SSC English vershion math question 2025 Rajshahi board

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Rajshahi Board – 2025
Mathematics (Multiple Choice Questions)
[According to the Syllabus of 2025]
Subject Code: 109 | Time: 30 Minutes | Full Marks: 30

[N.B. Fill in the circle corresponding to the correct answer on the supplied OMR sheet with a ballpoint pen. Each question carries 1 mark. No mark is allowed on the question paper.]

  1. A parallelogram inscribed in a circle is a —

(a) Rhombus (b) Rectangle (c) Square (d) Trapezium

  1. How many ex-circles (escribed circles) can be drawn for a triangle?

(a) 1 (b) 2 (c) 3 (d) 4

Answer questions 3 and 4 based on the following information:

Class Interval 21 – 30 31 – 40 41 – 50 51 – 60
Frequency 6 16 20 14
  1. What is the value of F_c for calculating the median?

(a) 16 (b) 20 (c) 22 (d) 42

  1. What is the mode of the given data?

(a) 47 (b) 45 (c) 37 (d) 35

  1. How many lines of symmetry does a square have?

(a) 2 (b) 4 (c) 6 (d) 8

  1. For a sequence with 1st term 4 and common difference 2 —
  2. The series = 8 + 10 + 12 + \dots
  3. The 10th term = 26

iii. The sum of the first 15 terms = 300

Which one of the following is correct?

(a) i & ii (b) i & iii (c) ii & iii (d) i, ii & iii

  1. \log_{3\sqrt{3}}(3) = ?

(a) \frac{1}{2} (b) \frac{2}{3} (c) \frac{4}{3} (d) \frac{3}{2}

  1. Which one of the following is a discrete variable?

(a) Age (b) Height (c) Weight (d) Population

  1. Which one of the following is a natural number?

(a) -3 (b) \sqrt{3} (c) \frac{3}{2} (d) 3

  1. How many proper subsets does the set \{4, 5, 6, 7, 8\} have?

(a) 10 (b) 31 (c) 32 (d) 33

  1. If a^2 + \frac{1}{a^2} = 18 —
  2. a - \frac{1}{a} = 4
  3. (a + \frac{1}{a})^2 = 20

iii. a^3 - \frac{1}{a^3} = 76

Which one of the following is correct?

(a) i & ii (b) i & iii (c) ii & iii (d) i, ii & iii

  1. If \tan\theta = \sqrt{3}, then \sec\theta = ?

(a) \frac{2}{\sqrt{3}} (b) \frac{2}{3} (c) \frac{\sqrt{3}}{2} (d) 2

  1. What is the length (in cm) of a chord of a circle with radius 30 cm, which is at a distance of 9 cm from the center?

(a) 12 (b) 21 (c) 24 (d) 42

  1. If x = -5, in which quadrant does the point obtained from the equation 3x - 2y = 5 lie?

(a) First (b) Second (c) Third (d) Fourth

  1. The ratio of two numbers is 2 : 3 and their L.C.M. is 24. What is their H.C.F.?

(a) 8 (b) 4 (c) 2 (d) 1

  1. How many independent data inputs are required to construct a specific quadrilateral?

(a) 2 (b) 3 (c) 4 (d) 5

  1. If the difference between the two acute angles of a right-angled triangle is 10^\circ, what is the measure of the larger acute angle?

(a) 40^\circ (b) 50^\circ (c) 55^\circ (d) 80^\circ

  1. If 2.8^{1-x} = 1, what is the value of x?

(a) \frac{2}{3} (b) \frac{3}{4} (c) \frac{4}{3} (d) \frac{3}{2}

  1. If f(x) = x^2 - 5x - 6, for which values of x will f(x) = 0?

(a) 2, -3 (b) 1, -6 (c) -1, 6 (d) -2, 3

  1. In an equilateral triangle \Delta ABC, if BD = 2 cm, what is the length of AD in cm?

(a) 4\sqrt{3} (b) \frac{4}{\sqrt{3}} (c) 2\sqrt{3} (d) \sqrt{3}

  1. What is the measure of each interior angle of a regular hexagon?

(a) 135^\circ (b) 120^\circ (c) 108^\circ (d) 90^\circ

  1. What is the characteristic of the common logarithm of 0.00000786?

(a) \bar{6} (b) \bar{5} (c) 5 (d) 6

  1. Two circles with diameters 8 cm and 6 cm touch each other internally. What is the distance between their centers?

(a) 14 cm (b) 7 cm (c) 2 cm (d) 1 cm

  1. If \sin(90^\circ - \theta) = \frac{\sqrt{3}}{2}, then \theta = ?

(a) 30^\circ (b) 45^\circ (c) 60^\circ (d) 90^\circ

  1. Which one can be drawn if the perimeter and one angle are given?

(a) Rhombus (b) Rectangle (c) Parallelogram (d) Trapezium

  1. \Delta LMN and \Delta PQR are similar. If MN : QR = 4 : 5, then \Delta PQR : \Delta LMN = ?

(a) 16 : 25 (b) 4 : 5 (c) 5 : 4 (d) 25 : 16

  1. For a right circular cylinder with base radius 5 cm and height 6 cm —
  2. Base area = 25\pi sq cm
  3. Volume = 150\pi cu cm

iii. Curved surface area = 60\pi sq cm

Which one of the following is correct?

(a) i & ii (b) i & iii (c) ii & iii (d) i, ii & iii

  1. What is the solution set of the equation \sqrt{4x - 7} + 1 = 0?

(a) \{\frac{8}{4}\} (b) \{\frac{4}{8}\} (c) \{\emptyset\} (d) \{2\}

  1. \frac{1 + \cot^2 A}{1 - \cos^2 A} = ?

(a) \csc^4 A (b) \sin^4 A (c) \cot^4 A (d) \cos^4 A

  1. While drawing a 50^\circ angle in a right-angled triangle, which one of the following is correct?

(a) Base > Perpendicular (b) Base < Perpendicular (c) Base = Perpendicular (d) Perpendicular = Hypotenuse

Answer Key:

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

 

 

Mathematics (Creative Questions)

Rajshahi Board – 2025
Subject Code: 109 | Time: 2 Hours 30 Minutes | Full Marks: 70

[Note: Answer any 7 questions taking at least 2 from Group-A (Algebra), 2 from Group-B (Geometry), 2 from Group-C (Trigonometry & Mensuration), and 1 from Group-D (Statistics).]

Group A — Algebra

  1. x^4 + x^{-4} = 119 and y = \sqrt{5} - \sqrt{2}.

(a) If (2p + q, 5) = (7, q), find the value of (p, q). [2]

(b) Prove that x^2 - 3x - 1 = 0 when x > 0. [4]

(c) Find the value of \frac{y^3 + 27}{y^3}. [4]

  1. (i) A = \frac{4^{n-1}}{(2^{n+1})^{n-1} \div (2^{n-1})^{n-1}}, B = \log_{\sqrt{3}}\sqrt{9}.

(ii) \frac{p^2 + q^2}{q^2 + r^2} = \frac{(p - q)^2}{(q - r)^2}.

(a) Simplify: (3c^{-1} + 2d^{-1})^{-1}. [2]

(b) Show that A = B. [4]

(c) Prove that p, q, r are in continued proportion. [4]

  1. 7 + f + g + 448 + h is a part of a geometric series.

(a) Which term of the series 125 + 25 + 5 + \dots is \frac{1}{125}? [2]

(b) Find the values of g and h. [4]

(c) Considering the first term of the given series as the first term and the common ratio as the common difference of an arithmetic series, find the value of n if the sum of its first n terms is 987. [4]

Group B — Geometry

  1. In \Delta ABC, P, Q, R are the midpoints of sides AB, AC, and BC respectively.

(a) If the area of a circle is 12\pi sq cm, find its diameter. [2]

(b) Prove that PQ \parallel BC and PQ = \frac{1}{2}BC. [4]

(c) Prove that AB + AC > 2AR. [4]

  1. O is the center of the circle DEF, and ray CD and ray CE are two tangents to the circle.

(a) Prove that the diameter is the largest chord of a circle. [2]

(b) Prove that \angle DOE = 2\angle DFE. [4]

(c) Prove that line segment CO is the perpendicular bisector of the chord of contact DE. [4]

  1. The base of a triangle a = 4 cm, one base angle \angle x = 60^\circ, and the sum of the other two sides s = 9 cm.

(a) If one side of a rhombus is a and one angle is \angle x, draw the rhombus. [Drawing marks required] [2]

(b) Draw the triangle with drawing marks and description. [4]

(c) Draw the incircle of an equilateral triangle having side length \frac{s}{2}. [Drawing marks and description required] [4]

Group C — Trigonometry & Mensuration

  1. a = \sec\theta, b = \csc\theta, and c = \tan\theta.

(a) Show that b\sqrt{a^2 - 1} = a. [2]

(b) If a + c = x, prove that \sin\theta = \frac{x^2 - 1}{x^2 + 1}. [4]

(c) If \frac{1}{a} + \frac{1}{b} = \sqrt{2}, find the value of \theta, where \theta is an acute angle. [4]

  1. (i) A tree leaned over in a storm without separating completely. The broken part makes a 30^\circ angle with the ground and touches the ground at a distance of 10\sqrt{3} meters from the base of the tree.

(ii) An airplane is flying at a point between two places P and Q. The angles of depression of P and Q from the airplane are 60^\circ and 45^\circ respectively.

(a) If A = 60^\circ, find the value of 3\sin A - 4\sin^3 A. [2]

(b) Find the total height/length of the tree. [4]

(c) If PQ = 1200 meters, find the height of the airplane from the ground. [4]

  1. (i) If the side length of an equilateral triangle is increased by 4 meters, its area increases by 16\sqrt{3} sq meters.

(ii) The inner and outer diameters of an iron pipe are 14 cm and 16 cm respectively, and the height of the pipe is 4.5 meters.

(a) The total surface area of a cube is 300 sq cm. Find the length of its diagonal. [2]

(b) Find the perimeter of the equilateral triangle. [4]

(c) If 1 cu cm of iron weighs 7.2 grams, calculate the weight of the iron in the pipe. [4]

Group D — Statistics

  1. The frequency distribution table of marks obtained in Mathematics by 60 students of Class 10 at D.S. High School is as follows:
Class Interval 44 – 48 49 – 53 54 – 58 59 – 63 64 – 68 69 – 73
Frequency 4 11 13 19 8 5

(a) Find the midpoint of the class preceding the modal class. [2]

(b) Find the mean using the shortcut method. [4]

(c) Draw a frequency polygon for the given data with a brief description. [4]

  1. A frequency distribution table is given below:
Class Interval 31 – 40 41 – 50 51 – 60 61 – 70 71 – 80 81 – 90 91 – 100
Frequency 4 6 8 12 9 7 4

(a) Find the mean of the numbers 6, 9, 8, 0, 5, 2. [2]

(b) Find the median from the given table. [4]

(c) Draw an Ogive curve for the given data with a brief description. [4]

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