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: