Sub. code 0081
NEB — GRADE XII
2081
Old Question
Mathematics Question Paper 2081 (Old 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.
Pass Marks : 32
सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)
This old question question paper is for Class 12 Mathematics, 2081 (subject code 0081), carrying full marks of 75 with a pass mark of 32, to be completed within 3hrs. Answers with step-by-step solutions are available for every question below.
Group A
Rewrite the correct options of each questions in your same answer sheet.
The permutation of ‘n’ things taken ‘r’ at a time when each things may occur any numbers of times is...
n ways
rᵣ ways
nʳ ways
(n×r) ways
Which one of the following is Euler’s form of complex number −i ?
e^{πi/4}
e^{3πi/2}
e^{−3πi/2}
e^{πi/2}
In ΔABC, ∠A = 30°, ∠B = 45°, which one of the following is ac ?
√2 / (√3 + 1)
(3 + 1) / √2
(√3 + 1) / (2√2)
2√2 / (√3 + 1)
Which one of the following has transverse axis and conjugate axis ?
y² − 4x + 4x + 4 = 0
xy² − 3x − 6 = 0
2y² + 3x² − 6 = 0
2x² + 2y² = 72
It is given that a and b are two vectors such that |a × b| = |a · b|.
What is the angle between a and b ?
π
π/2
π/4
π/6
In a school there were 100 students, 35% students failed in mathematics, 20% students failed in science and 15% failed in both the subjects. A student selected at random, the probability of the student fail in mathematics given that failed in science already is
3/7
4/7
3/4
1/4
Which one of the following is the derivative of cosec h⁻¹(x) ?
1 / (x√(x² + 1))
−1 / (x√(x² + 1))
1 / (x√(1 − x²)), (|x| < 1)
−1 / (x√(1 − x²)), (|x| < 1)
Which one of the following is equal to
limₓ→0 (e^{3x} − 1) / 2x ?
0
1/2
3/2
3
Which one of the following represents the equation of normal to the curve
x² = 2y at the point (−2, 2) ?
2x + y + 6 = 0
2x − 2y + 6 = 0
2x − y + 6 = 0
x − 2y + 6 = 0
Which one of the following is the solution of differential equation
x dy − y dx = 0 ?
x = cy
y = cx
xy = c
x − y = c
In Gauss elimination method, the coefficient of the variables of the element aᵢⱼ where i = j are known as...
pivot element
common element
non basic element
basic element
Group B
Short answer questions
Write the number of the total terms in the expansion of
Write the middle term in the expansion of when is even.
What is the sum of binomial coefficients in the expansion $ (1 + x)^n $?
Write in series form form for
Write in series form.
Find the value of
,
where and are imaginary cube roots of unity.
Solve the following system of equations using inverse matrix method:
in a triangle , prove that
Find the eccentricity and foci of the ellipse
Find the equations of tangent and normal to the circle at the point .
In a rhombus, two of the diagonals are perpendicular to each other. Verify it by taking vector dot product of two vectors.
Write the order of differential equation
Write the derivative of with respect to .
Write an example of exact differential equation in and .
Write the integral of
State L-Hospital's rule.
The supply and price of a commodity for the last six year is given below.
Price in Rs. per kg | 100 | 110 | 112 | 115 | 120 | 140 |
|---|---|---|---|---|---|---|
Supply in kg | 30 | 40 | 45 | 20 | 55 | 55 |
Find the coefficient of correlation between price and supply.
Estimate supply in kg on which rate of price is Rs 150.
Integrate
Using simplex method maximize subject to , ,
Group C
Long answer questions
If , prove that
C₁ + 2C₂ + 3C₃ + ⋯ + nCₙ − ½(n · 2ⁿ) = 0
Find the square root of using De-Moivre's theorem.
Use principle of mathematical induction to prove that
1 + 3 + 5 + 7 + ⋯ + (2n − 1) = n²
Find the equation of the parabola whose focus is at the point and the directrix is .
Find the area of parallelogram whose diagonals are represented by the vectors and .
In a triangle , , and . Solve the triangle.
Water flows in an inverted conical tank at the rate of . When the depth of water is , how fast is the level rising, if the radius of base and height of the tank are and respectively?
The concept of anti-derivative is necessary for solving a differential equation. Justify the statement with an example.
A differential equation of first degree and first order is homogeneous if it satisfies the condition
dy/dx = f(y/x)
Justify the statement with an example and solve it.