SSC Comilla Board English Vershion Math Question

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Cumilla Board-2025
Mathematics (Multiple Choice Questions)

[According to the Syllabus of 2025]
Subject Code: 1 0 9
Time: 30 minutes | Full Marks: 30

[N.B. – Fill the circle completely with a ballpoint pen corresponding to the correct/best answer in the supplied Multiple Choice Answer Sheet. Value of each question is 1. No mark/sign should be given on the question paper.]
1. If b, a, c are in continued proportion, then—
i. $a^2 = bc$ ii. $\frac{b}{a} = \frac{c}{a}$ iii. $\frac{a+b}{a-b} = \frac{c+a}{c-a}$
Which one of the following is correct?
a) i & ii b) i & iii c) ii & iii d) i, ii & iii
Read the following stem and answer questions 2 and 3:
[Diagram: Triangle ABC, D is a point on side BC. $BC = 18$ cm, $\angle ADC = 60^\circ$ , $\angle C = 30^\circ$ , $\angle EAB = 30^\circ$ ]

SSC Comilla board English vershion math question

Table of Contents

What is the length of AC?
a) 9 m b) $9\sqrt{3}$ m c) $12\sqrt{3}$ m d) 36 m
3. What is the length of AD in meters?
a) $36\sqrt{3}$ b) 36 c) $12\sqrt{3}$ d) 12
4. If two circles of radii 2 cm and 3 cm touch each other externally, what is the distance between their centers?
a) 5 cm b) 4 cm c) 3 cm d) 1 cm
5. What is the measure of each interior angle at a vertex of a regular pentagon?
a) 72° b) 90° c) 108° d) 144°
6. Under which condition if $a^x = a^y$ , then $x = y$ ?
a) $a < 0, a \neq 1$ b) $a > 0, y < 1$ c) $a > 0, a \neq 1$ d) $a > 0, a \neq 1$
7. If $\log_4 2 = 4^{2n}$ , what is the value of $n$ ?
a) 2 b) $\frac{1}{2}$ c) 4 d) 10
8. In a right-angled triangle PQR, $\angle Q = 1$ right angle and $\angle P = 2\angle R$ , which one of the following is correct?
a) $PR = 2QR$ b) $PQ = 2PR$ c) $PR = 2PQ$ d) $QR = 2PQ$
9. If $A = \{6, 7, 8, 9, 11, 12, 13\}$ , $B = \{x : x \in A \text{ and } x \text{ is a multiple of } 3\}$ , which one is set B?
a) $\{6, 9\}$ b) $\{6, 12\}$ c) $\{9, 12\}$ d) $\{6, 9, 12\}$
Answer questions 10 and 11 based on the following table:

Class Interval	31 – 40	41 – 50	51 – 60	61 – 70	71 – 80
Frequency	4	6	10	8	2

10. What is the frequency of the median class?
a) 10 b) 8 c) 6 d) 4
11. What is the mode?
a) 17 b) 57.67 c) 56 d) 51
12. If the range of a data set is 67 and the maximum value is 85, what is the minimum value?
a) 17 b) 18 c) 19 d) 20
13. If $f(x) = x^3 - x - 24$ , for which value of $x$ will $f(x) = 0$ ?
a) 2 b) 3 c) 4 d) 6
14. The angle inscribed in a major arc of a circle is an—
a) Complementary angle b) Right angle c) Acute angle d) Obtuse angle
15. If $2x + \frac{2}{x} = 3$ , what is the value of $x^2 + \frac{1}{x^2}$ ?
a) $\frac{1}{4}$ b) 1 c) $\frac{9}{4}$ d) $\frac{17}{4}$
16. $0.2 \times 0.1\dot{6}$ = ?
a) 0.0032 b) 0.037 c) 0.32 d) $0.3\dot{2}$
17. The area of a square is how many times the area of the square drawn on its diagonal?
a) Half b) Equal c) Double d) Four times
18. What is the root of the equation $(x - 4)^2 = 0$ ?
a) 1 b) 2 c) 3 d) 4
19. What is the 8th term of the series $64 + 32 + 16 + 8 + \dots$ ?
a) $\frac{1}{4}$ b) $\frac{1}{2}$ c) 2 d) 4
Answer questions 20 and 21 according to the following stem:
$x^2 = \sqrt{5}x - 1$
20. What is the value of $x + \frac{1}{x}$ ?
a) – 3 b) $-\sqrt{5}$ c) $\sqrt{5}$ d) 3
21. What is the value of $x^3 + \frac{1}{x^3}$ ?
a) 0 b) $2\sqrt{5}$ c) $3\sqrt{5}$ d) $8\sqrt{5}$

SSC Rajshahi board English vershion math question

22. What is the minimum number of independent data required to draw a parallelogram?
a) 6 b) 5 c) 4 d) 3
23.

$AB = 2$ , Base $BC = \sqrt{3}$ , $\angle ACB = \theta$ ]
What is the value of $\theta$ in the figure?
a) 90° b) 60° c) 45° d) 30°
24. What is the number of proper subsets of the set $P = \{2, 4, 6, 8\}$ ?
a) 4 b) 8 c) 15 d) 16
25. What is the order of rotational symmetry of a circle?
a) 0 b) 1 c) 2 d) Infinite
26. What is the characteristic of the common logarithm of 0.0035?
a) 3 b) 2 c) 1 d) $\bar{3}$
27. If the diameter of a circle is 26 cm, what is its area in sq. cm?
a) 2132.72 b) 530.93 c) 163.36 d) 81.68
28. $x + 3y = 1$
$2x + 6y = 2$
The system of equations is—
i. Consistent ii. Mutually dependent iii. Has infinitely many solutions
Which one of the following is correct?
a) i & ii b) i & iii c) ii & iii d) i, ii & iii
29.

$\angle BOC$ , $\angle AOB$ , $\angle AOC$ , $\angle BOD$ , $\angle AOD$ , $\angle DOC$ ]
Which one is the complementary angle of $\angle BOC$ ?
a) $\angle AOC$ b) $\angle BOD$ c) $\angle AOD$ d) $\angle DOC$
30.

$AD = 6\text{ cm}$ , $AB = 10\text{ cm}$ , with shaded region]
What is the area of the shaded region of the rectangle in sq. cm?
a) 28.27 b) 31.73 c) 33.27 d) 60
Answer Key:

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
b	c	d	a	c	c	b	c	d	a	b	b	b	d	a
16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
b	a	d	b	c	b	d	b	c	d	a	b	d	a	b

Mathematics (Creative Questions)

Time: 2 hours 30 minutes | Full Marks: 70
[N.B. – Answer seven questions taking two from Group-A, two from Group-B, two from Group-C and one from Group-D.]

Group A – Algebra

1. $x^2 + \frac{1}{x^2} = 322$ and $a = 9 + 4\sqrt{5}$ ; where $x > 0, a > 0$ .
a. Find the value of $x - \frac{1}{x}$ .
b. Prove that $x\sqrt{x} - \frac{1}{x\sqrt{x}} = 76$ .
c. Prove that the value of $(\sqrt{a} - 2)$ is an irrational number.
2. (i) $ax + bx - 6ab = 0$ ; $a \neq \pm b$ .
(ii) The area of a land is 864 sq. meters. The ratios of the length and breadth of that land to the length and breadth of another land are $4 : 3$ and $3 : 2$ respectively.
a. The ratio of two numbers is $4 : 5$ ; their L.C.M is 60; find the two numbers.
b. Find the value of $\frac{x + 3a}{x - 3a} + \frac{x + 3b}{x - 3b}$ .
c. Find the area of the other land.
3. The n-th terms of an arithmetic and a geometric series are $25 - 4n$ and $2^{2n-1}$ respectively.
a. If $4^{2p-1} = 128$ , find the value of $p$ .
b. If the sum of the first $n$ terms of the arithmetic series is -187, find the value of $n$ .
c. Find the sum of the first seven terms of the geometric series.
Group B – Geometry
4. S and T are the midpoints of sides PQ and PR of $\Delta PQR$ respectively.
a. If $AB = 6\text{ cm}$ , $AC = 8\text{ cm}$ and $\angle BAC = 60^\circ$ , what is the area of $\Delta ABC$ ?
b. Prove that $ST \parallel QR$ and $QR = 2ST$ .
c. Prove that Area of $\Delta PST = \frac{1}{4}$ (Area of $\Delta PQR$ ).
5. Two base-adjacent angles of a triangle are $\angle B = 60^\circ$ and $\angle C = 45^\circ$ , and the perpendicular distance from the vertex to the base is 6 cm.
a. Find the center of a circle. [Drawing signs are compulsory]
b. Draw the triangle. [Signs and descriptions of construction are compulsory]
c. Taking the perpendicular length of the triangle as the side length of a square, draw an inscribed circle of that square. [Signs and descriptions of construction are compulsory]
6. KLMN is an inscribed quadrilateral in a circle with center O.
a. Draw a tangent at any point of a circle. [Drawing signs are compulsory]
b. If $\angle MLN + \angle NLK = 90^\circ$ , prove that M, O, and K lie on the same straight line.
c. Prove that $\angle LMN + \angle LKN = 180^\circ$ .
Group C – Trigonometry and Mensuration
7. $\sec\alpha + \tan\alpha = \frac{5}{3}$ and $\sin\theta + \cos\theta = p$ .
a. If $\sin(60^\circ - \alpha) = \frac{1}{2}$ , find the value of $\sec\alpha$ .
b. Find the value of $\sin\alpha + \cos\alpha$ .
c. If $2p - 1 = \sqrt{3}$ , find the value of $\theta$ , where $\theta$ is an acute angle.
8.

In Figure-1, $DA \parallel BC$
a. If $\tan 3x = \cot 6x$ , find the value of $x$ .
b. Find the length of AB from Figure-1.
c. Find the length of PQ from Figure-2.
9. (i) The area of a rectangle is 150 sq. meters. If its length were 5 m less, it would be a square.
(ii) The length of a diagonal of a face of a cube is $6\sqrt{2}\text{ cm}$ .
a. If the difference between the diameter and circumference of a circle is 60 cm, find its radius.
b. Find the length of the diagonal of the rectangle.
c. Find the total surface area and volume of the cube.
Group D – Statistics
10. A frequency distribution table is given below:

Class Interval	21-30	31-40	41-50	51-60	61-70
Frequency	8	12	15	18	7

a. Find the midpoint of the modal class.
b. Find the mean using the shortcut method from the given table.
c. Draw an ogive curve of the given data with a brief description.
11. The frequency distribution table of marks obtained in Science by 50 students of class 10 is given below:

Class Interval	31-40	41-50	51-60	61-70	71-80	81-90	91-100
Frequency	6	8	10	12	5	7	2

a. Find the value of $f_1 + f_2$ from the table, where $f_1$ and $f_2$ bear their usual meanings.
b. Find the median from the given table.
c. Draw a frequency polygon from the given table with a brief description.