Series RTEQ.P. Code 87/0/-1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Annual Exam
Time allowed : 3 HoursMaximum Marks : 80
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 38 questions. All questions are compulsory.
(ii)This question paper is divided into five sections – A, B, C, D and E.
(iii)In Section A, Question numbers 1 to 18 are multiple choice questions (MCQs) and Question numbers 19 to 20 are Assertion–Reason based questions of 1 mark each.
(iv)In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 26 to 31 are short answer (SA) type questions carrying 03 marks each.
(vi)In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 05 marks each.
(vii)In Section E, Question numbers 36 to 38 are case-based integrated units of assessment carrying 04 marks each, with sub-parts.
(viii)There is no overall choice. However, an internal choice has been provided in some questions. Attempt only one of the alternatives in such questions.
(ix)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(x)Use of calculators is not allowed.
SECTION A
This section comprises 20 multiple choice questions (MCQs) of 1 mark each.
1.1
The longest chord of a circle is its
(A) radius(B) diameter(C) arc(D) secant
2.1
The perpendicular from the centre of a circle to a chord
(A) equals the radius(B) has no special property(C) bisects the chord(D) is parallel to the chord
3.1
A chord of length 16 cm is drawn in a circle of radius 10 cm. Its distance from the centre is
(A) 6 cm(B) 4 cm(C) 12 cm(D) 8 cm
4.1
The angle in a semicircle is
(A) 90°(B) 180°(C) 45°(D) 60°
5.1
Equal chords of a circle are
(A) parallel(B) perpendicular(C) equidistant from the centre(D) always diameters
6.1
Using Heron’s formula, the area of a triangle with sides 3 cm, 4 cm and 5 cm is
(A) 12 cm²(B) 7.5 cm²(C) 10 cm²(D) 6 cm²
7.1
The circumference of a circle of radius 7 cm is (π = 22/7)
(A) 44 cm(B) 154 cm(C) 49 cm(D) 22 cm
8.1
The area of a parallelogram with base 8 cm and height 5 cm is
(A) 40 cm²(B) 80 cm²(C) 13 cm²(D) 20 cm²
9.1
The length of an arc of angle 90° of a circle of radius 14 cm is (π = 22/7)
(A) 22 cm(B) 44 cm(C) 88 cm(D) 11 cm
10.1
The semi-perimeter of a triangle with sides 5 cm, 6 cm and 7 cm is
(A) 6 cm(B) 12 cm(C) 9 cm(D) 18 cm
11.1
The probability of getting a head when a fair coin is tossed once is
(A) 0(B) 1/2(C) 1(D) 2
12.1
The probability of a sure event is
(A) 1(B) it depends(C) 0(D) 1/2
13.1
The number of outcomes in the sample space when two coins are tossed is
(A) 3(B) 8(C) 4(D) 2
14.1
A bag has 3 red and 5 blue balls. The probability of drawing a red ball is
(A) 5/8(B) 1/3(C) 3/5(D) 3/8
15.1
The next term of the sequence 3, 7, 11, 15, … is
(A) 18(B) 20(C) 21(D) 19
16.1
The sum of the first 100 natural numbers is
(A) 10100(B) 5000(C) 5050(D) 5100
17.1
The common ratio of the geometric progression 2, 6, 18, … is
(A) 3(B) 4(C) 2(D) 12
18.1
For the sequence with aₙ = 2n + 1, the 5th term is
(A) 9(B) 10(C) 12(D) 11
19.1
Assertion (A): A chord whose length equals the diameter passes through the centre.Reason (R): The diameter is the longest chord of a circle.
(A) Both A and R are true, and R is the correct explanation of A.(B) Both A and R are true, but R is not the correct explanation of A.(C) A is true, but R is false.(D) A is false, but R is true.
20.1
Assertion (A): 1, 2, 4, 8, … is an arithmetic progression.Reason (R): In an arithmetic progression, the difference between consecutive terms is constant.
(A) Both A and R are true, and R is the correct explanation of A.(B) Both A and R are true, but R is not the correct explanation of A.(C) A is true, but R is false.(D) A is false, but R is true.
SECTION B
This section comprises 5 very short answer (VSA) type questions of 2 marks each.
21.2
A die is rolled. Find P(an even number greater than 2) and P(not a 6).
ORFind the sum of the first 60 natural numbers.
22.2
A circle has radius 17 cm and a chord of 30 cm. Find the distance of the chord from the centre.
ORFind the area of a sector of radius 21 cm with angle 120°. (π = 22/7)
23.2
An isosceles triangle has sides 10, 10 and 12 cm. Find its area in two ways.
24.2
A card is drawn from cards numbered 1 to 20. Find P(multiple of 3) and P(prime).
25.2
O is the centre and ∠AOB = 140°. C is on the major arc and D is on the minor arc. Find ∠ACB and ∠ADB.
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
t₁ = 1 and tₙ = 3tₙ₋₁ + 1. Find the first five terms. Is 364 a term? If so, which one?
ORParallel chords of 10 cm and 24 cm lie in a circle of radius 13 cm. Find the distance between them if they are (a) on opposite sides of the centre and (b) on the same side.
27.3
An AP has 5th term 19 and 12th term 47. Find a, d and the 30th term.
ORFor the GP 3, 6, 12, …: (a) find the 10th term; (b) find which term is 384; (c) write the recursive rule.
28.3
A paper cup is tossed 200 times. It lands on its bottom 64 times, on its top 36 times and on its side 100 times. (a) Find the experimental probability of each. (b) Check that they add up to 1. (c) Is it correct to assume each outcome has probability 1/3? Why?
29.3
A triangle has sides 26, 28 and 30 cm. Find its area, and the altitude to the side of 28 cm.
30.3
A coin is tossed and a spinner numbered 1 to 4 is spun. (a) How many outcomes are there? (b) Find P(heads and an odd number). (c) Find P(tails and an even number).
31.3
ABCD is cyclic with ∠A = (x + 20)°, ∠C = (2x + 10)°, ∠B = (3y − 10)° and ∠D = (y + 30)°. Find x, y and all four angles.
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
A bag has 4 red, 5 blue and 3 green balls. (a) Find P(red). (b) Find P(not green). (c) Find P(red or blue). (d) A ball is drawn, replaced, and a second ball drawn. Find P(both blue). (e) A bag of 600 balls has the same proportions. Estimate the number of green balls.
ORAn 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.
33.5
A running ground is a rectangle 84 m long and 70 m wide, with a semicircle on each 70 m side. (a) Find its perimeter. (b) Find its area. (c) Find the cost of fencing at ₹20 per m. (d) Find the cost of turfing at ₹5 per m². (e) Find the area of the two semicircular ends together. (π = 22/7)
34.5
A circle has radius 10 cm. (a) Find the distance from the centre of a chord AB = 16 cm. (b) Find the distance of a chord CD = 12 cm. (c) Which chord is closer to the centre, and why? (d) If AB ∥ CD and they are on opposite sides of the centre, how far apart are they? (e) How far apart are they if they are on the same side?
35.5
Riya saves ₹200 in week 1, ₹250 in week 2, and ₹50 more each week. (a) How much does she save in week 10? (b) In which week does she save ₹1,200? (c) Find her total savings over the first 10 weeks. (d) Under another plan she saves ₹10 in week 1 and doubles it each week. How much does she save in week 10? (e) Which plan gives more in week 10, and what kind of progression is each?
ORIn a circle of radius 10 cm, chord AB subtends 90° at the centre O. Find (a) the length of AB, (b) its distance from O, (c) the area of the minor sector, (d) the area of ΔAOB, (e) the area of the minor segment. (π = 3.14)
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
A farmer has a triangular field with sides 50 m, 120 m and 130 m.(i) Find the semi-perimeter of the field.1(ii) Is the field a right triangle? Give a reason.1(iii) Find the area of the field using Heron’s formula.2OR(iii) Find the length of the perpendicular from the opposite corner to the 130 m side.2
37.
Twenty cards numbered 1 to 20 are put in a box and one card is drawn at random.(i) Find the probability that the number is even.1(ii) Find the probability that the number is a multiple of 5.1(iii) Find the probability that the number is prime, and the probability that it is not prime.2OR(iii) Two coins are tossed together. Draw a tree diagram and find the probability of getting at least one head.2
38.
An auditorium has 20 seats in the first row, and each row has 2 more seats than the row in front. There are 25 rows.(i) How many seats are there in the 10th row?1(ii) Which row has 60 seats?1(iii) Find the total number of seats in the auditorium.2OR(iii) Find the total number of seats in the first 10 rows.2
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