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MATHS TEST PAPER
XI –: (SET – A)
SETS RELATION & FUNCTIONS Time : 3 hrs
STRAIGHT LINE AND CONIC SECTION
Max. Marks : 100
Each question carries 1 mark
1.
Find the centre and radius of the circle 2x 2  2y2  x  0.
2.
Find the equation of parabola whose vertex (0, 0), passing through (5, 2) and symmetric with respect
to y-axis.
3.
Find the distance between the lines 3x  4y  7  0 & 6x  8y  10.
4.
Find the distance of the point (3, 5) from the line (10 y) / 296  0.
5.
Find the angle between the lines y  3x  5  0 and
6.
Find the equation of the right bisector of the line segment joining the points (3, 4) and (-1, 2).
7.
Write the following set in Set Builder form.
3y  x  6  0 .
2 3 4 5 6 8
A , , , , , 
1 2 3 4 5 7 
8.
9.
10.
What is the domain and range of the greatest integer function F(x) = [x].
If E & O denote the set of even & odd numbers respectively, find E – O.
Write the following set in Roster form.
A = {x : x is a positive integer less than 10 and 2x – 1 is an odd number}
Each question carries 4 marks
11. An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the
base. How wide is it 2 m from the vertex of the parabola ?
12.
A man running a racecourse notes that the sum of the distances from the two flag posts from him is
always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the
man.
13.
Find the centre and radius of the circle whose equation is :
14.
Find the coordinates of the foot of perpendicular from the point  1, 3 to the line 3x  4y  16  0 .
15.
If p and q are the lengths of perpendiculars from the origin to the lines x cos   ysin   k cos2 and
720 2
121
108y2
x  18y 

 36x
20
11
3
x sec   y cosec   k , respectively, prove that p 2  4q 2  k 2 .
16.
Find the equation of a line drawn perpendicular to the line
x y
  1 through the point, where it meets
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the y-axis.
17.
Let the opposite angular points of a square be (3, 4) and (1, -1). Find the coordinates of the remaining
angular points.
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18.
Find the domain and range of function f  x   16  x 2
19.
Find the domain of the function f  x  
x 2  2x  1
.
x 2  8x  12
20.
In a survey of 400 students in a school, 100 were listed as taking apple juice, 150 as taking orange
juice and 75 were listed as taking both apple as well as orange juice. Find how many students were
taking neither apple juice nor orange juice.
21. A market research group conducted a survey of 1000 consumers and reported that 720 consumers like
product A and 450 consumers like product B, what is the least number that must have liked both
products?
22.
Let A = {1, 2, 3, 4, 5, 6}. Define relation R from A to A by R  (x, y) : y  x  1
(i)
Depict this relation using an arrow diagram
(ii)
Write down domain, co-domain.
Each question carries 6 marks
23.
Show that the equation 9x 2 16y2 18x  32y 151  0 represent a hyperbola. Find the coordinates of
the centre, lengths of the axes, eccentricity, latus-rectum, coordinates of foci and vertices, equations of
the directrices of the hyperbola.
24.
(i)
Derive the formula of the coordinates of the centroid of a triangle whose vertices are
A(x1, y1, z1 ), B(x 2 , y2 , z2 ) & C(x3 , y3 , z3 ).
(ii)
Find the values of a, b & c if the centroid of the triangle with vertices P(2a, 2, 6), Q(4,3b, 10)
& R(8,14, 2c) is the origin.
25.
Find the equations of the straight lines which pass through the origin and trisect the intercept of the
line 3x  4y  12 between the axes.
26.
Show that the equation of the line passing through the origin and making an angle  with the
line y  mx  c is
27.
y m  tan 

.
x 1 m tan 
Let f and g be real functions defined by f (x)  x  2 and g(x)  4  x 2 . Then, find each of he
following functions :
(i)
f g
(ii)
f g
(v)
ff
(vi) gg
(iii) fg
(iv)
f
g
1
 x2.
log10 (1  x)
28.
Find the domain of definition of the function f (x) given by f (x) 
29.
In a survey of 25 students, if was found that 15 had taken Mathematics, 12 had taken Physics and 11
had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics,
4 had taken Physics and Chemistry and 3 had taken all the three subjects. Find the number of students
that had
(i)
Only Chemistry
(ii)
Physics and Chemistry but not Mathematics
(iii) Only one of the subjects
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