HSEB Nepal

a) A body of weight w is suspended by strings of length 3 m and 4 m attached to two points in the same horizontal line whose distance apart is 5 m. Find the tensions along the strings.

b) A uniform beam, 4 m long, is supported in a horizontal position by two props which are 3 m apart, so that the beam projects one meter beyond one of the props. Show that the force on one of the props is double of that on the other. (Grade 12 HSEB)

11. Lives of two models of refrigerators turned in for new models in a recent survey are.. (Grade 12 HSEB)

10. Find the direction cosines of two lines which are connected by the relations 2l + 2m ñ n = 0, mn + nl + lm = 0.(Grade 12 HSEB)

9. For any positive integer n, prove that,(Grade 12 HSEB)

b) Define linearly independent vectors. Show that the following vectors are linearly dependent.(Grade-12 HSEB)

a) What is a conic section? Find the equation of the tangent to the parabola y2 = 8x which is parallel to the straight line 2x ñ 3y + 7 = 0. Also find its point of contact.(Grade-12  HSEB)

7 a) State the first mean value theorem of differential calculus and interpret it geometrically. Using it to f (x) =sin x on [0, x], prove that sin x ≤ x for x ≥ 0.

Find the integral (Grade-12 HSEB)

b) What is a group? If a binary operation * is defined on a set .(Grade-12 HSEB)

c) The average percentage of failures in a certain examination is 40. What is the probability that out of 5 candidates, at least 3 will be passed in the examination.-(Grade-12 HSEB)

c) The average percentage of failures in a certain examination is 40. What is the probability that out of 5 candidates, at least 3 will be passed in the examination.-(Grade-12 HSEB)

Solve the differential equation

Find the integral

c) Find the cosines of the angle between the vectors:

रुपायन : लिङ् ग , व च न , प रुष र आदर लिङ्गका आधारमा वाक्य   परि वर्तन ( रुपायन ) पुलि ङ्गबाट स्त्रि लिङ्गमा परि वर्त न ग र्दा वा स्त्रिलिङ्गबा ट पु लि ङ्गमा परि व र् तन ग र् दा , क र् ता र क्रि या परि व र्त न ग र्नु प र्छ । साथै क र्ता ले लिने विशे षणलाई पनि क र्ता अ नु सार परि वर्त न ग र्नु प र्छ । लिङ्ग परि व र्त न ग र्दा वचन , प रु ष वा आदर परिवर्तन गर्नुहुदैन । लिङ्ग ( का आधारमा ) परिवर्तनका के ही उदाहरण ह रू य स प्रकार छ नः क . उसको भाइ घरम छ । ( स्त्रि लिङ् ग ) = उसकी बिहनी घरम छे । ख . उ नी मिहिनेती छिन । ( पुलिङ्ग ) = उ नी मिहिनेती छन् । वचनका आधारमा वाक्य परि वतन वचनका आधारमा वाक्य परि व र् तनका केहि उदाह र णहरु य स प्रकार छ न : क . ऊ गीत गा उँछ । ( बह वचन ) =   ऊ गीत गाउ छ। ख . मरी बिहनीका साथी सा॑ असल छन । ( एक वच न ) = मरी बिहनीका साथी सा ह्रै असल छ न । = मरी बिहनीकी साथी सा ह्रै असल छ । ग .   मेरा काका का छोर...