Secondary Education Examination · Class 10

SEE 2082 Optional Mathematics question paper, Technical Stream

SEE 2082 Optional Mathematics (Technical Stream, RE-2023) 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-2023

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
If $(x - a)$ is a factor of polynomial f(x), what is the value of f(a)? Write it.
यदि बहुपदीय f(x) को एउटा गुणनखण्ड $(x - a)$ भए f(a) को मान कति हुन्छ, लेख्नुहोस् ।
Answer: $f(a) = 0$
Question 21 mark
What is the nᵗʰ term of a geometric series having first term 'a' and common ratio 'r'? Write it.
पहिलो पद 'a' र समान अनुपात 'r' भएको गुणोत्तर श्रेणीको n औँ पद कति हुन्छ, लेख्नुहोस् ।
Answer: $t_{n} = a\cdot r^{n-1}$
Question 31 mark
Write the interval notation for $-2 \le x \le 5$ .
$-2 \le x \le 5$ लाई अन्तराल सङ्केतमा लेख्नुहोस् ।
Answer: $[-2, 5]$ Both ends carry "or equal to" $(\le )$ , so both limits are included. The interval is therefore closed, and takes a square bracket at each end.
Question 41 mark
Write the determinant of singular matrix.
एकल मेट्रिक्सको डिटरमिन्यान्ट लेख्नुहोस् ।
Answer: 0 (zero) A singular (singular) matrix is a matrix whose determinant is zero — and therefore its inverse matrix does not exist.
Question 51 mark
The slopes of two straight lines $L_{1}$ and $L_{2}$ are $m_{1}$ and $m_{2}$ respectively. Write the formula for finding the angle between them.
दुई सरल रेखाहरू $L_{1}$ र $L_{2}$ को भुकाव क्रमशः $m_{1}$ र $m_{2}$ भए ती रेखाहरूबिचको कोण पत्ता लगाउने सूत्र लेख्नुहोस् ।
Answer: $\tan \theta = \pm (m_{1} - m_{2}) / (1 + m_{1}m_{2})$
Question 61 mark
Write the equation of circle whose centre is (h, k) and radius 'r' units.
केन्द्र (h, k) र अर्धव्यास 'r' एकाइ भएको वृत्तको समीकरण लेख्नुहोस् ।
Answer: $(x - h)^{2} + (y - k)^{2} = r^{2}$ (If the center is the origin (0, 0) this becomes $x^{2} + y^{2} = r^{2}$ .)
Question 71 mark
Express $\cos 2\theta$ in terms of $\sin \theta$ .
$\cos 2\theta$ लाई $\sin \theta$ को रूपमा व्यक्त गर्नुहोस् ।
Answer: $\cos 2\theta = 1 - 2\sin^{2}\theta$
Question 81 mark
Express $2\cos ((C + D)/2) \cdot \cos ((C - D)/2)$ in terms of sum or difference form.
$2\cos ((C + D)/2) \cdot \cos ((C - D)/2)$ लाई योग वा अन्तरको रूपमा व्यक्त गर्नुहोस् ।
Answer: $2\cos ((C + D)/2) \cdot \cos ((C - D)/2) =$ cosC + cosD
Question 91 mark
If the vectors a⃗ and b⃗ are perpendicular to each other, then what is the value of a⃗ $\cdot \vec{b}$ ? Write it.
यदि भेक्टरहरू a⃗ र b⃗ आपसमा लम्ब छन् भने a⃗ $\cdot \vec{b}$ को मान कति हुन्छ ? लेख्नुहोस् ।
Answer: a⃗ $\cdot \vec{b} = 0$
Question 101 mark
If the point P lies on the circumference of inversion circle, then where does the inversion point P' lie? Write it.
यदि उत्क्रम वृत्तको परिधिमा बिन्दु P पर्छ भने उत्क्रम बिन्दु P' कता पर्छ ? लेख्नुहोस् ।
Answer: P' also lies on the same circumference — that is, at the same position as P (P' and P are the same point). Reason: By the definition of inversion $OP \times OP' = r^{2}$ . Since P lies on the circumference, OP = r, therefore $r \times OP' = r^{2}$ ⟹ OP' = r. As P' lies on the ray OP and at the same distance from the centre, P' and P are the same point.
Question 112 marks
Find the remainder when $x^{3} - x^{2} + 1$ is divided by $(x - 2)$ using remainder theorem.
शेष साध्य प्रयोग गरी $x^{3} - x^{2} + 1$ लाई $(x - 2)$ ले भाग गर्दा आउने शेष पत्ता लगाउनुहोस् ।
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Question 122 marks
Draw the graph of the parabola $y = x^{2}$ .
पाराबोला $y = x^{2}$ को लेखाचित्र खिच्नुहोस् ।
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Question 132 marks
Prove that the matrix $[ 3 -2$ ; $-7 5 ]$ is the inverse of the matrix [ 5 2 ; 7 3 ].
मेट्रिक्स [ 5 2 ; 7 3 ] को विपरीत मेट्रिक्स $[ 3 -2$ ; $-7 5 ]$ हुन्छ भनी प्रमाणित गर्नुहोस् ।
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Question 142 marks
Find the slope of the line parallel to the line $3x - 4y = 10$ .
रेखा $3x - 4y = 10$ सँग समानान्तर हुने रेखाको भुकाव पत्ता लगाउनुहोस् ।
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Question 152 marks
Prove that: $\operatorname{cosec} \theta - \cot \theta = \tan (\theta /2)$
प्रमाणित गर्नुहोस्: $\operatorname{cosec} \theta - \cot \theta = \tan (\theta /2)$
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Question 162 marks
Solve: $3\tan^{2}\theta - 1 = 0 (0^\circ \le \theta \le 90^\circ )$
हल गर्नुहोस्: $3\tan^{2}\theta - 1 = 0 (0^\circ \le \theta \le 90^\circ )$
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Question 172 marks
If a⃗ $= 6\vec{i}$ + 2j⃗ and b⃗ $= 2\vec{i}$ + Kj⃗ are perpendicular to each other, find the value of 'k'.
यदि a⃗ $= 6\vec{i}$ + 2j⃗ र b⃗ $= 2\vec{i}$ + Kj⃗ आपसमा लम्ब छन् भने 'k' को मान पत्ता लगाउनुहोस् ।
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Question 182 marks
In a continuous data, the quartile deviation and first quartile are 14 and 12 respectively. Find the third quartile.
कुनै अविच्छिन्न तथ्याङ्कको चतुर्थांशीय भिन्नता र पहिलो चतुर्थांश क्रमशः 14 र 12 छन् । तेस्रो चतुर्थांश पत्ता लगाउनुहोस् ।
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Question 193 marks
If $f(x) = 2x - 3, g(x) = (x + 2)/3$ and $g^{-1}(x) =$ fof(x), find the value of 'x'.
यदि $f(x) = 2x - 3, g(x) = (x + 2)/3$ र $g^{-1}(x) =$ fof(x) भएको अवस्थामा 'x' को मान पत्ता लगाउनुहोस् ।
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Question 203 marks
Find the maximum value of the objective function $z = 2x + 3y$ under the constraints $x + y \le 6, x - y \ge 2$ and $y \ge 0$ .
शर्तहरू $x + y \le 6, x - y \ge 2$ र $y \ge 0$ को आधारमा उद्देश्य फलन $z = 2x + 3y$ को अधिकतम मान पत्ता लगाउनुहोस् ।
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Question 213 marks
If the function $f(x) = 4x - 1$ is defined, Find the value of f(2.999) and f(3.001). Is function f(x) continuous at the point $x = 3$ ? Give reason.
यदि फलन $f(x) = 4x - 1$ परिभाषित छ भने, (a) f(2.999) र f(3.001) को मान पत्ता लगाउनुहोस् । (b) के फलन f(x) बिन्दु $x = 3$ मा निरन्तर छ ? कारण दिनुहोस् ।
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Question 223 marks
Solve by matrix method: $3x + y = 9$ and $2x - y = 1$
मेट्रिक्स विधिबाट हल गर्नुहोस्: $3x + y = 9$ र $2x - y = 1$
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Question 233 marks
The angle between a pair of straight lines represented by equation $2x^{2} +$ kxy $+ 3y^{2} = 0$ is $45^\circ$ , find the value of k.
समीकरण $2x^{2} +$ kxy $+ 3y^{2} = 0$ ले प्रतिनिधित्व गर्ने एक जोडा रेखाहरूबिचका एउटा कोण $45^\circ$ भए k को मान पत्ता लगाउनुहोस् ।
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Question 243 marks
Prove that: $(1 + \tan \theta ) / (1 - \tan \theta ) = (1 + \sin 2\theta ) / \cos 2\theta$
प्रमाणित गर्नुहोस् : $(1 + \tan \theta ) / (1 - \tan \theta ) = (1 + \sin 2\theta ) / \cos 2\theta$
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Question 253 marks
If $A + B + C = \pi^{c}$ , prove that: $\cos 2A + \cos 2B - \cos 2C = 1 - 2$ sinA $\cdot$ sinB $\cdot$ cosC
यदि $A + B + C = \pi^{c}$ भए, प्रमाणित गर्नुहोस् : $\cos 2A + \cos 2B - \cos 2C = 1 - 2$ sinA $\cdot$ sinB $\cdot$ cosC
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Question 263 marks
The angles of elevation of the top of a tower observed from the points at the distances of 45 m and 20 m from the tower are complementary. Find the height of tower.
एउटा स्तम्भबाट 45 m र 20 m टाढा रहेका बिन्दुबाट स्तम्भको टुप्पोमा हेर्दा उन्नतांश कोणहरू सम्पूरक हुन्छ भने स्तम्भको उचाइ पत्ता लगाउनुहोस् ।
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Question 273 marks
Find the vertices of the image formed when a unit square is transformed by the matrix [ 3 0 ; 1 1 ].
मेट्रिक्स [ 3 0 ; 1 1 ] ले एकाइ वर्गलाई स्थानान्तरण गर्दा बन्ने प्रतिबिम्बका शीर्षबिन्दु पत्ता लगाउनुहोस् ।
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Question 283 marks
Find the mean deviation from the mean of the given data. Class Interval │ 10-30 │ 30-50 │ 50-70 │ 70-90 │ 90-110 ───────────────┼───────┼───────┼───────┼───────┼──────── Frequency │ 2 │ 3 │ 4 │ 2 │ 4
दिइएको तथ्याङ्कको मध्यकबाट मध्यक भिन्नता पत्ता लगाउनुहोस् : वर्गान्तर │ 10-30 │ 30-50 │ 50-70 │ 70-90 │ 90-110 ─────────┼───────┼───────┼───────┼───────┼──────── बारम्बारता │ 2 │ 3 │ 4 │ 2 │ 4
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Question 293 marks
Find the standard deviation from the data given below. Marks Obtained │ 0-10 │ 10-20 │ 20-30 │ 30-40 │ 40-50 ───────────────────────────┼──────┼───────┼───────┼───────┼─────── No. of Students │ 5 │ 4 │ 4 │ 6 │ 1
तल दिइएको तथ्याङ्कको आधारमा स्तरीय भिन्नता पत्ता लगाउनुहोस् : प्राप्ताङ्क (Marks Obtained) │ 0-10 │ 10-20 │ 20-30 │ 30-40 │ 40-50 ───────────────────────────┼──────┼───────┼───────┼───────┼─────── विद्यार्थी सङ्ख्या (No.) │ 5 │ 4 │ 4 │ 6 │ 1
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Question 304 marks
The fifth and tenth terms of an arithmetic series are 8 and 3 respectively. How many terms should be taken from the first so as to make their sum zero? Find it.
एउटा समानान्तरीय श्रेणीको पाँचौँ पद र दशौँ पद क्रमशः 8 र 3 छन् । सो श्रेणीको पहिलो कतिओटा पदको योगफल शून्य हुन्छ ? पत्ता लगाउनुहोस् ।
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Question 314 marks
Find the equation of the circle passing through the points (3, 0), (0, 0) and (0, 2).
बिन्दुहरू (3, 0), (0, 0) र (0, 2) भएर जाने वृत्तको समीकरण पत्ता लगाउनुहोस् ।
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Question 324 marks
In a quadrilateral PQRS, the mid points of the sides PQ, QR, RS and SP are A, B, C and D respectively. Prove by vector method that ABCD is a parallelogram.
चतुर्भुज PQRS मा भुजाहरू PQ, QR, RS र SP का मध्यबिन्दु क्रमशः A, B, C र D छन् । भेक्टर विधिबाट ABCD एउटा समानान्तर चतुर्भुज हो भनी प्रमाणित गर्नुहोस् ।
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Question 334 marks
$\triangle$ ABC with vertices $A(3, 3), B(1, -1)$ and C(5, 0) is reflected on the x-axis. The image so obtained is rotated through $-90^\circ$ about the origin. Find the co-ordinates of the vertices of the images thus formed. Also present the object and the images in the same graph paper.
शीर्षबिन्दुहरू $A(3, 3), B(1, -1)$ र C(5, 0) भएको $\triangle$ ABC लाई x-अक्षमा परावर्तन गरिएको छ । प्राप्त प्रतिबिम्बलाई उद्गम बिन्दुको वरिपरि $-90^\circ$ मा परिक्रमण गरिएको छ । यसरी प्राप्त प्रतिबिम्बका शीर्षबिन्दुका निर्देशाङ्क पत्ता लगाउनुहोस् । साथै वस्तु र प्रतिबिम्बलाई एउटै लेखाचित्रमा प्रस्तुत गर्नुहोस् ।
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Questions learners ask

How many questions and marks are in the SEE 2082 Optional Mathematics (Technical Stream, RE-2023) 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 Technical Stream, code RE-2023, 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/technical-stream · GyanMul Prep

SEE 2082 Optional Mathematics question paper, Technical Stream

SEE 2082 Optional Mathematics (Technical Stream, RE-2023) 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-2023

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

If $(x - a)$ is a factor of polynomial f(x), what is the value of f(a)? Write it.

यदि बहुपदीय f(x) को एउटा गुणनखण्ड $(x - a)$ भए f(a) को मान कति हुन्छ, लेख्नुहोस् ।

Answer:

f(a) = 0

Question 21 mark

What is the nᵗʰ term of a geometric series having first term 'a' and common ratio 'r'? Write it.

पहिलो पद 'a' र समान अनुपात 'r' भएको गुणोत्तर श्रेणीको n औँ पद कति हुन्छ, लेख्नुहोस् ।

Answer:

t_{n} = a\cdot r^{n-1}

Question 31 mark

Write the interval notation for $-2 \le x \le 5$ .

$-2 \le x \le 5$ लाई अन्तराल सङ्केतमा लेख्नुहोस् ।

Answer:

[-2, 5]

Both ends carry "or equal to"

(\le )

, so both limits are included. The interval is therefore closed, and takes a square bracket at each end.

Question 41 mark

Write the determinant of singular matrix.

एकल मेट्रिक्सको डिटरमिन्यान्ट लेख्नुहोस् ।

Answer: 0 (zero) A singular (singular) matrix is a matrix whose determinant is zero — and therefore its inverse matrix does not exist.

Question 51 mark

The slopes of two straight lines $L_{1}$ and $L_{2}$ are $m_{1}$ and $m_{2}$ respectively. Write the formula for finding the angle between them.

दुई सरल रेखाहरू $L_{1}$ र $L_{2}$ को भुकाव क्रमशः $m_{1}$ र $m_{2}$ भए ती रेखाहरूबिचको कोण पत्ता लगाउने सूत्र लेख्नुहोस् ।

Answer:

\tan \theta = \pm (m_{1} - m_{2}) / (1 + m_{1}m_{2})

Question 61 mark

Write the equation of circle whose centre is (h, k) and radius 'r' units.

केन्द्र (h, k) र अर्धव्यास 'r' एकाइ भएको वृत्तको समीकरण लेख्नुहोस् ।

Answer:

(x - h)^{2} + (y - k)^{2} = r^{2}

(If the center is the origin (0, 0) this becomes

x^{2} + y^{2} = r^{2}

Question 71 mark

Express $\cos 2\theta$ in terms of $\sin \theta$ .

$\cos 2\theta$ लाई $\sin \theta$ को रूपमा व्यक्त गर्नुहोस् ।

Answer:

\cos 2\theta = 1 - 2\sin^{2}\theta

Question 81 mark

Express $2\cos ((C + D)/2) \cdot \cos ((C - D)/2)$ in terms of sum or difference form.

$2\cos ((C + D)/2) \cdot \cos ((C - D)/2)$ लाई योग वा अन्तरको रूपमा व्यक्त गर्नुहोस् ।

Answer:

2\cos ((C + D)/2) \cdot \cos ((C - D)/2) =

cosC + cosD

Question 91 mark

If the vectors a⃗ and b⃗ are perpendicular to each other, then what is the value of a⃗ $\cdot \vec{b}$ ? Write it.

यदि भेक्टरहरू a⃗ र b⃗ आपसमा लम्ब छन् भने a⃗ $\cdot \vec{b}$ को मान कति हुन्छ ? लेख्नुहोस् ।

Answer: a⃗

\cdot \vec{b} = 0

Question 101 mark

If the point P lies on the circumference of inversion circle, then where does the inversion point P' lie? Write it.

यदि उत्क्रम वृत्तको परिधिमा बिन्दु P पर्छ भने उत्क्रम बिन्दु P' कता पर्छ ? लेख्नुहोस् ।

Answer: P' also lies on the same circumference — that is, at the same position as P (P' and P are the same point). Reason: By the definition of inversion

OP \times OP' = r^{2}

. Since P lies on the circumference, OP = r, therefore

r \times OP' = r^{2}

⟹ OP' = r. As P' lies on the ray OP and at the same distance from the centre, P' and P are the same point.

Question 112 marks

Find the remainder when $x^{3} - x^{2} + 1$ is divided by $(x - 2)$ using remainder theorem.

शेष साध्य प्रयोग गरी $x^{3} - x^{2} + 1$ लाई $(x - 2)$ ले भाग गर्दा आउने शेष पत्ता लगाउनुहोस् ।

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Question 122 marks

Draw the graph of the parabola $y = x^{2}$ .

पाराबोला $y = x^{2}$ को लेखाचित्र खिच्नुहोस् ।

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Question 132 marks

Prove that the matrix $[ 3 -2$ ; $-7 5 ]$ is the inverse of the matrix [ 5 2 ; 7 3 ].

मेट्रिक्स [ 5 2 ; 7 3 ] को विपरीत मेट्रिक्स $[ 3 -2$ ; $-7 5 ]$ हुन्छ भनी प्रमाणित गर्नुहोस् ।

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Question 142 marks

Find the slope of the line parallel to the line $3x - 4y = 10$ .

रेखा $3x - 4y = 10$ सँग समानान्तर हुने रेखाको भुकाव पत्ता लगाउनुहोस् ।

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Question 152 marks

Prove that: $\operatorname{cosec} \theta - \cot \theta = \tan (\theta /2)$

प्रमाणित गर्नुहोस्: $\operatorname{cosec} \theta - \cot \theta = \tan (\theta /2)$

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Question 162 marks

Solve: $3\tan^{2}\theta - 1 = 0 (0^\circ \le \theta \le 90^\circ )$

हल गर्नुहोस्: $3\tan^{2}\theta - 1 = 0 (0^\circ \le \theta \le 90^\circ )$

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Question 172 marks

If a⃗ $= 6\vec{i}$ + 2j⃗ and b⃗ $= 2\vec{i}$ + Kj⃗ are perpendicular to each other, find the value of 'k'.

यदि a⃗ $= 6\vec{i}$ + 2j⃗ र b⃗ $= 2\vec{i}$ + Kj⃗ आपसमा लम्ब छन् भने 'k' को मान पत्ता लगाउनुहोस् ।

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Question 182 marks

In a continuous data, the quartile deviation and first quartile are 14 and 12 respectively. Find the third quartile.

कुनै अविच्छिन्न तथ्याङ्कको चतुर्थांशीय भिन्नता र पहिलो चतुर्थांश क्रमशः 14 र 12 छन् । तेस्रो चतुर्थांश पत्ता लगाउनुहोस् ।

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Question 193 marks

If $f(x) = 2x - 3, g(x) = (x + 2)/3$ and $g^{-1}(x) =$ fof(x), find the value of 'x'.

यदि $f(x) = 2x - 3, g(x) = (x + 2)/3$ र $g^{-1}(x) =$ fof(x) भएको अवस्थामा 'x' को मान पत्ता लगाउनुहोस् ।

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Question 203 marks

Find the maximum value of the objective function $z = 2x + 3y$ under the constraints $x + y \le 6, x - y \ge 2$ and $y \ge 0$ .

शर्तहरू $x + y \le 6, x - y \ge 2$ र $y \ge 0$ को आधारमा उद्देश्य फलन $z = 2x + 3y$ को अधिकतम मान पत्ता लगाउनुहोस् ।

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Question 213 marks

If the function $f(x) = 4x - 1$ is defined, Find the value of f(2.999) and f(3.001). Is function f(x) continuous at the point $x = 3$ ? Give reason.

यदि फलन $f(x) = 4x - 1$ परिभाषित छ भने, (a) f(2.999) र f(3.001) को मान पत्ता लगाउनुहोस् । (b) के फलन f(x) बिन्दु $x = 3$ मा निरन्तर छ ? कारण दिनुहोस् ।

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Question 223 marks

Solve by matrix method: $3x + y = 9$ and $2x - y = 1$

मेट्रिक्स विधिबाट हल गर्नुहोस्: $3x + y = 9$ र $2x - y = 1$

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Question 233 marks

The angle between a pair of straight lines represented by equation $2x^{2} +$ kxy $+ 3y^{2} = 0$ is $45^\circ$ , find the value of k.

समीकरण $2x^{2} +$ kxy $+ 3y^{2} = 0$ ले प्रतिनिधित्व गर्ने एक जोडा रेखाहरूबिचका एउटा कोण $45^\circ$ भए k को मान पत्ता लगाउनुहोस् ।

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Question 243 marks

Prove that: $(1 + \tan \theta ) / (1 - \tan \theta ) = (1 + \sin 2\theta ) / \cos 2\theta$

प्रमाणित गर्नुहोस् : $(1 + \tan \theta ) / (1 - \tan \theta ) = (1 + \sin 2\theta ) / \cos 2\theta$

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Question 253 marks

If $A + B + C = \pi^{c}$ , prove that: $\cos 2A + \cos 2B - \cos 2C = 1 - 2$ sinA $\cdot$ sinB $\cdot$ cosC

यदि $A + B + C = \pi^{c}$ भए, प्रमाणित गर्नुहोस् : $\cos 2A + \cos 2B - \cos 2C = 1 - 2$ sinA $\cdot$ sinB $\cdot$ cosC

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Question 263 marks

The angles of elevation of the top of a tower observed from the points at the distances of 45 m and 20 m from the tower are complementary. Find the height of tower.

एउटा स्तम्भबाट 45 m र 20 m टाढा रहेका बिन्दुबाट स्तम्भको टुप्पोमा हेर्दा उन्नतांश कोणहरू सम्पूरक हुन्छ भने स्तम्भको उचाइ पत्ता लगाउनुहोस् ।

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Question 273 marks

Find the vertices of the image formed when a unit square is transformed by the matrix [ 3 0 ; 1 1 ].

मेट्रिक्स [ 3 0 ; 1 1 ] ले एकाइ वर्गलाई स्थानान्तरण गर्दा बन्ने प्रतिबिम्बका शीर्षबिन्दु पत्ता लगाउनुहोस् ।

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Question 283 marks

Find the mean deviation from the mean of the given data. Class Interval │ 10-30 │ 30-50 │ 50-70 │ 70-90 │ 90-110 ───────────────┼───────┼───────┼───────┼───────┼──────── Frequency │ 2 │ 3 │ 4 │ 2 │ 4

दिइएको तथ्याङ्कको मध्यकबाट मध्यक भिन्नता पत्ता लगाउनुहोस् : वर्गान्तर │ 10-30 │ 30-50 │ 50-70 │ 70-90 │ 90-110 ─────────┼───────┼───────┼───────┼───────┼──────── बारम्बारता │ 2 │ 3 │ 4 │ 2 │ 4

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Question 293 marks

Find the standard deviation from the data given below. Marks Obtained │ 0-10 │ 10-20 │ 20-30 │ 30-40 │ 40-50 ───────────────────────────┼──────┼───────┼───────┼───────┼─────── No. of Students │ 5 │ 4 │ 4 │ 6 │ 1

तल दिइएको तथ्याङ्कको आधारमा स्तरीय भिन्नता पत्ता लगाउनुहोस् : प्राप्ताङ्क (Marks Obtained) │ 0-10 │ 10-20 │ 20-30 │ 30-40 │ 40-50 ───────────────────────────┼──────┼───────┼───────┼───────┼─────── विद्यार्थी सङ्ख्या (No.) │ 5 │ 4 │ 4 │ 6 │ 1

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Question 304 marks

The fifth and tenth terms of an arithmetic series are 8 and 3 respectively. How many terms should be taken from the first so as to make their sum zero? Find it.

एउटा समानान्तरीय श्रेणीको पाँचौँ पद र दशौँ पद क्रमशः 8 र 3 छन् । सो श्रेणीको पहिलो कतिओटा पदको योगफल शून्य हुन्छ ? पत्ता लगाउनुहोस् ।

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Question 314 marks

Find the equation of the circle passing through the points (3, 0), (0, 0) and (0, 2).

बिन्दुहरू (3, 0), (0, 0) र (0, 2) भएर जाने वृत्तको समीकरण पत्ता लगाउनुहोस् ।

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Question 324 marks

In a quadrilateral PQRS, the mid points of the sides PQ, QR, RS and SP are A, B, C and D respectively. Prove by vector method that ABCD is a parallelogram.

चतुर्भुज PQRS मा भुजाहरू PQ, QR, RS र SP का मध्यबिन्दु क्रमशः A, B, C र D छन् । भेक्टर विधिबाट ABCD एउटा समानान्तर चतुर्भुज हो भनी प्रमाणित गर्नुहोस् ।

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Question 334 marks

$\triangle$ ABC with vertices $A(3, 3), B(1, -1)$ and C(5, 0) is reflected on the x-axis. The image so obtained is rotated through $-90^\circ$ about the origin. Find the co-ordinates of the vertices of the images thus formed. Also present the object and the images in the same graph paper.

शीर्षबिन्दुहरू $A(3, 3), B(1, -1)$ र C(5, 0) भएको $\triangle$ ABC लाई x-अक्षमा परावर्तन गरिएको छ । प्राप्त प्रतिबिम्बलाई उद्गम बिन्दुको वरिपरि $-90^\circ$ मा परिक्रमण गरिएको छ । यसरी प्राप्त प्रतिबिम्बका शीर्षबिन्दुका निर्देशाङ्क पत्ता लगाउनुहोस् । साथै वस्तु र प्रतिबिम्बलाई एउटै लेखाचित्रमा प्रस्तुत गर्नुहोस् ।

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Questions learners ask

How many questions and marks are in the SEE 2082 Optional Mathematics (Technical Stream, RE-2023) 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 Technical Stream, code RE-2023, 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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