indore public school eastern campus
MID TERM EXAM 2020-21
Class-XI
Time : 90 min
SUBJECT : MATHEMATICS
M.M. : 40
General Instructions
(1)
(2)
(3)
(4)
(5)
All questions are compulsory.
This question paper contains 26 questions.
Question no. 1 to 20 in Section-A are very short answer questions and carry 1 mark each.
Question no. 21 to 24 in Section-B are short answer questions and carry 3 marks each.
Question no. 25 and 26 in Section-C are long answer questions and carry 4 marks each.
Q.
No.
1.
2.
SECTION-A (MCQ's)
M.M.
Two finite sets have m and n elements. The number of subsets of the first set is 112 more than that
of the second set. The values of m and n are, respectively,
(a) 4, 7
(b) 7, 4
(c) 4, 4
(d) 7, 7
01
If f  x   x3 
(a) 2x 3
3.
4.
1
 1
, then f  x   f   is equal to
x
x3
1
(b) 2 3
x
2
7.
8.
01
(c) x2  y2  2x  2y  1  0
(b) 2
The value of sin20 sin40 sin60 sin80 is
3
5
(a)
(b)
16
16
(c)
2
(d)
1
2
01
(c)
3
16
(d)
1
16
01
The quadratic equation whose one rational root is 3  2 is
(a) x 2  7x  5  0
(b) x 2  7x  6  0
(c) x 2  7x  6  0
(d) x 2  6x  7  0
The inclination of the line x  y  3  0 with the positive direction of x-axis is
(b) 135
(c) –45
(d) –135
The two lines ax  by  c and a' x  b' y  c ' are perpendicular if
(a) aa' bb'  0
10.
01
The greatest value of sinxcos x is
(a) 45
9.
(D) x  [2, 4)
The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit
is:
(a) x2  y2  2x  2y  1  0
(b) x2  y2  2x  2y  1  0
(a) 1
6.
(d) 1
If [x] – 5[x] + 6 = 0, where [ . ] denote the greatest integer function, then
(A) x  [3, 4]
(B) x  (2, 3]
(C) x  [2, 3]
(c) x2  y2  2x  2y  0
5.
01
(c) 0
(b) ab'  ba'
(c) ab' a'b'  0
(d) ab' ba'  0
The equation of the circle having centre (1, –2) and passing through the point of intersection of the
lines 3x + y = 14 and 2x + 5y = 18 is
(a) x2  y2  2x  4y  20  0
(b) x2  y2  2x  4y  20  0
(c) x2  y2  2x  4y  20  0
(d) x2  y2  2x  4y  20  0
01
01
01
01
XI-MATHEMATICS
MID-TERM EXAM
2 | Page
SECTION-A (Fill in the Blanks & True / False)
11.
The ordered pair (5, 2) belongs to the relation R = {(x, y) : y = x – 5, x, y  Z}. (T/F)
01
12.
If A is any set, then A  A .(T/F)
01
13.
Given that M = {1,2,3,4,5,6,7,8,9} and if B = {1,2,3,4,5,6,7,8,9}, then B  M . (T/F)
01
14.
If a, b, c are in A.P., then the straight lines ax + by + c = 0 will always pass through_______.
01
15.
The line which cuts off equal intercept from the axes and pass through the point (1, –2) is_______.
01
SECTION-A (Very Short Answer Type Questions)
1
?
1  2cos x
16.
What is the Range of f  x  
17.
Solve 8  5x  3  7 .
01
18.
If a circle passes through the point (0, 0) (a, 0), (0, b) then find the coordinates of its centre.
01
19.
Find the equation of the circle which touches x-axis and whose centre is (1, 2).
01
20.
Solve 5 
01
5  3x
8.
2
01
SECTION-B (Short Answer Type Questions)
3 cosec 20  sec 20 .
21.
Find the value of
03
22.
The roots of the quadratic equation
23.
Prove that 2 > n for all positive integers n.
24.
Find the angle between the lines y  3x  5  0 and
1
1 1 1
   , a  b  0 is
ab x a b x
n
03
03
3y  x  6  0 .
03
SECTION-C (Long Answer Type Questions)
25.
26.
20 A manufacturer has 600 litres of a 12% solution of acid. How many litres of a 30% acid solution
must be added to it so that acid content in the resulting mixture will be more than 15% but less than
18%?
n
n
For every positive integer n, prove that 7 – 3 is divisible by 4.

04
04