Sub. code 0081
NEB — GRADE XII
2080
Old Question
Class 12 Mathematics Old Question 2080
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, 2080 (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 questions in your answer sheets
Consider ‘*’ is binary operation on set A. Which one of the following is associative law? a, b, c, e and a⁻¹ are elements of A.
a * b = b * a
(a*b) * c =a*(b*c)
a *a⁻¹ = a⁻¹ * a = e
One of the root of a quadratic equation is 3 + 2√5. What is the sum of roots of the quadratic equation?
-11
3 - 2√5
6
4√5
What is the domain of y = sin⁻¹x?
(-1, 1)
(-∞, ∞)
[0, 1]
[-1, 1]
Which one of the following is general solution for 2cosθ - 1 = 0?
nπ + (-1)ⁿ π/3, n ∈ I
nπ ± π/3, n ∈ I
nπ + π/3, n ∈ I
2nπ ± π/3, n ∈ I
Which one of the following conics is represented by the equation 4x² - 16x + y² = 48?
Hyperbola
Ellipse
Parabola
Circle
Consider a⃗ × b⃗ = c⃗ × d⃗ and a⃗ × c⃗ = b⃗ × d⃗. Which one of the following is parallel to (b⃗ - c⃗)?
a-b
a-c
a-d
c-d
Consider A and B be two dependent events. If , and , what is ?
1/52
1/26
1/13
1/2
What is the derivative of with respect to ?
a)
2cosh(x/4)
Which of the following is the integral value of ?
Two simultaneous linear equations are given as 2x + y = 5 and x + 4y = 6.
What is the equation obtained after eliminating x?
7y = 5
7y = 6
7y = 7
What is the amount of gravity exerted by the earth on the mass of 100 kg?
g is acceleration due to gravity.
100 Newtons
100g Newtons
g/100 Newtons
100/g Newtons
Group B
Short answer questions
For any positive integer , .
Name the theorem for positive integer .
Reduce the given statement when we replace by ?
What does '' represent in the above statement?
What does '' represent in the above statement?
Write any one application of the above statement?
How many three digit numbers can be formed from the digits 2, 3, 4, 5, 6, 7?
For what value of , the coefficients of and are equal in the expansion ?
Consider tan⁻¹(1/2) + cot⁻¹(3) = tan⁻¹x. What is the value of x?
Show that .
The height (x) in cm and weight (y) in kg are given for 5 persons in a community.
X | 160 | 162 | 165 | 161 | 162 |
|---|---|---|---|---|---|
Y | 63 | 62 | 64 | 60 | 61 |
Find the correlation coefficient between X and Y and regression coefficient Y on X.
In the figure, f(x) is a function defined in [a, b].
Name the theorem applicable to the figure.
Write the necessary conditions of the theorem.
What does f′(c) represent?
Write the equation of tangent at C(x₁, y₁).
Write the equation of normal at C(x₁, y₁).
Solve:
Using L-Hospital's rule, evaluate:
Using Simplex method, maximize , subject to the constraints , ; ; .
Two like parallel forces and act at points and respectively. Show that if they interchange positions, the point of application of the resultant is displaced by a distance of , where .
Consider a hypothetical economy of two industries A and B represented by the table given below:
Producer | User A | User B | Final Demand | Total Output |
|---|---|---|---|---|
A | 500 | 350 | 150 | 1000 |
B | 320 | 360 | 120 | 800 |
The data are in millions of rupees of products. Determine the output vector of the economy if final demand of A is increased by 10% and the final demand of B is decreased by 10%
Group C
Long answer questions
If , show that
Using mathematical induction, prove that: for .
Use Cramer's rule to solve the system of linear equations.
] , ,
Find the foci and centre of the hyperbola with equation:
9x² − 16y² − 144 = 0
Find the direction cosines of the plane passing through the points
(2, 0, 0) and (0, 2, 2)
Find the equation of the plane passing through the points and and parallel to the line .
If
Does obey the Mean Value Theorem in ? Give reason with process.
Prove that
An equation relating to stability of an aeroplane is . Where is the velocity and are constants. Under which condition the solution of the equation does not exist? Give reason.
Paper Overview & Analysis
2080
Year
Old Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
39
Question Items
Question Type Breakdown
Group Breakdown
Chapter Breakdown
| Derivative and its Application | 4 items | 10 marks |
| Trigonometry | 3 items | 4 marks |
| Vectors | 3 items | 5 marks |
| Complex Number | 2 items | 2 marks |
| Conic Sections | 2 items | 3 marks |
| Anti-Derivatives | 2 items | 4 marks |
| Binomial Theorem | 2 items | 5 marks |
| Probability | 1 item | 1 mark |
| System of Linear Equations | 1 item | 1 mark |
| Dynamics | 1 item | 1 mark |
| Permutation and Combination | 1 item | 2 marks |
| Correlation and Regression | 1 item | — |
| Linear Programming Problems | 1 item | 5 marks |
| Statics | 1 item | 5 marks |
| Sequence and Series | 1 item | 2 marks |
| Matrix Based System of Linear Equations | 1 item | 4 marks |
| Differential Equations | 1 item | 3 marks |
Chapter breakdown covers 28 of 39 question items on this paper — the rest aren't tagged to a chapter yet.