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
Find the mid-point of the line segment joining (−3, 7) and (9, −1).
2.1
Find the distance of the point (8, −6) from the origin.
3.1
Find the point dividing the join of (2, −5) and (12, 10) internally in the ratio 2 : 3.
4.1
In triangle PQR, right-angled at Q, PQ = 8 cm and QR = 6 cm. Find tan P.
5.1
Find the value of tan 0° + cos 0° + sin 90°.
6.1
Find the value of 1 + tan² 60°.
7.1
If cos A = 5/13 (A acute), find sin A.
8.1
Find the value of cos 30° + sin 60°.
9.1
Find the distance of the point (−7, 24) from the origin.
10.1
The mid-point of AB is the origin and A is (3, −5). Find B.
SECTION B
This section comprises 4 very short answer (VSA) type questions of 2 marks each.
11.2
Prove that sec² θ + cosec² θ = sec² θ cosec² θ.
12.2
Evaluate: sin 75°/cos 15° + cos 48° − sin 42°.
13.2
Find x if PQ = QR where P(6, −1), Q(1, 3) and R(x, 8).
14.2
Find the ratio in which the x-axis divides the line segment joining A(2, −4) and B(5, 6). Also find the point of division.
SECTION C
This section comprises 4 short answer (SA) type questions of 3 marks each.
15.3
If sin θ + cos θ = 7/5, find the values of sin θ cos θ and tan θ + cot θ.
16.3
Prove that (cos A − sin A + 1)/(cos A + sin A − 1) = cosec A + cot A.
17.3
A(2, 1), B(5, 2), C(6, 5) and D(p, 4) are the vertices of a parallelogram ABCD taken in order. Find p.
18.3
Show that the points A(0, 0), B(3, 4), C(8, 4) and D(5, 0), taken in order, form a rhombus but not a square.
SECTION D
This section comprises 2 long answer (LA) type questions of 5 marks each.
19.5
Prove that (tan A + sec A − 1)/(tan A − sec A + 1) = (1 + sin A)/cos A.
20.5
Show that the points A(0, −1), B(2, 1) and C(0, 3) are the vertices of an isosceles right-angled triangle. Also show that the mid-point of the hypotenuse is equidistant from all three vertices.
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