Series RTEQ.P. Code 93/1/0
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
3/4 written as a percentage is
(A) 43%(B) 25%(C) 34%(D) 75%
2.1
20% of 450 is
(A) 20(B) 90(C) 900(D) 45
3.1
A shirt marked ₹800 is sold at a 10% discount. The selling price is
(A) ₹880(B) ₹80(C) ₹720(D) ₹790
4.1
The hypotenuse of a right triangle whose other sides are 6 cm and 8 cm is
(A) 14 cm(B) 10 cm(C) 48 cm(D) 12 cm
5.1
Which of these is a Pythagorean triple?
(A) (6, 7, 8)(B) (2, 3, 4)(C) (4, 5, 6)(D) (5, 12, 13)
6.1
The diagonal of a square of side 5 cm is
(A) 5 cm(B) 10 cm(C) 5√2 cm(D) 25 cm
7.1
6 workers finish a job in 10 days. Working at the same rate, 12 workers will finish it in
(A) 10 days(B) 12 days(C) 20 days(D) 5 days
8.1
In a pie chart, the angle of the sector for 25% of the data is
(A) 25°(B) 45°(C) 100°(D) 90°
9.1
60 divided in the ratio 1 : 2 : 3 gives
(A) 15, 15, 30(B) 5, 10, 45(C) 20, 20, 20(D) 10, 20, 30
10.1
The number of faces of a cube is
(A) 4(B) 6(C) 8(D) 12
11.1
The number of edges of a cuboid is
(A) 8(B) 12(C) 24(D) 6
12.1
The mean of 4, 6, 8, 10 and 12 is
(A) 8(B) 40(C) 6(D) 10
13.1
The median of 3, 9, 5, 7, 1 is
(A) 9(B) 25(C) 5(D) 7
14.1
"Think of a number, add 5, double it, subtract 10, then halve it." The result is always
(A) 0(B) 5(C) 10(D) the number you started with
15.1
3x + 2x − x simplifies to
(A) 6x(B) x(C) 4x(D) 5x
16.1
The area of a rectangle 12 m long and 5 m wide is
(A) 120 m²(B) 17 m²(C) 34 m²(D) 60 m²
17.1
The area of a parallelogram with base 9 cm and height 4 cm is
(A) 18 cm²(B) 36 cm²(C) 13 cm²(D) 26 cm²
18.1
The area of a trapezium with parallel sides 8 cm and 6 cm and height 5 cm is
(A) 40 cm²(B) 24 cm²(C) 70 cm²(D) 35 cm²
19.1
Assertion (A): A triangle with sides 3 cm, 4 cm and 5 cm is right-angled.Reason (R): If the square of the longest side equals the sum of the squares of the other two sides, the triangle is right-angled.
(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): A 10% increase followed by a 10% decrease brings a price back to the original.Reason (R): 10% of a larger number is more than 10% of a smaller number.
(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 rhombus has area 96 cm² and one diagonal of 16 cm. Find the other diagonal.
ORThe mean of 6 numbers is 15. If the number 25 is removed, what is the mean of the remaining numbers?
22.2
Divide ₹900 between two people in the ratio 4 : 5.
ORThe price of a bag increases from ₹400 to ₹460. Find the percentage increase.
23.2
A shirt priced ₹800 is sold at a 15% discount. Find (a) the discount and (b) the selling price.
24.2
The mean of 5 numbers is 12. A sixth number, 18, is added. Find the new mean.
25.2
In the date trick (month × 5, add 6, × 4, add 9, × 5, add the day), the final answer is 781. Find the date.
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
A trapezium has parallel sides 14 cm and 22 cm, and height 9 cm. (a) Find its area. (b) A diagonal splits it into two triangles. Find the area of each. (c) Check that they add up to the area in (a).
ORA square has side 7 cm. (a) Find the square of its diagonal. (b) Find the area of the square drawn on the diagonal. (c) How many times the original area is this?
27.3
A square pyramid has a square base and 4 triangular faces. (a) Count its faces (F), vertices (V) and edges (E). (b) Check whether F + V − E = 2.
ORA town's population is 20,000. It increases by 10% each year. Find the population (a) after 1 year and (b) after 2 years.
28.3
8 workers complete a job in 15 days. (a) How many workers are needed to finish it in 10 days? (b) In 6 days? (c) What stays constant?
29.3
A right triangle has legs 9 cm and 12 cm. Find (a) the hypotenuse, (b) the area and (c) the altitude drawn to the hypotenuse.
30.3
A rectangular plot is 40 m × 25 m. A path 2.5 m wide runs along the inside of its boundary. Find the area of the path.
31.3
A friend picks a 2 × 2 grid from a calendar and says its numbers add up to 52. (a) Write the sum in terms of the top-left number a. (b) Find a. (c) Write all four numbers.
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
(a) Find the hypotenuse of an isosceles right triangle whose equal sides are 1 unit each. (b) Find the side of a square whose area is double that of a square of side 5 cm. (c) Which of these are right triangles: (8, 15, 17), (7, 24, 25), (6, 9, 11)? Show working.
33.5
Karim's coins double each time he goes around a tree, and he pays the genie c coins after each round. (a) If c = 24 and he has 0 coins after 3 rounds and 3 payments, how many coins did he start with? (b) If he starts with 14 coins, what value of c leaves him with exactly 0 after 3 rounds? (c) Write the general rule relating the starting coins x and c.
34.5
Start with a shaded equilateral triangle. At each step, join the midpoints of every shaded triangle and remove the middle one (Sierpinski triangle). (a) How many shaded triangles are there after steps 1, 2 and 3? (b) After n steps? (c) What fraction of the original area is still shaded after step 3?
ORProve that if (a,b,c) is a Baudhayana triple, then (ka,kb,kc) is also a Baudhayana triple for any positive integer k.
35.5
A shopkeeper buys an item for ₹1200, marks its price 25% above cost, then gives a 10% discount on the marked price. Find (a) the marked price, (b) the selling price, (c) the profit and (d) the profit percentage.
ORShyamala bought a vase at ₹2650 and sells it at an 18% loss. Find the selling price, showing your working.
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
A TV is priced at ₹20,000. The shop gives a 15% discount, and then 18% GST is added to the discounted price.(i) Find the discount.1(ii) Find the price after the discount.1(iii) Find the final price including GST.2OR(iii) If the price of ₹20,000 rises by 10% one year and by another 10% the next year, find the price after two years.2
37.
A rectangular garden is 30 m long and 20 m wide. A path 2 m wide runs inside it along all four sides.(i) Find the area of the garden.1(ii) Find the length and breadth of the garden inside the path.1(iii) Find the area of the path.2OR(iii) Find the cost of fencing the garden at ₹50 per metre.2
38.
The marks (out of 10) of 10 students in a quiz are 6, 8, 5, 9, 8, 7, 8, 4, 10, 5.(i) Find the mode.1(ii) Find the mean.1(iii) Find the median.2OR(iii) Find the range, and the number of students who scored more than the mean.2
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