Series RTEQ.P. Code 12/1/-1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Periodic Test 3
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
Name the similarity criterion used when one angle of a triangle equals one angle of another and the sides including these angles are proportional.
2.1
A vertical stick 2 m long casts a shadow 1.2 m long. At the same time a tower casts a shadow 18 m long. Find the height of the tower.
3.1
Quadrilateral ABCD ~ quadrilateral PQRS with AB = 14 cm, PQ = 21 cm and CD = 10 cm. Find RS.
4.1
Δ ABC ~ Δ PQR with ∠A = 35° and ∠Q = 75°. Find ∠R.
5.1
In Δ ABC, DE || BC with D on AB and E on AC. If AD/DB = 3/4 and AE = 6 cm, find EC.
6.1
If x, x + 10 and 3x are in AP, find x.
7.1
Find the sum of the first 12 natural numbers.
8.1
How many terms are there in the AP 7, 10, 13, …, 100?
9.1
Find the 6th term of the AP with first term 7 and common difference −2.
10.1
Find the common difference of the AP 1/3, 1/6, 0, −1/6, …
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Δ ABC ~ Δ DEF with AB = 9 cm and DE = 6 cm. The altitude from A to BC in Δ ABC is 12 cm. Find the corresponding altitude from D in Δ DEF.
12.2
In Δ ABC, AB = 16 cm and AC = 24 cm. D is on AB with AD = 6 cm and E is on AC with AE = 9 cm. Is DE || BC? Give reasons.
13.2
How many multiples of 6 lie between 100 and 300?
14.2
In an AP, a₆ = 19 and a₁₁ = 39. Find the 20th term.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
In Δ PQR, PQ = 6 cm, PR = 9 cm and ∠P = 50°. In Δ XYZ, XY = 8 cm, XZ = 12 cm and ∠X = 50°. Show that the triangles are similar and, if QR = 7.5 cm, find YZ.
16.3
In Δ ABC, DE || BC with AD = 2x + 1, DB = x + 2, AE = 3x and EC = x + 4. Find x.
17.3
The sum of the first n terms of a list is 3n² + 4n. Show that it is an AP and find its 20th term.
18.3
The 4th term of an AP is 9 and its 9th term is 24. Find the sum of the first 16 terms.
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
ABCD is a trapezium with AB || DC. Its diagonals AC and BD meet at O. If AO = 3x − 1, OC = 5x − 3, BO = 2x + 1 and OD = 6x − 5, find x and the length of diagonal AC.
20.5
Logs are stacked in rows with 24 logs in the bottom row, 23 in the next row, 22 in the next, and so on. The stack contains 180 logs. How many rows are there, and how many logs are in the top row?
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