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Top 10 Model Question Sets ... 247 चाहनासँग \( £ 5000 \) छ। सो दिनमा विनिमय दर \( £ 1= \) रु. 150 र 1 अमेरिकन डलर = रु. 125 रहेको छ । Chahana has £5000. The exchange rate of pound sterling on the day is \( £ 1= \) Rs. 150 and the exchange rate of 1 American dollar \( = \) Rs. 125. (a) खरिददर र बिक्रीदर भन्नाले के बुभिन्छ ? What do you mean by buying rate and selling rate? [1U] (b) \( £ 5000 \) सँग कति अमेरिकन डलर साट्न सकिन्छ ? How many American dollars can be exchanged with \( £ 5000 \) ? [1HA] (c) यदि अमेरिकन डलरको तुलनामा नेपाली मुद्रा \( 5 \% \) ले अवमूल्यन भयो र पाउन्ड स्टर्लिडको तुलनामा चाहि नेपाली मुद्रामा \( 2 \% \) ले अधिमूल्यन भयो भने, पाउन्ड स्टर्लिङको तुलनामा अमेरिकी डलरमा कति प्रतिशतले अवमूल्यन वा अधिमूल्यन भयो ? पत्ता लगाउनुहोस् । If there is \( 5 \% \) devaluation in Nepali currency in comparison to American dollars and \( 2 \% \) revaluation in Nepali currency in comparison to pound sterling, by what percentage is the US dollar revaluated or devaluated in comparison to the pound sterling? Find it. एक जना गणित शिक्षकले आफ्नो कक्षाका प्रत्येक विद्यार्थीलाई वर्गाकार आधार भएको पिरामिड बनाउने प्रयोगात्मक कार्य दिन्छन् । प्रतिभाले आधारको क्षेत्रफल \( 64 \mathrm{~cm}^{2} \) र पूरा सतहको क्षेत्रफल \( 144 \mathrm{~cm}^{2} \) भएको पिरामिड बनार्उंधिन् । नम्रताले भने प्रत्येक किनारा प्रतिभाको भन्दा दोब्बर हुने गरी बनाउँछिन् । A math teacher assigns a practical work of preparing square based pyramid to each student of the class. Prativa prepares a pyramid of base area \( 64 \mathrm{~cm}^{2} \) and total surface area \( 144 \mathrm{~cm}^{2} \). Namrata makes each edge just double of the edges of the pyramid made by Prativa. (a) प्रतिभाको पिरामिडको छड्के सतहको उचाइ पत्ता लगाउनुहोस् । Find the slant height of Prativa's pyramid. [1K] (b) नम्रताको पिरामिडको पूरा सतहको क्षेत्रफल कति होला ? What is the total surface area of Namrata's pyramid? [2U] (c) प्रतिभाले दाबी गई्छिन कि उनको पिरामिडको आयतन नम्रताको पिरामिडको आयतनको \( 25 \% \) छ। के यो सही हो ? होइन भने यो कति प्रतिशत छ ? गणना गरी तय गर्नुहोस् । Prativa claims that the volume of her pyramid is \( 25 \% \) of the volume of the Namrata's pyramid. Is it true? If not, then what percent is it? Decide by calculation. [1HA] एउटा व्यस्त पार्कको एकापट्टि कुनामा एउटा आइसक्रिमको पसल छ। पसलेले उचाइ 7 cm र भित्री आयतन \( 32.34 . \mathrm{cm}^{3} \)
Geometry Feb 11, 2025
10. (a) हल गर्नुहोस् (Solve): \( 5^{1-x}+5^{x-2}=5 \) (b) यदि \( a^{2}=b+c, b^{2}=c+a \) र \( c^{2}=a+b \) भए प्रमाणित गर्नुहोस् (If \( a^{2}=b+c, b^{2}=c+a \) and \( c^{2}=a+b \) then prove that): \( \frac{1}{a+1}+\frac{1}{\mathrm{~b}+1}+\frac{1}{c+1}=1 \) Ans: (a) 0,2 [2]
Algebra Feb 11, 2025
c) If \( 10 \% \) discoum. the item. d) If \( 13 \% \) VAT on the selling price of an article amounts to Rs 130 selling price of the article. e) If \( 20 \% \) of profit on the cost price of an item amounts to Rs 400 , find price of the item.
Arithmetic Feb 10, 2025
c) The area of a rectangle is \( 70 \mathrm{~cm}^{2} \) and it is 7 m broad. \( \begin{array}{ll}\text { (i) Find its length } & \text { (ii) Find its perimeter }\end{array} \)
Geometry Feb 10, 2025
(ii) Find the perimeter of the garden. (iv) Find the length of wire required to fence the garden The area of a rectangle is \( 70 \mathrm{~cm}^{2} \) and it is 7 m broad. \( \begin{array}{ll}\text { i) Find its length } & \text { (ib) Find its perimeler }\end{array} \)
Geometry Feb 10, 2025
14. 21 मिटर उचाइको रंख हावाले भाँचिएको छ र त्यसको माथिल्लो भागले \( 30^{\circ} \) को कोण बनाएर जमिन छोएको छ । A tree of height 21 m is broken by wind and its top has touched the ground by making an angle of \( 30^{\circ} \). (a) भाँचिएको भागले बाँकी भागसंग बनाएको कोण पत्ता लगाउनुहोस् । Find the angle formed by broken part with remaining part. [1K] [Ans: \( 60^{\circ} \) ] (b) रुखको फेदबाट, रखको बाँकी भागको उचाइ पत्ता लगाउनुहोस् । From the bottom of the tree, find the height of the remaining part of the tree.[1U] [Ans: 7 m\( ] \) (c) रखको भाँचिएको भागको लम्बाइ गणना गर्नुहोस् । Calculate the length of the broken part of the tree. [1A] [Ans: 14 m\( ] \) (d) रखखो फेददेखि भाँचिएको हखको दुपाले जमिनमा छोएसम्मको दुरी पत्ता लगाउनुहोस् । Find the distance from the bottom of the tree to the top of the broken part touched on the ground. [1HA] [Ans: \( 7 \sqrt{3} \mathrm{~m} \) ]
Trigonometry Feb 10, 2025
10. (a) हल गर्नुहोस् (Solve): \( 5^{1-x}+5^{x-1}=5 \frac{1}{5} \) \( \left\{\begin{array}{l}\text { (b) यदि } a^{2}=b+c, b^{2}=c+a \text { र } c^{2}=a+b \text { भए प्रमाणित गर्नुहोस् (If } a^{2}=b+c, b^{2}=c+a \text { and } c^{2}=a+b \text { then prove that): } \\ \frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}=1\end{array}\right. \)
Algebra Feb 10, 2025
a. If \( \mathrm{A}(-3,2), \mathrm{B}(-5,4) \) and \( \mathrm{C}(-2,6) \) are the vertices of \( \triangle \mathrm{ABC} \) in a graph and rotate it through \( 90^{\circ} \) in clockwise direction about origin. Write down the coordinates of the vertices of the image. (3) b. If the center of a circle \( \mathrm{O}(5,4) \) and \( \mathrm{A}(9,4) \) be any point its circumference, find the radius of the circle. (1)
Geometry Feb 10, 2025
\( \begin{array}{ll}\int x^{2} e^{3 x^{3}} d x & \text { c. } \int\left(1+\frac{1}{x^{2}}\right) e^{x-\frac{1}{x}} d x \\ \int \sec ^{2} x e^{\tan x+1} d x & \text { f. } \int e^{\sin x \cos x} \cos 2 x d x \\ \int \frac{e^{2 x}}{e^{x}+1} d x\end{array} \)
Calculus Feb 09, 2025
a) A petrol tank has \( 3.6 \times 10^{3} \) litres of petrol. If \( 1.5 \times 10^{4} \) litres of petrol is added into it how much petrol does it have now? b) An underground water tank contains \( 1.8 \times 10^{4} \) litres of water. When \( 1.8 \times 10^{3} \) litres of water is used up how much water is left in the tank?
Arithmetic Feb 09, 2025
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