Practice Model set-I
Subject :- opt. Maths
Grade :- X
Attempt the entire questions.
F.M. = 100
P.M.= 40
Time :- 3 hours
Group ‘A’ [5×(1+1)]=10
1. a) Find the inverse of the function f(x) =
2.
3.
4.
5.
.
b) State factor theorem.
a) Define continuity of a function at a point.
b) Define singular matrix.
a) Find the slope of the line x-5 y = 4.
b) Write the condition of generating a parabola, by the intersection of a cone and a
plane surface.
a) Express cosC – cosD in the form of product.
b) Solve: cot2x – 3 = 0 (0o
900)
⃗⃗ to be parallel.
a) Write the condition for the two vectors ⃗
b) What is the combined transformation of rotation R1[O, 80o] followed by R2[O, 40o].
Group B [13×2 = 26]
6. a) If f(x)= x+2 and g(x)= 2x+3 then find fog-1 (2).
b) If x+2 is the factor of 3x3+ kx2 – 2x – 8, calculate the value of k.
c) Dose the term 302 lie on the arithmetic series 3+ 8+ 13 + 18 +……..
7.
a) If the matrix(
) and (
) are inverse to each other, find the value
of m.
b) What matrix pre multiplies (
) to get (-9 , 5 ) ?
8. a) Find the angle between the lines pair of straight lines represented by x2 – 2xycot -y2
= 0.
b) Find the equation of the circle having (1, 3) and (2, -5) as the end points of a
diameter.
9. a) Prove that: sin4B + cos4B = 1 - sin22B
b) If Prove that: cos20o + cos100o + cos140o = 0
c) Solve: cos2A= sinA (0o
90o)
10. a) If the position of the vector of the point A is 2⃗
midpoint M of the line joining A and B is ⃗
point B.
b) In the given figure ⃗⃗⃗⃗⃗⃗ ⃗ and ⃗⃗⃗⃗⃗⃗ ⃗⃗. If ⃗⃗⃗⃗⃗⃗
⃗ and the position vector of the
⃗, find the position vector of the
⃗⃗⃗⃗⃗⃗ , find the ⃗⃗⃗⃗⃗⃗⃗
c) A frequency distribution has the mean 100 and the coefficient
of variation 10 . Find the standard deviation.
Group C [11×4=44]
2
11. Solve graphically: x -x-2=0 .
12. The sum of the first ten terms of an arithmetic series is 50 and its fifth term is treble of
the second term. Calculate the sum of the first twenty terms of the series.
13. A function f(x) is defined below:
f(x) = {
Is this function continuous at x = 4? Test.
14. Solve by matrix method: 2x -3y = 7 and 4y – 3x + 10 = 0 .
15. Find the equation of the straight line passing through the point (-1, -2) and making
angle of 30o with the line x + √ y + 5 = 0.
16. Prove that: cos20o.cos40o.cos60o.cos80o =
17. If A + B + C = 180o prove that:
18. The angles of elevation of the top of a tower from two points at a distance of ‘x’ and ‘y’
from the base and in the same straight line with it are complementary. Prove that the
height of the tower is√ .
19. Find the 2×2 matrix which transforms the unit square to a parallelogram
(
)
20. Compute mean deviation from mean and its coefficient from the given data :
Marks
2030-40 40-50 50-60 60-70 70-80 80-90 90obtained 30
100
No. of
5
15
10
8
8
5
2
1
students
21. Compute the standard deviation and its coefficient from the given data:
Scores
0-5
No. of students 5
5-10
20
10-15
15
15-20
20
20-25
10
Group‘D’
22. Find the maximum value of z=5x+9y under the constraints: x+y≤10, 2x+3y≤24, x≥0 ,
y≥0.
23. Find the equation of circle which passes through the points (2, -2), (6, 6) and (5, 7).
24. If P and Q are the mid-points of the diagonal AC and BD of a quadrilateral ABCD. Prove
that:
⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗
⃗⃗⃗⃗⃗⃗⃗
25. Translate the quadrilateral OABC having vertices O(0,0), A(2, 0), B(3, 2)
and C(1, 2) by translation vector T=( ). Reflect the image so formed on
the line x=3. Represent the images and object in the same graph paper.
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