Sub. code 0081
NEB — GRADE XII
2082
Model Question
Class 12 Mathematics Model 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 model 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 in your answer sheet.
The number of ways in which three different digit numbers that can be formed from the integers 0, 1, 2, 3 and 4 is
60
48
125
24
The sum of the first ‘n’ odd natural numbers is
n(n + 1)
n(n + 1) / 2
n²
n(n + 1)(2n + 1) / 6
Which of the following is the area of a triangle ABC
abc / 4R
√[s(s − a)(s − b)(s − c)]
1/2 bc sin A
all of the above
The eccentricity of the hyperbola 3x² − y² = 15 is
√(2/3)
2 / √3
3
2
If and are two vectors such that , then the angle between them is:
$0$
$\frac{\pi}{4}$
$\frac{\pi}{6}$
Karl Pearson’s correlation coefficient is independent of:
change of origin only
change of scale only
change of origin and scale both
none of them
The function is:
differentiable but not continuous at $x = 0$
continuous but not differentiable at $x = 0$
both continuous and differentiable at $x = 0$
neither continuous nor differentiable at
The point on the curve at which the tangent is parallel to the x-axis is:
$(2, 4)$
$(2, 2)$
$(-2, 2)$
$\frac{1}{\sqrt{3}} \tan^{-1}\left(\frac{x}{\sqrt{3}}\right) + c$
$\frac{1}{\sqrt{3}} \tan^{-1}\left(\frac{\sqrt{3}x}{1}\right) + c$
$\sqrt{3} \tan^{-1}\left(\frac{x}{\sqrt{3}}\right) + c$
The order and degree of the differential equation
are:
3 and 2
3 and 1
3 and 4
3 and 3
In Gauss elimination method, the coefficient of the first variable in the first equation must be:
zero
non-zero
negative
positive
Group B
Short answer question
Find the eccentricity and the focus of the ellipse
From 10 persons, in how many ways can a selection of 4 be made:
when one particular person is always included?
when two particular persons are always excluded?
Find the fifth term of
Find the coefficient of in the expansion of
Expand the following up to four terms:
Write the expansion for
Find the number of terms in the expansion of
In any $\triangle ABC$, if $a^4 + b^4 + c^4 = 2c^2(a^2 + b^2)$, prove that $C = 45^\circ$ or $135^\circ$
If $A = 30^\circ$, $B = 45^\circ$ and $a = 6\sqrt{2}$, solve the triangle.
Using vector method, prove that
$\frac{a}{\sin A} = \frac{b}{\sin B}$
Find the unit vector perpendicular to each of the vectors
$2\hat{i} - \hat{j} + \hat{k}$ and $3\hat{i} + 4\hat{j} - \hat{k}$
Compute the following from the given data:
Age in years () | 5 | 15 | 30 | 45 | 50 | 60 |
|---|---|---|---|---|---|---|
Weight in kg () | 10 | 35 | 50 | 65 | 55 | 45 |
Find the correlation between age and weight.
Estimate the most probable age of the weight 37 kg.
Write the derivative of .
Define L’Hospital’s rule.
Find the point on the curve where the tangent is parallel to the x-axis.
Write the integral of
Define linear form of a differential equation.
Evaluate:
Solve:
Solve the following system of equations by Gauss-Seidel method:
Using simplex method, solve the following LP problem:
Maximize subject to
Group C
Long answer question
Using row equivalent matries solve the system:
Prove by principle of mathematical induction that is divisible by 7.
If , prove that
A tangent to the parabola makes an angle of with the axis of . Find the equation of the tangent.
Define Euler’s form of the complex number. Express the complex number in polar form
Find the equations of the tangents to the circle
which are parallel to the line
.
A man of height 1.5 m walks away from a lamp post of height 4.5 m at the rate of 20 cm/s. How fast is the shadow lengthening when he is 4.2 m from the post?
Integrate:
Solve:
Paper Overview & Analysis
2082
Year
Model Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
43
Question Items
Question Type Breakdown
Group Breakdown