateral.
24. Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.
25. Three coins were tossed 30 times simultaneously. Each time the number of heads
occurring was noted down as follows:
0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0
Prepare a frequency distribution table for the data given above.
CBSE TEST PAPER-01
1 Find the range of the following data: 25, 20 30, 18, 16, 15
(a) 15 (b) 10 (c) 5 (d) 20
2 Find the median of the given data: 7, 8, 7, 7, 9, 10, 13.
(a) 7 (b) 9 (c) 8 (d) 10
3 Find the mode of the given data: 7, 9, 11, 13, 9 13, 9, 9, 7, 8.
(a) 10 (b) 9 (c) 11 (d) 8
4 Find the mean of the first five multiples of 3?
(a) 9 (b) 12 (c) 14 (d ) None of these
5 The mean of 7 observations is 20. If the mean of the first 4 observations is 12 & that of last 4 observations is 28, find the 4th observations?
6 If the mean of 5 observation x, x + 4, x + 8, x + 12, x + 16 is 13, find the mean of the observations?
7 The class marks of the observations are 17, 21, 25, 29, 33, 37, 41, 45. Find the class intervals.
8 The value of π upto 15 decimal places is : 3. 419078023195679 (i) List the digits from 0 to 9 & make frequency distributions of the digit after the decimal points. (ii) What are the most * the least frequently occurring digits?
9 A random survey of the number of children of various age grout playing in the park was found: Age [in years] 1 – 2 2 – 3 3 – 5 5 – 7 7 – 10 No. of children’s 3 5 7 10 13 Draw a histogram to represent the data above?
10 (i) Find the mean of the following data: 25, 27, 19, 29, 21, 23, 25, 30, 28, 20. Show that the sum of deviation of all the observations from the mean is zero. (ii) Find the median of the data given above.
11 If the mean of the following data is 21. Find the value of P.
Y 8 20 P 3 2
12 In a mathematics test given to 10 students, the following marks [out of 100] are recorded as: 82, 41, 39, 52, 53, 45, 96, 47, 50, 60. Find out the mean & median of the above marks.
13 Prove that the sum of the deviations of individuals observations from the mean is zero.
1. Out of 35 students Participating in a debate 10 are girls. The Probability that winner is a boy is
(a) 1 (b) 2 7 (c) 3 7 (d) 5 7
2. There are 5 balls, each of the colours white, blue, green, red and yellow in a bag. If 1 balls is drawn from the bag, then the Probability that the ball drawn is red is
(a) 4 5 (b) 1 4 (c) 1 5 (d) 1 20
3. If P(e)= 0.25 what is the value of P(not E)
(a) 0.5 (b) 1 (c) 0 (d) 0.75
4. Sum of the probabilities of all events of a trial is
(a) less than 1 (b) greater than 1 (c) lies between 0 and 1 (d) 1
5. A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table: Outcome 1 2 3 4 5 6 Frequency 179 150 157 149 175 190 Find the probability of getting each outcome.
6. Two coins are tossed 729 times and the out comes are: No tail: 189, One tail: 297, Two tails: 243 Find the Probability of the occurrence of each of these events.
7. A bag contains 15 cards bearing numbers 1, 2, 3, 4, ……….. , 14, 15. A card is drawn from the bag. Find the Probability that it bears : (i) a Prime number (ii) A number divisible by 2
8. A coin is tossed 400 times and outcomes are Tail: 230 Head:170 Find the probability of having a (i) Head (ii) Tail
9. The marks obtained by 30 students is given in the following table:
Marks 70 58 60 52 65 75 68 No. of Students 3 5 4 7 6 2 3
Find the Probability that a student secures.
(i) 60 marks (ii) 75 marks (iii) Less than 60 marks
11. The ages of 30 workers in a factory are as follows
Age (in yrs) 21-23 23-25 25-27 27-29 29-31 31-33 33-35 No. of works 3 4 5 6 5 4 3
Find the probability that the age of a works lies in the interval
(i) 27-29 (ii) 29-35 (iii) 21-27
12. A die is thrown once. Find the probability of getting
(i) a prime number (ii) a number less then 5
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