Sub. code 0081
NEB — GRADE XII
2083
Old Question
Mathematics Question Paper 2083 (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, 2083 (subject code 0081), carrying full marks of 75 with a pass mark of 32, to be completed within 3 Hours. Answers with step-by-step solutions are available for every question below.
Group A
Rewrite the correct option of each question in your same answer sheet.
Which one of the following represents
Which one is the highest Common Factor (HCF) of , , and ?
Which one of the following is equation of circle which touches -axis and whose centre is at ?
In any triangle ABC, , and , then which is equal to ?
If and be two vectors then the projection of the vector on is:
A and B are dependent events. , and , which one of the following is ?
Which one is the derivative of ?
What is the value of ?
Which one is the solution of ?
The integrating factor for the differential equation is
After forward row reduction in Gauss elimination method, if the augmented matrix of given system of three linear equations reduces to following form,
then the system of equations has:
Unique solutions
Infinitely many solutions
No solutions
Only one solution
In a projectile, initial velocity is and angle of projection is , what is its time of flight?
Group B
State the principle of mathematical induction.
Write the general term of .
When does given linear equations become inconsistent?
State De Moivre's theorem for positive integral power.
Write any one property of combination.
How many word can be formed from the letter of the word "DAUGHTER" so that vowels always come together?
Find the cube roots of .
Find the solution of triangle given by , and .
Two vectors and are given. Is the area of parallelogram formed by and , a whole number? Find it by calculation.
Find the equation of tangent to the curve at .
Find the equation of hyperbola with focus at and eccentricity .
The height in inches (X) and weight in kg (Y) of 7 students are given below:
Height (X) | 60 | 61 | 62 | 63 | 64 | 65 | 66 |
|---|---|---|---|---|---|---|---|
Weight (Y) | 62 | 63 | 61 | 64 | 66 | 67 | 64 |
Find the correlation coefficient between X and Y and also find regression coefficient of X on Y.
If a particle moves in a path given by , write the velocity.
Write the derivative of with respect to x.
Write the integral of .
Write the integral of .
Write the order of .
Using L. Hospital's rule, find the limit of .
Solve: .
Use simplex method to solve maximize subject to constraints
.
A mass of 10 kg is acted on by a constant force which in 5 seconds, produced a velocity of 20 m per second. Find the force if the mass was initially at rest.
A particle of mass 5 kg slides down a 30° inclination of the plane. If smooth inclined plane to the horizontal is . Find the acceleration of the particle and reaction between the particle and the plane.
Group C
A Committee of 5 members is to be formed from 6 boys and 4 girls. In how many ways can this be done so as to include at most three girls?
Prove that using principle of mathematical induction.
The total cost of 2 pen and 3 book is Rs. 1,100 and the total cost of 4 pen and 1 book in Rs. 700. Find the cost of a pen and a book using Cramer's rule.
Prove that: .
Find vertex, focus, and equation of directrix of conic .
Find the angle between and .
A container is made up of a hollow inverted right circular cone whose height is 24 cm and the radius at the top is 16 cm. Water is flowing in the container at the rate of and find rate of change of depth of water when depth is 12 cm.
Integrate: .
Solve: .