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Sub. code 0081

NEB — GRADE XII

Model Question

Class 12 Mathematics Model Question

The candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

समय (Time) : 3 Hoursपूर्णाङ्क (Full Marks) : 75

Pass Marks : 32

सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)

This model question paper is for Class 12 Mathematics, (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.

11 marks[11*1= 11]
1.
[1]

What is an arrangement of the natural numbers called?

a.

Induction

b.

Permutation

c.

Combination

d.

Expectation

2.
[1]

Let be the cube roots of unity. Under which operation is the set closed?

a.

Addition

b.

Subtraction

c.

Multiplication

d.

Division

3.
[1]

What is the domain of ?

a.

$x \geq 1$ or $x \leq -1$

b.

$(-\infty, \infty)$

c.

$-1 < x < 1$

d.

4.
[1]

is a parallelogram. Which one of the following represents area of the parallelogram?

a.

Magnitude of vector product of two vectors along $\overrightarrow{AB}$ and $\overrightarrow{BD}$

b.

Magnitude of vector product of two vectors along $\overrightarrow{AB}$ and $\overrightarrow{DC}$

c.

Magnitude of vector product of two vectors along $\overrightarrow{AC}$ and $\overrightarrow{BC}$

d.

Magnitude of vector product of two vectors along and

5.
[1]

If a conic section has eccentricity , what is the equation of that conic section?

a.

$\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$

b.

$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$

c.

d.

6.
[1]

If for integer , what is the general value of ?

a.

$2n\pi \pm \dfrac{2\pi}{3}$

b.

$n\pi + (-1)^n \dfrac{\pi}{3}$

c.

$n\pi - \dfrac{\pi}{3}$

d.

7.
[1]

Let and be two dependent events. If , and , what is the value of ?

a.

Equal to $P(B/A)$

b.

Equal to $P(A)$

c.

Less than $P(A \cap B)$

d.

Less than

8.
[1]

The edge of a cube increases from to . What would be the approximate increment in volume?

a.

$10^3 \text{ cm}^3$

b.

$10.025^3 \text{ cm}^3$

c.

$7.5187 \text{ cm}^3$

d.

9.
[1]

What is the integrating factor of the differential equation
?

a.

$\tan x$

b.

$e^{\tan x}$

c.

$\sec^2 x$

d.

10.
[1]

What is the number of solutions of the system of linear equations
and ?

a.

One solution

b.

No solution

c.

Infinite solutions

d.

More than one solution

11.
[1]

Forces and are acting along ceiling and floor of a rectangular room. What is the nature of the forces?

a.

Like

b.

Unlike

c.

Collinear

d.

Parallel

Group B

[8 x 5 = 40]
12.

For any positive integer ,

a.
[1]

How many terms are there in the expressions?

b.

Write the binomial coefficients in the expansion.

c.
[1]

Write the general term of the expansion.

d.
[1]

Write the relation among $C(n,r-1)$, $C(n+1,r)$ and $C(n,r)$.

e.
[1]

What is the value of $C_0 + C_1 + C_2 + \cdots + C_n$?

13.
a.
[3]

Using the principle of mathematical induction, show that:

b.
[2]

Find the quadratic equation whose one of the roots is . 

14.
a.
[2]

If $\vec{a}$, $\vec{b}$ and $\vec{c}$ are any three vectors such that
$\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ for $\vec{a} \ne (0,0)$, show that $\vec{b} = \vec{c}$.

b.
[3]

Given and , express and in terms of .

15.
[5]

The price in Rupees and demand in unit of 6 days of a week is given as:

X

10

12

13

12

16

15

Y

40

38

43

45

37

43

Calculate the Pearson’s coefficient of correlation and the regression coefficients of on .

16.
a.
[1]

Write the integral of

b.
[1]

What is the integral of

c.
[1]

Define L’Hospital’s rule.

d.
[1 + 1]

Write the slope of the tangent and normal to the curve at .

17.

a.
[2]

Solve:

b.
[3]

Verify Rolle’s theorem for in .

18.
[5]

Using simplex method, maximize

subject to , ,  

19.
[5]

A particle is projected with a velocity and greatest height is , prove the horizontal range is:

Or
19.

The cost function in thousands of rupees for producing units of maths textbooks is given by:
, 

a) Find the marginal cost function. [3]
b) Find the marginal cost for producing 12,000 maths textbooks. [2]

Group C

24 marks[3*8= 24]
20.
a.
[4]

Using matrix methods, solve the following system of linear equations:

b.

Apply De-Moivre’s theorem to find the value of

c.
[2]

Prove that
\hfill

21.
a.
[2]

Find the direction cosines of the line joining the points and .

b.
[4]

Find the angle between the two diagonals of a cube.

c.
[2]

Find the vertices of the conic section:
.

22.
a.
[2]

If the limiting value of
at is $2f(x)$.

b.
[3]

Write any one homogeneous differential equation in and solve it.

c.
[3]

The concept of anti-derivative is necessary for solving a differential equation. Justify this statement with example.

Mathematics — Model Question NEB Exam

Paper Overview & Analysis

Year

Model Question

Type

75

Full Marks

32

Pass Marks

3 Hours

Duration

39

Question Items

Question Type Breakdown

Short Answer28
MCQ11

Group Breakdown

Group A11 questions · 11 marks
Group B19 questions · 8 x 5 = 40
Group C9 questions · 24 marks

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Mathematics Model Question