Secondary Education Examination · Class 10

SEE 2082 Optional Mathematics question paper, Bagmati Province

SEE 2082 Optional Mathematics (Bagmati Province, RE-2021'A') has 33 questions worth 75 marks, with 3 hours to answer them. It has 10 of 1 mark, 8 of 2 marks, 11 of 3 marks and 4 of 4 marks.

The SEE examination is conducted by the National Examinations Board (NEB), Nepal. This paper was typed up from the original and checked by the GyanMul team.

Every question is given in Nepali and English, as the paper prints it.

33 questions
75 marks
3 hours
Code RE-2021'A'

Sit this paper as a timed mock test, freeनेपालीमा पढ्नुहोस्

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Questions

Answers are shown for the 10 one-mark questions. They are GyanMul's model answers: the NEB does not publish an answer key, so these are not the board's answers.

Question 11 mark
Write the definition of identity function.
एकात्मक फलनको परिभाषा लेख्नुहोस् ।
Answer: A function f : A → A defined by f(x) = x for every $x \in A$ is called an identity function — every element is its own image.
Question 21 mark
If a and b are two positive numbers, write the relation between their arithmetic mean (AM) and geometric mean (GM).
यदि a र b दुई धनात्मक सङ्ख्याहरू भए तिनीहरूको समानान्तरीय मध्यमा (AM) र गुणोत्तर मध्यमा (GM) बिचको सम्बन्ध लेख्नुहोस् ।
Answer: $AM \ge GM$ , that is $(a + b)/2 \ge \sqrt{ab}$ , with equality only when a = b.
Question 31 mark
Write the condition of the continuity of the function f(x) at the point x = a.
फलन f(x) विन्दु x = a मा निरन्तर हुने अवस्था लेख्नुहोस् ।
Answer: f(x) is continuous at x = a if f(a) is defined, $\lim_{x \to a} f(x)$ exists, and $\lim_{x \to a} f(x) = f(a)$ .
Question 41 mark
What is the inverse matrix of matrix (1 0 / 0 1)? Write it.
मेट्रिक्स (1 0 / 0 1) को विपरीत मेट्रिक्स के हुन्छ, लेख्नुहोस् ।
Answer: The matrix is the $2\times 2$ identity matrix I, and $I^{-1} = I = [ 1 0$ ; 0 1 ].
Question 51 mark
Under what condition are the pair of straight lines represented by the equation $ax^{2} + 2$ hxy + $by^{2} = 0$ coincident? Write it.
समीकरण $ax^{2} + 2$ hxy + $by^{2} = 0$ ले जनाउने जोडा रेखाहरू कुन अवस्थामा सम्पाती हुन्छन् ? लेख्नुहोस् ।
Answer: The lines are coincident when $h^{2} = ab$ .
Question 61 mark
In which condition is a circle formed when a plane surface intersects a cone? Write it.
कुन अवस्थामा एउटा सोलीलाई समतलीय सतहले प्रतिच्छेदन गर्दा वृत्त बन्छ, लेख्नुहोस् ।
Answer: When the plane cuts the cone parallel to its base, that is perpendicular to the axis of the cone.
Question 71 mark
Express sinA in terms of $\tan (A/2)$ .
sinA लाई $\tan (A/2)$ को रूपमा व्यक्त गर्नुहोस् ।
Answer: sinA $= 2 \tan (A/2) / (1 + \tan^{2}(A/2))$
Question 81 mark
Express $Cos(A-B) - Cos(A+B)$ as a product.
$Cos(A-B) - Cos(A+B)$ लाई गुणनफलको रूपमा व्यक्त गर्नुहोस् ।
Answer: $\cos (A - B) - \cos (A + B) = 2$ sinA sinB
Question 91 mark
Write the formula to find the angle $\theta$ between the vectors a⃗ and b⃗.
भेक्टरहरू a⃗ र b⃗ बिचको कोण $\theta$ पत्ता लगाउने सूत्र लेख्नुहोस् ।
Answer: $\cos \theta = (\vec{a} \cdot \vec{b}$ )/(|a⃗| |b⃗|), so $\theta = \cos^{-1}[(\vec{a} \cdot \vec{b}$ )/(|a⃗| |b⃗|)].
Question 101 mark
In an inversion transformation, if a point P lies at the centre of inversion circle then where does its image P' lie? Write it.
विपरीत स्थानान्तरणमा यदि बिन्दु P उत्क्रम वृत्तको केन्द्रविन्दुमा पर्दछ भने P को प्रतिबिम्ब P' कहाँ पर्दछ, लेख्नुहोस् ।
Answer: The image lies at infinity — it is undefined, because $OP \times OP′ = r^{2}$ cannot be satisfied when $OP = 0$ .
Question 112 marks
If $y - 2$ is a factor of polynomial $p(y) = y^{3} - 2ay^{2} + ay - 2$ , find the value of a.
यदि बहुपदीय $p(y) = y^{3} - 2ay^{2} + ay - 2$ को एउटा गुणन खण्ड $y - 2$ भए a को मान पत्ता लगाउनुहोस् ।
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Question 122 marks
Show the inequality $2x + y \le 2$ in the graph paper.
असमानता $2x + y \le 2$ लाई लेखा चित्रमा देखाउनुहोस् ।
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Question 132 marks
If the equations $ax - 5y = 3$ and $4x + 3y = 4$ have $D = 26$ , find the value of 'a' using Cramer's rule.
यदि समीकरणहरू $ax - 5y = 3$ र $4x + 3y = 4$ मा $D = 26$ भए क्रामरको नियम प्रयोग गरी 'a' को मान पत्ता लगाउनुहोस् ।
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Question 142 marks
Find the separate equation of the pair of lines represented by the equation $6x^{2} + 5xy - 6y^{2} - 3x + 2y = 0$ .
समीकरण $6x^{2} + 5xy - 6y^{2} - 3x + 2y = 0$ ले प्रतिनिधित्व गर्ने जोडा रेखाहरूको छुट्टा छुट्टै समीकरण पत्ता लगाउनुहोस् ।
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Question 152 marks
Without using calculator and trigonometric table prove that: $\sin 75^\circ \cdot \cos 15^\circ = (2 + \sqrt{3})/4$
क्याल्कुलेटर र त्रिकोणमितीय तालिका प्रयोग नगरी प्रमाणित गर्नुहोस् : $\sin 75^\circ \cdot \cos 15^\circ = (2 + \sqrt{3})/4$
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Question 162 marks
Solve: $\sin 2x -$ sinx $= 0 (0^\circ \le x \le 90^\circ )$
हल गर्नुहोस्: $\sin 2x -$ sinx $= 0 (0^\circ \le x \le 90^\circ )$
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Question 172 marks
Find the angle between the vectors 3i⃗ + 4j⃗ and 8i⃗ $- 6\vec{j}$ .
भेक्टरहरू 3i⃗ + 4j⃗ र 8i⃗ $- 6\vec{j}$ बिचको कोण पत्ता लगाउनुहोस् ।
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Question 182 marks
In a continuous series if $\sum f|m - \bar{x}| = 1134, N = 100$ and mean (x̄) $= 40$ , find the mean deviation and its coefficient.
कुनै एउटा निरन्तर श्रेणीमा $\sum f|m - \bar{x}| = 1134, N = 100$ र मध्यक (x̄) $= 40$ भए मध्यक भिन्नता र यसको गुणाङ्क पत्ता लगाउनुहोस् ।
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Question 193 marks
If f(x) = (2x + 5)/3 and g(x) = (x + 5)/2 such that $g\circ g(x) = f^{-1}(x)$ , find the value of x.
यदि f(x) = (2x + 5)/3 र g(x) = (x + 5)/2 मा $g\circ g(x) = f^{-1}(x)$ भए x को मान पत्ता लगाउनुहोस् ।
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Question 203 marks
Solve graphically: $y = x^{2}$ and $y = 2x + 3$
लेखाचित्र विधिद्वारा हल गर्नुहोस्: $y = x^{2}$ and $y = 2x + 3$
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Question 213 marks
Function f(x) is defined as follows. f(x) = x + 2 for $x < 2$ $f(x) = 4$ for $x = 2$ $f(x) = 3x - 2$ for $x > 2$ Is the function f(x) continuous at the point $x = 2$ ? Give reason.
फलन f(x) निम्नानुसार परिभाषित छ । f(x) = x + 2 for $x < 2$ $f(x) = 4$ for $x = 2$ $f(x) = 3x - 2$ for $x > 2$ के फलन f(x) विन्दु $x = 2$ मा निरन्तर छ ? कारण दिनुहोस् ।
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Question 223 marks
Solve by using matrix method: $2x - 3y = 7$ and $3x - 4y = 10$
मेट्रिक्स विधिको प्रयोग गरी हल गर्नुहोस् : $2x - 3y = 7$ र $3x - 4y = 10$
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Question 233 marks
If the co-ordinates of one end of a diameter of the circle $x^{2} + y^{2} - 2x - 10y + 1 = 0$ is (1, 0), find the co-ordinates of the other end.
यदि वृत्त $x^{2} + y^{2} - 2x - 10y + 1 = 0$ को एउटा व्यासको एक छेउको निर्देशाङ्कहरू (1, 0) भए अर्को छेउको निर्देशाङ्कहरू पत्ता लगाउनुहोस् ।
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Question 243 marks
Prove that: $4\sin^{3}\theta \cdot \cos 3\theta + 4\cos^{3}\theta \cdot \sin 3\theta = 3\sin 4\theta$
प्रमाणित गर्नुहोस्: $4\sin^{3}\theta \cdot \cos 3\theta + 4\cos^{3}\theta \cdot \sin 3\theta = 3\sin 4\theta$
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Question 253 marks
If $P + Q + R = 180^\circ$ , prove that: $\sin (P + Q - R) + \sin (Q + R - P) + \sin (R + P - Q) = 4$ sinP $\cdot$ sinQ $\cdot$ sinR
यदि $P + Q + R = 180^\circ$ भए प्रमाणित गर्नुहोस् : $\sin (P + Q - R) + \sin (Q + R - P) + \sin (R + P - Q) = 4$ sinP $\cdot$ sinQ $\cdot$ sinR
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Question 263 marks
The angles of depression of the top and bottom of a pole 20 m high observed from the top of a tower are found to be $30^\circ$ and $60^\circ$ respectively. Find the height of the tower.
एउटा धरहराको टुप्पोबाट त्यसको ठिक अगाडि रहेको 20 मिटर अग्लो एउटा खम्बाको टुप्पो र फेदमा हेर्दा अवनती कोणहरू क्रमशः $30^\circ$ र $60^\circ$ पाइयो भने धरहराको उचाइ पत्ता लगाउनुहोस् ।
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Question 273 marks
Find the co-ordinates of the vertices of image triangle of the $\Delta$ ABC with vertices A(3, 6), B(4, 2) and C(2, 2) under the reflection on the x-axis by matrix method.
शीर्षविन्दुहरू A(3, 6), B(4, 2) र C(2, 2) भएको $\Delta$ ABC लाई x-अक्षमा परावर्तन गर्दा प्राप्त हुने प्रतिबिम्ब त्रिभुजको शीर्षविन्दुहरूका निर्देशाङ्कहरू मेट्रिक्स विधिद्वारा पत्ता लगाउनुहोस् ।
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Question 283 marks
Calculate the quartile deviation of the data given below where the first quartile is 16.25. Marks obtained : $0-10 | 10-20 | 20-30 | 30-40 | 40-50$ No. of Students : 6 | 8 | 12 | 11 | 7
तल दिइएको तथ्याङ्कको पहिलो चतुर्थांश 16.25 भए चतुर्थांशीय भिन्नता पत्ता लगाउनुहोस् : प्राप्ताङ्क (Marks obtained) : $0-10 | 10-20 | 20-30 | 30-40 | 40-50$ विद्यार्थी सङ्ख्या (No. of Students) : 6 | 8 | 12 | 11 | 7
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Question 293 marks
Calculate the standard deviation from the given data. Marks obtained : $0-10 | 0-20 | 0-30 | 0-40 | 0-50$ No. of Students : 5 | 15 | 35 | 40 | 50
दिइएको तथ्याङ्कबाट स्तरीय भिन्नता निकाल्नुहोस् : प्राप्ताङ्क (Marks obtained) : $0-10 | 0-20 | 0-30 | 0-40 | 0-50$ विद्यार्थी सङ्ख्या (No. of Students) : 5 | 15 | 35 | 40 | 50
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Question 304 marks
The sum of three consecutive numbers of a geometric series is 56. If 1, 7 and 21 be subtracted from the numbers respectively, they form an arithmetic series. Find the numbers.
गुणोत्तर श्रेणीमा रहेका तीनओटा क्रमिक सङ्ख्याहरूको योगफल 56 छ । यदि ती सङ्ख्याहरूबाट क्रमशः 1, 7 र 21 घटाउँदा सङ्ख्याहरू समानान्तरीय श्रेणीमा हुन्छन् भने ती सङ्ख्याहरू पत्ता लगाउनुहोस् ।
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Question 314 marks
The co-ordinates of vertices P and R of a square PQRS are (3, 7) and $(-1, 3)$ respectively. Find the equation of diagonal QS.
एउटा वर्ग PQRS को शीर्षविन्दुहरू P र R का निर्देशाङ्कहरू क्रमशः (3, 7) र $(-1, 3)$ छन् भने विकर्ण QS को समीकरण पत्ता लगाउनुहोस् ।
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Question 324 marks
Prove by vector method that the diagonals of rhombus MNOP are perpendicular to each other.
समबाहु चतुर्भुज MNOP को विकर्णहरू आपसमा लम्ब हुन्छन् भनी भेक्टरविधिद्वारा प्रमाणित गर्नुहोस् ।
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Question 334 marks
R denotes the reflection on the line $y = -x$ and S denotes the rotation about origin through $180^\circ$ . Find the single transformation represented by combined transformation RoS. Using the same single transformation, find the co-ordinates of the vertices of the image of $\Delta$ ABC having vertices $A(1, 2), B(-4, 3)$ and C(3, 5). Also present $\Delta$ ABC and its image on the same graph paper.
R ले रेखा $y = -x$ मा हुने परावर्तन र S ले उद्गमविन्दु वरिपरि $180^\circ$ मा हुने परिक्रमणलाई जनाउँछ भने संयुक्त स्थानान्तरण RoS ले जनाउने एकल स्थानान्तरण पत्ता लगाउनुहोस् । सोही एकल स्थानान्तरण प्रयोग गरी शीर्षविन्दुहरू $A(1, 2), B(-4, 3)$ र C(3, 5) भएको $\Delta$ ABC लाई स्थानान्तरण गर्दा बन्ने प्रतिबिम्बको शीर्षविन्दुहरूका निर्देशाङ्कहरू पत्ता लगाउनुहोस् । साथै $\Delta$ ABC र यसको प्रतिविम्बलाई एउटै लेखा चित्रमा प्रस्तुत गर्नुहोस् ।
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How many questions and marks are in the SEE 2082 Optional Mathematics (Bagmati Province, RE-2021'A') paper?: 33 questions worth 75 marks. There are 10 of 1 mark, 8 of 2 marks, 11 of 3 marks and 4 of 4 marks.
How much time is given for this paper?: 3 hours (180 minutes).
Is this the real board paper?: Yes. It is the SEE 2082 paper printed for Bagmati Province, code RE-2021'A', typed up from the original and checked by the GyanMul team.
Are the answers included?: Answers to the 10 one-mark questions are on this page (GyanMul's model answers; the NEB does not publish an answer key). Worked answers and the marking for every other question are in GyanMul Prep, free with an account.
Can I download this paper as a PDF?: Yes. Press "Print / Save as PDF" at the top of the page and choose "Save as PDF" in your browser's print window.

Source: prep.gyanmul.com/see/past-papers/optional-mathematics/2082/bagmati · GyanMul Prep

SEE 2082 Optional Mathematics question paper, Bagmati Province

SEE 2082 Optional Mathematics (Bagmati Province, RE-2021'A') has 33 questions worth 75 marks, with 3 hours to answer them. It has 10 of 1 mark, 8 of 2 marks, 11 of 3 marks and 4 of 4 marks.

The SEE examination is conducted by the National Examinations Board (NEB), Nepal. This paper was typed up from the original and checked by the GyanMul team.

Every question is given in Nepali and English, as the paper prints it.

33 questions

75 marks

3 hours

Code RE-2021'A'

The account is free. Timer, marking, worked answers and help from Gurubaa, in one place.

Questions

Answers are shown for the 10 one-mark questions. They are GyanMul's model answers: the NEB does not publish an answer key, so these are not the board's answers.

Question 11 mark

Write the definition of identity function.

एकात्मक फलनको परिभाषा लेख्नुहोस् ।

Answer: A function f : A → A defined by f(x) = x for every

x \in A

is called an identity function — every element is its own image.

Question 21 mark

If a and b are two positive numbers, write the relation between their arithmetic mean (AM) and geometric mean (GM).

यदि a र b दुई धनात्मक सङ्ख्याहरू भए तिनीहरूको समानान्तरीय मध्यमा (AM) र गुणोत्तर मध्यमा (GM) बिचको सम्बन्ध लेख्नुहोस् ।

Answer:

AM \ge GM

, that is

(a + b)/2 \ge \sqrt{ab}

, with equality only when a = b.

Question 31 mark

Write the condition of the continuity of the function f(x) at the point x = a.

फलन f(x) विन्दु x = a मा निरन्तर हुने अवस्था लेख्नुहोस् ।

Answer: f(x) is continuous at x = a if f(a) is defined,

\lim_{x \to a} f(x)

exists, and

\lim_{x \to a} f(x) = f(a)

Question 41 mark

What is the inverse matrix of matrix (1 0 / 0 1)? Write it.

मेट्रिक्स (1 0 / 0 1) को विपरीत मेट्रिक्स के हुन्छ, लेख्नुहोस् ।

Answer: The matrix is the

2\times 2

identity matrix I, and

I^{-1} = I = [ 1 0

; 0 1 ].

Question 51 mark

Under what condition are the pair of straight lines represented by the equation $ax^{2} + 2$ hxy + $by^{2} = 0$ coincident? Write it.

समीकरण $ax^{2} + 2$ hxy + $by^{2} = 0$ ले जनाउने जोडा रेखाहरू कुन अवस्थामा सम्पाती हुन्छन् ? लेख्नुहोस् ।

Answer: The lines are coincident when

h^{2} = ab

Question 61 mark

In which condition is a circle formed when a plane surface intersects a cone? Write it.

कुन अवस्थामा एउटा सोलीलाई समतलीय सतहले प्रतिच्छेदन गर्दा वृत्त बन्छ, लेख्नुहोस् ।

Answer: When the plane cuts the cone parallel to its base, that is perpendicular to the axis of the cone.

Question 71 mark

Express sinA in terms of $\tan (A/2)$ .

sinA लाई $\tan (A/2)$ को रूपमा व्यक्त गर्नुहोस् ।

Answer: sinA

= 2 \tan (A/2) / (1 + \tan^{2}(A/2))

Question 81 mark

Express $Cos(A-B) - Cos(A+B)$ as a product.

$Cos(A-B) - Cos(A+B)$ लाई गुणनफलको रूपमा व्यक्त गर्नुहोस् ।

Answer:

\cos (A - B) - \cos (A + B) = 2

sinA sinB

Question 91 mark

Write the formula to find the angle $\theta$ between the vectors a⃗ and b⃗.

भेक्टरहरू a⃗ र b⃗ बिचको कोण $\theta$ पत्ता लगाउने सूत्र लेख्नुहोस् ।

Answer:

\cos \theta = (\vec{a} \cdot \vec{b}

)/(|a⃗| |b⃗|), so

\theta = \cos^{-1}[(\vec{a} \cdot \vec{b}

)/(|a⃗| |b⃗|)].

Question 101 mark

In an inversion transformation, if a point P lies at the centre of inversion circle then where does its image P' lie? Write it.

विपरीत स्थानान्तरणमा यदि बिन्दु P उत्क्रम वृत्तको केन्द्रविन्दुमा पर्दछ भने P को प्रतिबिम्ब P' कहाँ पर्दछ, लेख्नुहोस् ।

Answer: The image lies at infinity — it is undefined, because

OP \times OP′ = r^{2}

cannot be satisfied when

OP = 0

Question 112 marks

If $y - 2$ is a factor of polynomial $p(y) = y^{3} - 2ay^{2} + ay - 2$ , find the value of a.

यदि बहुपदीय $p(y) = y^{3} - 2ay^{2} + ay - 2$ को एउटा गुणन खण्ड $y - 2$ भए a को मान पत्ता लगाउनुहोस् ।

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Question 122 marks

Show the inequality $2x + y \le 2$ in the graph paper.

असमानता $2x + y \le 2$ लाई लेखा चित्रमा देखाउनुहोस् ।

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Question 132 marks

If the equations $ax - 5y = 3$ and $4x + 3y = 4$ have $D = 26$ , find the value of 'a' using Cramer's rule.

यदि समीकरणहरू $ax - 5y = 3$ र $4x + 3y = 4$ मा $D = 26$ भए क्रामरको नियम प्रयोग गरी 'a' को मान पत्ता लगाउनुहोस् ।

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Question 142 marks

Find the separate equation of the pair of lines represented by the equation $6x^{2} + 5xy - 6y^{2} - 3x + 2y = 0$ .

समीकरण $6x^{2} + 5xy - 6y^{2} - 3x + 2y = 0$ ले प्रतिनिधित्व गर्ने जोडा रेखाहरूको छुट्टा छुट्टै समीकरण पत्ता लगाउनुहोस् ।

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Question 152 marks

Without using calculator and trigonometric table prove that: $\sin 75^\circ \cdot \cos 15^\circ = (2 + \sqrt{3})/4$

क्याल्कुलेटर र त्रिकोणमितीय तालिका प्रयोग नगरी प्रमाणित गर्नुहोस् : $\sin 75^\circ \cdot \cos 15^\circ = (2 + \sqrt{3})/4$

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Question 162 marks

Solve: $\sin 2x -$ sinx $= 0 (0^\circ \le x \le 90^\circ )$

हल गर्नुहोस्: $\sin 2x -$ sinx $= 0 (0^\circ \le x \le 90^\circ )$

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Question 172 marks

Find the angle between the vectors 3i⃗ + 4j⃗ and 8i⃗ $- 6\vec{j}$ .

भेक्टरहरू 3i⃗ + 4j⃗ र 8i⃗ $- 6\vec{j}$ बिचको कोण पत्ता लगाउनुहोस् ।

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Question 182 marks

In a continuous series if $\sum f|m - \bar{x}| = 1134, N = 100$ and mean (x̄) $= 40$ , find the mean deviation and its coefficient.

कुनै एउटा निरन्तर श्रेणीमा $\sum f|m - \bar{x}| = 1134, N = 100$ र मध्यक (x̄) $= 40$ भए मध्यक भिन्नता र यसको गुणाङ्क पत्ता लगाउनुहोस् ।

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Question 193 marks

If f(x) = (2x + 5)/3 and g(x) = (x + 5)/2 such that $g\circ g(x) = f^{-1}(x)$ , find the value of x.

यदि f(x) = (2x + 5)/3 र g(x) = (x + 5)/2 मा $g\circ g(x) = f^{-1}(x)$ भए x को मान पत्ता लगाउनुहोस् ।

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Question 203 marks

Solve graphically: $y = x^{2}$ and $y = 2x + 3$

लेखाचित्र विधिद्वारा हल गर्नुहोस्: $y = x^{2}$ and $y = 2x + 3$

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Question 213 marks

Function f(x) is defined as follows. f(x) = x + 2 for $x < 2$ $f(x) = 4$ for $x = 2$ $f(x) = 3x - 2$ for $x > 2$ Is the function f(x) continuous at the point $x = 2$ ? Give reason.

फलन f(x) निम्नानुसार परिभाषित छ । f(x) = x + 2 for $x < 2$ $f(x) = 4$ for $x = 2$ $f(x) = 3x - 2$ for $x > 2$ के फलन f(x) विन्दु $x = 2$ मा निरन्तर छ ? कारण दिनुहोस् ।

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Question 223 marks

Solve by using matrix method: $2x - 3y = 7$ and $3x - 4y = 10$

मेट्रिक्स विधिको प्रयोग गरी हल गर्नुहोस् : $2x - 3y = 7$ र $3x - 4y = 10$

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Question 233 marks

If the co-ordinates of one end of a diameter of the circle $x^{2} + y^{2} - 2x - 10y + 1 = 0$ is (1, 0), find the co-ordinates of the other end.

यदि वृत्त $x^{2} + y^{2} - 2x - 10y + 1 = 0$ को एउटा व्यासको एक छेउको निर्देशाङ्कहरू (1, 0) भए अर्को छेउको निर्देशाङ्कहरू पत्ता लगाउनुहोस् ।

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Question 243 marks

Prove that: $4\sin^{3}\theta \cdot \cos 3\theta + 4\cos^{3}\theta \cdot \sin 3\theta = 3\sin 4\theta$

प्रमाणित गर्नुहोस्: $4\sin^{3}\theta \cdot \cos 3\theta + 4\cos^{3}\theta \cdot \sin 3\theta = 3\sin 4\theta$

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Question 253 marks

If $P + Q + R = 180^\circ$ , prove that: $\sin (P + Q - R) + \sin (Q + R - P) + \sin (R + P - Q) = 4$ sinP $\cdot$ sinQ $\cdot$ sinR

यदि $P + Q + R = 180^\circ$ भए प्रमाणित गर्नुहोस् : $\sin (P + Q - R) + \sin (Q + R - P) + \sin (R + P - Q) = 4$ sinP $\cdot$ sinQ $\cdot$ sinR

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Question 263 marks

The angles of depression of the top and bottom of a pole 20 m high observed from the top of a tower are found to be $30^\circ$ and $60^\circ$ respectively. Find the height of the tower.

एउटा धरहराको टुप्पोबाट त्यसको ठिक अगाडि रहेको 20 मिटर अग्लो एउटा खम्बाको टुप्पो र फेदमा हेर्दा अवनती कोणहरू क्रमशः $30^\circ$ र $60^\circ$ पाइयो भने धरहराको उचाइ पत्ता लगाउनुहोस् ।

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Question 273 marks

Find the co-ordinates of the vertices of image triangle of the $\Delta$ ABC with vertices A(3, 6), B(4, 2) and C(2, 2) under the reflection on the x-axis by matrix method.

शीर्षविन्दुहरू A(3, 6), B(4, 2) र C(2, 2) भएको $\Delta$ ABC लाई x-अक्षमा परावर्तन गर्दा प्राप्त हुने प्रतिबिम्ब त्रिभुजको शीर्षविन्दुहरूका निर्देशाङ्कहरू मेट्रिक्स विधिद्वारा पत्ता लगाउनुहोस् ।

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Question 283 marks

Calculate the quartile deviation of the data given below where the first quartile is 16.25. Marks obtained : $0-10 | 10-20 | 20-30 | 30-40 | 40-50$ No. of Students : 6 | 8 | 12 | 11 | 7

तल दिइएको तथ्याङ्कको पहिलो चतुर्थांश 16.25 भए चतुर्थांशीय भिन्नता पत्ता लगाउनुहोस् : प्राप्ताङ्क (Marks obtained) : $0-10 | 10-20 | 20-30 | 30-40 | 40-50$ विद्यार्थी सङ्ख्या (No. of Students) : 6 | 8 | 12 | 11 | 7

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Question 293 marks

Calculate the standard deviation from the given data. Marks obtained : $0-10 | 0-20 | 0-30 | 0-40 | 0-50$ No. of Students : 5 | 15 | 35 | 40 | 50

दिइएको तथ्याङ्कबाट स्तरीय भिन्नता निकाल्नुहोस् : प्राप्ताङ्क (Marks obtained) : $0-10 | 0-20 | 0-30 | 0-40 | 0-50$ विद्यार्थी सङ्ख्या (No. of Students) : 5 | 15 | 35 | 40 | 50

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Question 304 marks

The sum of three consecutive numbers of a geometric series is 56. If 1, 7 and 21 be subtracted from the numbers respectively, they form an arithmetic series. Find the numbers.

गुणोत्तर श्रेणीमा रहेका तीनओटा क्रमिक सङ्ख्याहरूको योगफल 56 छ । यदि ती सङ्ख्याहरूबाट क्रमशः 1, 7 र 21 घटाउँदा सङ्ख्याहरू समानान्तरीय श्रेणीमा हुन्छन् भने ती सङ्ख्याहरू पत्ता लगाउनुहोस् ।

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Question 314 marks

The co-ordinates of vertices P and R of a square PQRS are (3, 7) and $(-1, 3)$ respectively. Find the equation of diagonal QS.

एउटा वर्ग PQRS को शीर्षविन्दुहरू P र R का निर्देशाङ्कहरू क्रमशः (3, 7) र $(-1, 3)$ छन् भने विकर्ण QS को समीकरण पत्ता लगाउनुहोस् ।

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Question 324 marks

Prove by vector method that the diagonals of rhombus MNOP are perpendicular to each other.

समबाहु चतुर्भुज MNOP को विकर्णहरू आपसमा लम्ब हुन्छन् भनी भेक्टरविधिद्वारा प्रमाणित गर्नुहोस् ।

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Question 334 marks

R denotes the reflection on the line $y = -x$ and S denotes the rotation about origin through $180^\circ$ . Find the single transformation represented by combined transformation RoS. Using the same single transformation, find the co-ordinates of the vertices of the image of $\Delta$ ABC having vertices $A(1, 2), B(-4, 3)$ and C(3, 5). Also present $\Delta$ ABC and its image on the same graph paper.

R ले रेखा $y = -x$ मा हुने परावर्तन र S ले उद्गमविन्दु वरिपरि $180^\circ$ मा हुने परिक्रमणलाई जनाउँछ भने संयुक्त स्थानान्तरण RoS ले जनाउने एकल स्थानान्तरण पत्ता लगाउनुहोस् । सोही एकल स्थानान्तरण प्रयोग गरी शीर्षविन्दुहरू $A(1, 2), B(-4, 3)$ र C(3, 5) भएको $\Delta$ ABC लाई स्थानान्तरण गर्दा बन्ने प्रतिबिम्बको शीर्षविन्दुहरूका निर्देशाङ्कहरू पत्ता लगाउनुहोस् । साथै $\Delta$ ABC र यसको प्रतिविम्बलाई एउटै लेखा चित्रमा प्रस्तुत गर्नुहोस् ।

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Questions learners ask

How many questions and marks are in the SEE 2082 Optional Mathematics (Bagmati Province, RE-2021'A') paper?

33 questions worth 75 marks. There are 10 of 1 mark, 8 of 2 marks, 11 of 3 marks and 4 of 4 marks.

How much time is given for this paper?

3 hours (180 minutes).

Is this the real board paper?

Yes. It is the SEE 2082 paper printed for Bagmati Province, code RE-2021'A', typed up from the original and checked by the GyanMul team.

Are the answers included?

Answers to the 10 one-mark questions are on this page (GyanMul's model answers; the NEB does not publish an answer key). Worked answers and the marking for every other question are in GyanMul Prep, free with an account.

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