Sub. code 2022
NEB — GRADE X
SE A
Model Question
Optional Mathematics Question Paper SE A (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.
Pass Marks : 32
सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)
This model question question paper is for Class 10 Optional Mathematics, SE A (subject code 2022), 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
Objective Questions.
Which one of the following is the minimum point of the parabola ?
If and , what is the value of ?
Which one of the following is related to ?
What is the value of ?
If , which one of the following is true?
What is the diameter of the circle ?
8
16
32
64
Which one of the following is the equation of the line perpendicular to the line ?
If and are reflections on the parallel lines and , respectively, then which of the following is the combined transformation of ?
Translation by vector
Translation by vector
Translation by vector
Translation by vector
What is the vector cross product magnitude of two vectors and if the angle between them is ?
If , which one of the following is true?
Function is continuous at .
Limit of the function does not exist at .
Limit of the function exists at .
is undefined.
Which of the following measures of central tendency is used in calculating the standard deviation?
Mode
Median
Mean
Range
Group B
A polynomial is given.
If , write the condition for to be a factor of .
If '' is a root of , find the other possible roots by using the rational root theorem.
Functions , and quadratic function are given.
If , find the value of .
Write in the vertex form of the parabola.
Describe the combined transformation involved to transform the function into .
Matrix is given.
Give reason whether is defined or not.
Find the matrix .
Draw the graph of quadratic equation .
The identity is given.
Convert the given identity in the form of .
If , then prove that: .
The angles of elevation of the top of the tower from two points and away from the foot of the tower on the same side are found to be complementary.
Draw a labelled diagram showing the height of a tower, the two points on the ground and angles of elevation.
Find the height of the tower.
Given a conditional identity.
Convert in the form of sum or difference.
Test the given identity when , and .
If , and , state any one reason that the given identity cannot be verified.
Line passes through the point .
Which transformation transforms the point into ?
If straight line makes an angle with the line , find the acute value of $\theta$.
Two circles A and B with equal radius and having the centre P(2, 3) and Q are given in the figure. is the equation of circle B.
Write the diameter form of the equation of the circle.
Find the coordinates of the centre Q and the radius of the circle B with equation .
Find the equation of the circle A.
Points and are joined by a straight line.
Find the image points of the line when transformed by a matrix .
Show the line and its image on the same graph paper.
Coordinates of vertices of are given in the figure alongside.
Write the scalar product of two vectors in terms of angle.
Express vector in terms of .
Prove that the vectors and are perpendicular.
The information of the monthly salary of the workers of two companies is given below.
Company | Average salary Rs. | Standard deviation |
X | 25,000 | 1250 |
Y | 40,000 | 1200 |
Write the formula to find the coefficient of variation.
If the coefficient of variation of the salary of workers of company Y is , find the coefficient of variation of salary of the workers of company X.
Based on the information given above, which company's workers have uniform salary? Why?
A function is defined as follows.
Define the continuity of the function.
Find the limiting value of when the value of is 2.
Find the value of at .
Find whether the function is continuous or discontinuous at . Justify your conclusion.
Group C
with vertices , and and its image with vertices , and are given.
Find a matrix '' that transforms to .
Find the equations of sides of and of .
Side of is parallel to which axis? Why?
Mahabir's statement: "The determinant of a matrix is equal to the determinant of its transpose ." To verify this, let and its transpose be Now,
Similarly,
Since,
Mahabir's statement is true.
Manu cuts a cone to form a conic section. He draws the outline of the edge of the conic section on the plane paper.
Write the name of the shape that would be formed when the cone is cut in such a way that the cutting plane surface is parallel to the base of the cone.
Manu draws a circle of diameter in which . Also, he claims that is the midpoint of $AB$, so, . Prove his claim by vector method.
Explain with reason whether Manu's claim would still be true if point D is closer to A, give reason.
If , and , find the value of .
The relation between height () of the tower and the horizontal distance () is given by a function . Where the slope of the tower .
Prove that:
The angle of elevation of the top of the tower is such that , find the value of slope ().
The function given above .
Suppose, .
Interchanging and , .
Manmohan claims, "If the angle of elevation increase which is taken from some point, the horizontal distance decreases." Verify his claim by giving suitable example.
The following data shows the wages per hour of the workers and their numbers in a factory.
Wage in Rs. | 0–200 | 200–400 | 400–600 | 600–800 | 800–1000 |
No. of workers () | 3 | 5 | 8 | 6 | 3 |
The factory measures how good a value of is by calculating the total squared wages because larger the value of greater will be the variation of the wages. Binaya found that the total squared wages can be represented by a function .
Calculate mean, standard deviation and coefficient of variation of the wages of the workers.
For what value of is the function continuous?
Binaya calculated . Will the function be continuous at with this value?
Paper Overview & Analysis
SE A
Year
Model Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
58
Question Items
Question Type Breakdown
Group Breakdown