Series RTEQ.P. Code 14/2/1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Board Mock · Full syllabus
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 LCM of 6, 72 and 120 is
(A) 6(B) 360(C) 720(D) 120
2.1
If p and q are co-prime numbers, then HCF(p, q) is
(A) q(B) 1(C) pq(D) p
3.1
If 1 is a zero of x² − 4x + k, then k is
(A) 3(B) −3(C) 4(D) 5
4.1
The graph of a polynomial y = p(x) cuts the x-axis at 3 points. The number of zeroes of p(x) is
(A) 3(B) 0(C) 1(D) 2
5.1
The lines x = 2 and y = 3 meet at the point
(A) (3, 2)(B) (2, 3)(C) (0, 0)(D) (2, 0)
6.1
The sum of the roots of 2x² − 7x + 3 = 0 is
(A) −7/2(B) 3/2(C) −3/2(D) 7/2
7.1
Which term of the AP 5, 8, 11, … is 32?
(A) 10th(B) 11th(C) 12th(D) 9th
8.1
Δ ABC ~ Δ DEF and AB/DE = 2/3. If BC = 6 cm, then EF is
(A) 12 cm(B) 6 cm(C) 4 cm(D) 9 cm
9.1
The mid-point of the join of (−2, 4) and (6, −8) is
(A) (−2, 2)(B) (2, −2)(C) (8, 12)(D) (4, −4)
10.1
The distance of the point (−5, 12) from the origin is
(A) √119 units(B) 13 units(C) 7 units(D) 17 units
11.1
The value of tan 45° + sin 90° is
(A) 1(B) 2(C) 0(D) √2
12.1
If sec A = 2 and A is acute, then A is
(A) 60°(B) 90°(C) 30°(D) 45°
13.1
The angle of elevation of the top of a 10 m tower from a point 10 m from its foot is
(A) 45°(B) 60°(C) 90°(D) 30°
14.1
The tangent at any point of a circle is ______ to the radius through the point of contact.
(A) perpendicular(B) parallel(C) equal(D) inclined at 45°
15.1
The area of a circle whose circumference is 22 cm is (π = 22/7)
(A) 22 cm²(B) 38.5 cm²(C) 77 cm²(D) 154 cm²
16.1
The total surface area of a solid hemisphere of radius 7 cm is (π = 22/7)
(A) 308 cm²(B) 462 cm²(C) 154 cm²(D) 616 cm²
17.1
The mean of the first five natural numbers is
(A) 2.5(B) 5(C) 3(D) 15
18.1
One card is drawn from a well-shuffled pack of 52 cards. The probability that it is a king is
(A) 4/13(B) 1/13(C) 1/52(D) 1/4
19.1
Assertion (A): The equation x² + x + 1 = 0 has no real roots.Reason (R): A quadratic equation has no real roots when its discriminant is negative.
(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): If the radius of a sphere is doubled, its volume becomes 8 times.Reason (R): The volume of a sphere is (4/3)πr².
(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
Find the HCF and LCM of 120 and 54 using prime factorisation.
ORFind the HCF and LCM of 70 and 196 using prime factorisation.
22.2
Show that 13 × 17 × 19 + 19 is a composite number.
ORShow that 9 × 11 × 13 + 13 is a composite number.
23.2
Find the values of k for which 3x² + kx + 12 = 0 has equal roots.
24.2
Find the values of y for which the distance between P(5, y) and Q(1, −2) is 5 units.
25.2
The centre of a circle is (2, −1) and one end of a diameter is (−3, 4). Find the other end of the diameter.
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
How many terms of the AP 3, 7, 11, … must be taken so that the sum is 210?
ORThe sum of the first n terms of an AP is 5n² − 3n. Find the first term, the common difference and the 10th term.
27.3
A circle is inscribed in a triangle ABC right angled at B, with AB = 15 cm and BC = 8 cm. Find the radius of the circle.
28.3
Prove that (sin A + cos A)(sec A + cosec A) = 2 + tan A + cot A.
ORIf 3 cot θ = 4, evaluate (5 sin θ − 3 cos θ)/(5 sin θ + 3 cos θ).
29.3
If sin θ + cos θ = 7/5, find the values of sin θ cos θ and tan θ + cot θ.
30.3
A boy 1.6 m tall looks at the top of a 21.6 m high building. He walks towards it so that the angle of elevation of the top changes from 30° to 60°. How far does he walk? (Use √3 = 1.732)
31.3
A capsule is a cylinder with a hemisphere at each end. Its total length is 25 cm and its diameter is 14 cm. Find its total surface area. (Use π = 22/7)
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
Two taps running together can fill a tank in 6 hours. The tap with the smaller pipe takes 5 hours more than the tap with the larger pipe to fill the tank alone. Find the time each tap alone takes to fill the tank.
ORFind the zeroes of 2x² − 3x − 2 and verify the relationship between the zeroes and the coefficients. Hence form a quadratic polynomial whose zeroes are the squares of the zeroes of 2x² − 3x − 2.
33.5
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.
34.5
Two parallel tangents touch a circle with centre O at A and B. A third tangent touches the circle at C and meets the parallel tangents at P and Q. Prove that ∠POQ = 90°.
35.5
Find the mean, median and mode of the data with classes 0-10, 10-20, 20-30, 30-40, 40-50, 50-60 with frequencies 4, 6, 10, 14, 8, 3.
ORTwo dice are thrown together. Find the probability that (i) the sum is 9 (ii) both dice show the same number (iii) the sum is at most 4 (iv) the product is a perfect square (v) the sum is odd.
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
At a school fair, 2 adult tickets and 3 child tickets cost ₹1,350, while 3 adult tickets and 2 child tickets cost ₹1,400. Let an adult ticket cost ₹x and a child ticket ₹y.(i) Write the pair of linear equations.1(ii) Find x + y.1(iii) Find the price of each kind of ticket.2OR(iii) Find the cost of 4 adult and 5 child tickets.2
37.
A circular park has a radius of 21 m. A path 3.5 m wide runs around it on the outside. (Use π = 22/7)(i) Find the circumference of the park.1(ii) Find the outer radius of the path.1(iii) Find the area of the path.2OR(iii) A sector of the park with angle 60° is used for flower beds. Find its area.2
38.
A box contains 5 red, 3 green and 2 blue marbles. One marble is taken out at random.(i) Find the probability that it is red.1(ii) Find the probability that it is not green.1(iii) If 2 more blue marbles are added, find the new probabilities of getting a blue marble and a red marble.2OR(iii) Two dice are thrown together. Find the probability of getting a doublet and of getting a sum of 7.2
✦ ✦ ✦