Sub. code 0081
NEB — GRADE XII
2082
Old Question
Class 12 Mathematics Old Question 2082
The candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.
Pass Marks : 32
सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)
This old question paper is for Class 12 Mathematics, 2082 (subject code 0081), carrying full marks of 75 with a pass mark of 32, to be completed within 3 Hours. Model answers are available for questions that have one — reveal them with a free account (a few reveals) or a paid plan (unlimited).
Group 'A'
Rewrite the correct option of each question in your same answer sheet.
Which one is the relation between permutation and combination of '' things taken '' things at a time?
If the system of equations and , what is the value of ?
Which one of the following is the value of ?
In which condition the line will be tangent to the circle ?
What is if and ?
(0,1,0)
If , and , which one of the following is ?
Which one of the following is the slope of normal to the curve at ?
−7
What is the integral of ?
Which one of the following is the homogeneous differential equation?
Which is the integrating factor of differential linear equation ?
Two simultaneous equations are given as and . What is the equation after eliminating ?
What is the maximum height attained by a particle in a projectile motion if initial velocity and angle of inclination are and ? []
Group 'B'
Write the expansion of ; .
Write the total number of permutations of a set having elements.
State De-Moivre's theorem.
Write the sum of cubes of first natural numbers.
Write the augmented matrix of the system of equation and .
A committee is to be chosen from '' boys and 6 girls and is to consist 2 boys and 3 girls. If 120 committees are formed, what is the number of boys represented by ''?
The square roots of any complex number are and . Write the complex number in polar form.
In any triangle PQR, if , prove that the sides are in A.P.
If and are two vectors, find the projection on .
Find the eccentricity of conic .
Find the eccentricity of ellipse whose major axis is four times its minor axis and passes through the point .
Consider the following data for supply () and the price () of a commodity for last six years.
Year in B.S. | 2075 | 2076 | 2077 | 2078 | 2079 | 2080 |
45 | 50 | 56 | 62 | 65 | 70 | |
65 | 70 | 75 |
Find the correlation coefficient between and .
Calculate the supply when the price of commodity is Rs. 150.
Write the derivative of .
Define L-Hospital's rule.
Write the condition where the curve has tangent parallel to y-axis.
Write the integral of .
Write the standard form of first order linear differential equation.
Find the derivative of .
Integrate: .
Using simplex method, maximize subject to constraint , , , , .
Two forces A and B acting parallel to the length and base of an inclined plane respectively, would each of them singly support a weight 'R' on the plane, prove that .
Group 'C'
If the middle term in the expansion is 1120, find the value of a.
Using mathematical induction, prove that .
Solve the following linear equations by using matrix method:
The scalar product of two vectors and cross product of two vectors are interrelated. Explain.
If the cosines of two angles of a triangle are proportional to the opposite sides, show that it is an isosceles triangle.
Establish the condition that the line may be normal to the parabola .
Find the rate of change of volume of a sphere with respect to its surface area when radius is .
Integrate:
Solve:
Paper Overview & Analysis
2082
Year
Old Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
41
Question Items
Question Type Breakdown
Group Breakdown
Chapter Breakdown
| Derivative and its Application | 6 items | 8 marks |
| Anti-Derivatives | 4 items | 8 marks |
| Differential Equations | 4 items | 6 marks |
| Permutation and Combination | 3 items | 4 marks |
| Matrix Based System of Linear Equations | 3 items | 5 marks |
| Trigonometry | 3 items | 6 marks |
| Vectors | 3 items | 6 marks |
| Conic Sections | 2 items | 4 marks |
| Binomial Theorem | 2 items | 3 marks |
| Complex Number | 2 items | 4 marks |
| Sequence and Series | 2 items | 4 marks |
| Probability | 1 item | 1 mark |
Chapter breakdown covers 35 of 41 question items on this paper — the rest aren't tagged to a chapter yet.
2 question items offered alternative ("OR") chapters and aren't attributed to either, since only one could be attempted.