Series RTEQ.P. Code 44/-1/0
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 4
Time allowed : 1½ HoursMaximum Marks : 40
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 20 questions. All questions are compulsory.
(ii)This question paper is divided into four sections – A, B, C and D.
(iii)In Section A, Question numbers 1 to 10 carry 1 mark each.
(iv)In Section B, Question numbers 11 to 14 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 15 to 18 are short answer (SA) type questions carrying 03 marks each.
(vi)In Section D, Question numbers 19 to 20 are long answer (LA) type questions carrying 05 marks each.
(vii)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(viii)Use of calculators is not allowed.
SECTION A
This section comprises 10 questions of 1 mark each.
1.1
What is the probability of an impossible event?
2.1
Write the sample space for rolling a 6-sided die.
3.1
What is the probability of getting an even number on a fair die?
4.1
Two fair coins are tossed. What is P(TT)?
5.1
A coin tossed 40 times shows heads 12 times. What is the relative frequency of heads?
6.1
Write the next term of the GP 2, 6, 18, …
7.1
Find the 8th term of the sequence uₙ = 2n − 1.
8.1
Is 1, −1, 1, −1, … a GP? If so, give the common ratio.
9.1
Find the sum of the first 50 natural numbers.
10.1
In the Virahānka–Fibonacci sequence, what comes after 13, 21?
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Find the nth term of the AP 11, 8, 5, 2, … and write its recursive rule.
12.2
A box has 5 green and 7 red balls. One is drawn at random. Find P(red) and P(not red).
13.2
A letter is picked from PROBABILITY. Find P(B or I).
14.2
A GP has common ratio 2 and 8th term 192. Find its 12th term.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
A die rolled 60 times shows a 6 fifteen times. (a) Find the experimental probability of a 6. (b) Find the theoretical probability. (c) About how many 6s would you expect in 6000 rolls, and why?
16.3
A coin is tossed three times. Using a tree diagram, find (a) the number of outcomes, (b) P(at least two heads), (c) P(no heads).
17.3
Harish earns ₹5,00,000 in year 1, and his salary rises by ₹20,000 each year. (a) Write the salary in year n. (b) In which year does it first reach ₹7,00,000? (c) What is his salary in year 15?
18.3
The Sierpiński square carpet keeps 8 of 9 small squares at each stage. (a) Find the number of shaded squares at stages 0 to 3. (b) Write the rule for stage n. (c) If the stage-0 area is 1, what is the shaded area at stage n?
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
In a sample of 50 students, the favourite sports were: cricket 22, football 13, hockey 9, kabaddi 6. (a) Find P(cricket). (b) Find P(not cricket). (c) Estimate how many of the school's 1200 students prefer kabaddi. (d) Find P(hockey or kabaddi). (e) Show that the four probabilities add up to 1.
20.5
An AP has 3rd term 12 and 50th term 106. (a) Find a and d. (b) Find the 29th term. (c) Is 100 a term? If so, which one? (d) Write the recursive rule. (e) Is 55 a term? Justify your answer.
✦ ✦ ✦