Saturday, January 18, 2020

SEE Model Question Prepared by CDC (2076) Optional Mathematics

SEE Model Question Prepared by CDC (2076) Optional Mathematics
SEE Model Question Prepared by CDC
2076
Subject: Optional Mathematics
Full marks:100                            Time: 3 hours
Group ‘A  5 × (1 + 1) = 10
Attempt all the questions.
1.    a) Define trigonometric function.
b)  What is arithmetic mean between two numbers a and b.
2.    a)  Write the name of the set of numbers which is continuous.    
b)   If matrix A = what is the value of |A|?
3.    a)  If the angle between two straight lines is θ and their slopes are m1and m2 respectively, write the formula to find the value of tan θ.
b) Which geometric figure will be formed if a plane intersects a cone parallel to its base? write it.
4.    a)   Express Sin 2A in terms of Tan A.
b)    Define angle of elevation.
5.    a)   What is the scalar product of two vectors a and b and if the angle between them is θ?     
b)   In an inversion transformation if P' is image of P and r is radius of circle with centre O, write the relation of OP, OP' and r.
                                                Group ‘B'  3× (2 + 2 +2) + 2 × (2 + 2) = 26
6.    a)    Find f -1(x) if f(x) = 4x + 5.
b)    If g(x) = 2x -1 and f (x) = 4x, find the value of go f(x).
c)    What will be the points of intersection of the curve f(x) = x2 - 1 and f(x) = 3.
7.    a)    If A =  , find |A| and write A1 is defined or not.
b)    According to Cramer's rule, find the values of D1 and D2 for ax + by = c and px + qy = r.
8.    a)  Find the slopes of two straight lines having equations 3x + 4y + 5 = 0 and 6x + 8y + 7 = 0 and write the relationship between them.
b)    Find the single equation for the pair of lines represented by 3x +2y = 0 and 2x - 3y = 0.
9.    a)  Convert sin6A.cos4A into sum or difference of sine or cosine.
b)    Express  in term of sub-multiple angle of Tangent.                    
c)    If 2 Sin2θ3find value of θ. (0°≤θ≤ 180°)
10. a)   Find the angle between vectors a and b and if , |a|=2  , |b|= 12 and  a. b    
b)    In the given figure, find AP and express p in terms of a and b.
                            
            c)  If the standard deviation of a set of data is 0.25, find its variance.
Group ‘C'  11× 4 = 44
11.      Solve:  x3 - 3 x3 - 4x + 12 = 0  
12.      Optimize P = 5x + 4y under the constraints x – 2y 1, x + y 4, x 0, y 0.
13.      For a real valued function f(x) = 2x + 3
a)     Find the values of f (2.95), f (2.99), f (3.01), f (3.05) and f (3).    
b)     Is this function continuous at x = 3?
14.     By using matrix method solve the following systems of equations:
         3x + 5y = 11, 2x 3y = 1
15.     Find the single equation to represent the equations of pair of straight lines passing through the origin and perpendicular to the lines represented by 2x2 5xy + 2y2 = 0.
16.     Find the value of:  sin 20°. sin 30°. sin 40°. sin 80°
17.       If A + B + C = πc, prove that: sin2 A sin2B + sin2C = 2sinAcosBsinC.
18.       From a place at the ground level in front of a tower the angle of elevations of the top and bottom of flagstaff 6m high situated at the top of a tower are observed 60° and 45° respectively. Find the height of the tower and the distance between the base of the tower and point of observation.
19.       Find the 2×2 matrix which transforms unit square to a parallelogram.
                                                                    
20.       Find the mean deviation and its coefficient from mean of the given data.
 (Marks obtained)
0-10
10-20
20-30
30-40
     40-50
 (No. of students)
2
3
6
5
4
21.       Find the standard deviation and coefficient of variation from given data.
 (Age)
0-4
4-8
8-12
12-16
16-20
  20-24
             
 (No. of Persons)
7
7
10
15
7
6
                                                             ‘Group D'  4× 5 = 20
22. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second dayetc, the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days? find it.
23. On the circumference of a wheel there are three points (5,7), (1, 7) and (5,1)  located such that the distance  from a fixed point to these points is always equal. Find coordinates of the fixed point. Also, find equation representing the locus that contains all three points.
24. By using vector method, prove that the quadrilateral formed by joining the midpoints of adjacent sides of a quadrilateral is a parallelogram?
25. The coordinates of vertices of a quadrilateral ABCD are A (1,1), B (2,3), C (4, 2) and D (3,2). Rotate this quadrilateral about origin through 180°. Reflect this image of quadrilateral about y = x. Write the name of transformation which denotes the    combined transformation of above two transformations.
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