Sub. code 0081
NEB — GRADE XII
2078
Old Question
Class 12 Mathematics Old Question 2078
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, 2078 (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 answer in your answer sheet
If 1, ω, ω² are the cube roots of unity, then:
ω = ω²
ω² = ω³
1 + ω + ω² = 0
1 + ω = ω²
The number of ways that 7 beads of different colours can be strung together so as to form a necklace is:
5040
2520
720
360
tan⁻¹(5/12) is equal to:
sin⁻¹(12/13)
sin⁻¹(12/13)
sec⁻¹(12/13)
cosec⁻¹(12/13)
If 2cosθ + 1 = 0, then the general value of θ is:
If 2cosθ + 1 = 0, then the general value of θ is:
nπ + 2π/3, n ∈ ℤ
2nπ ± 2π/3, n ∈ ℤ
2nπ + π/3, n ∈ ℤ
If a = 2i and b = 3j, then b × a is:
−6k
6k
6i
6j
The set of points whose sum of distances from two fixed points is constant represents:
Circle
Parabola
Hyperbola
Ellipse
Four unbiased coins are tossed successively. The mean and variance differ by:
1
2
3
4
d³y/dx³ + 5(d²y/dx²)² + 4(dy/dx)⁴ + 6 = 0 is:
1
2
3
4
According to L’Hospital’s rule,
lim(x→0) x³/sin x is equal to:
3/4
0
1/4
∞
For solving:
(i) 3x + 4y = 18
(ii) 3y − x = 7
Using Gauss elimination, apply:
eqn(i) + 4 eqn(ii)
eqn(i) + 3 eqn(ii)
eqn(i) + eqn(ii)
eqn(ii) + 3 eqn(i)
Force of gravity on 10 kg (g = 9.8 m/s²):
9.8 Joule
9.8 Newton
98 Joule
98 Newton
Group B
The binomial expression for two algebraic terms a and x is given as (a + x)ⁿ.
Write the binomial theorem for any positive integer n in expansion form.
Write the general term of the expansion.
Write any one property of binomial coefficients.
Write the single term for C(n,r) + C(n,r−1).
How many terms are there in the expression?
Given n⁴ < 10ⁿ for a fixed positive integer n ≥ 2, prove that (n + 1)⁴ < 10ⁿ⁺¹ using the principle of mathematical induction.
Evaluate:
cos (sin⁻¹(3/5) + sin⁻¹(5/13))
Using the vector method, find the area of the triangle with vertices A(1, 4, 6), B(−2, 5, 1) and C(1, −1, 1).
The information given below relates to the advertisement and sales of a departmental store in lakhs of Nepalese rupees.
Advertisement Expenditure (X) | Sales (Y) | |
|---|---|---|
Arithmetic mean | 20 | 100 |
Standard deviation | 3 | 12 |
Correlation coefficient between (X) and (Y) = 0.8 |
Find the two regression equations related to the above data.
What should be the advertisement expenditure if the departmental store wants to attain a sales target of Rs. 200 lakhs?
Suman and Nikita are studying the application of derivatives and integration in a class. They ask each other the quiz questions as given below. On the basis of these questions answer the following.
f′(x) and g′(x) are derivatives of the functions f(x) and g(x). What is the expression equal to
lim (x→a) f(x)/g(x) according to L’Hospital’s rule for form ∞/∞?
State Rolle’s Theorem.
What is the expression equal to ∫(1/(x² + a²)) dx?
What does ‘C’ represent in the expression?
Write a difference between derivative and antiderivative?
Integrate 1/(x^4 − 1) dx using the concept of partial fraction. Also, give an example of proper rational
fraction and improper rational fraction.
Write any one difference between like parallel forces and unlike parallel forces. A heavy uniform beam whose mass is 60 kg is suspended in a horizontal position by two vertical strings each of which can sustain a tension of 52.5 kg wt. How far from the centre of the beam must a body of mass 30 kg be placed so that one of the strings may just break?
If the demand function P = 85 − 4Q − Q², find the consumer’s surplus at demand 4 units and price 64 units. Also make a revenue function for demand equation P = 20 + 5Q − Q². Obtain the standard quadratic equation for marginal revenue. Q represents the number of units demanded and P represents the price.
Group C
A college hostel accommodating 1000 students: one of them came from abroad with infection of coronavirus, then the hostel was isolated. If the rate at which the virus spreads is assumed to be proportional to the product of the number N of infected students and the number of non-infected students, and the number of infected students is 50 after 4 days.
Express the above information in the form of the differential equation.
Solve the differential equation
Show that more than 95% of students will be infected after 10 days.
Solve by simplex method the LP problem to maximize
Z = 7x + 5y
subject to
x + 2y ≤ 6,
4x + 3y ≤ 12,
x ≥ 0, y ≥ 0.
State the Trapezoidal rule theorem. Also estimate the value of ∫₁⁵ x⁴ dx using Trapezoidal rule with 4 sub-intervals.
Using Simpson’s one-third rule, compute ∫₀² (3x + 1) dx. Also, find the error of approximation from its actual value.
Paper Overview & Analysis
2078
Year
Old Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
34
Question Items
Question Type Breakdown
Group Breakdown