1. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 01
Total Marks : 20 Max. Time : 19 min.
Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5 (3 marks 3 min.) [15, 15]
Multiple choice objective ('–1' negative marking) Q.6 (5 marks 4 min.) [5, 4]
Ques. No. 1 2 3 4 5 6 Total
Mark obtained
1. A circle is concentric with circle x2
+ y2
 2x + 4y  20 = 0 . If perimeter of the semicircle is 36 then
the equation of the circle is : [ use  = 22/7 ]
(A) x2
+ y2
 2x + 4y  44 = 0 (B) (x  1)2
+ (y + 2)2
= (126/11)2
(C) x2
+ y2
 2x + 4y  43 = 0 (D) x2
+ y2
 2x + 4y  49 = 0
2. Chords of the curve 4x2
+ y2
– x + 4y = 0 which subtend a right angle at the origin pass through a fixed
point whose co-ordinates are :
(A)
1
5
4
5
, 





 (B) 






1
5
4
5
, (C)
1
5
4
5
,





 (D)  






1
5
4
5
,
3. A is a point on either of two rays y + 3 |x|= 2 at a distance of
4
3
units from their point of intersection.
The coordinates of the foot of perpendicular from A on the bisector of the angle between them are
(A) 






2
3
2
, (B) (0, 0) (C) 2
3
2
,





 (D) (0, 4)
4. The equation of the image of the circle x2
+ y2
+ 16x  24y + 183 = 0 in the line mirror
4x + 7y + 13 = 0 is:
(A) x2
+ y2
+ 32x  4y + 235 = 0 (B) x2
+ y2
+ 32x + 4y  235 = 0
(C) x2
+ y2
+ 32x  4y  235 = 0 (D) x2
+ y2
+ 32x + 4y + 235 = 0
5. The circle x2
+ y2
+ 4x – 7y + 12 = 0 cuts an intercept on y-axis of length
(A) 3 (B) 4 (C) 7 (D) 1
6. In a parallelogram as shown in the figure (a  b) :
(A) equation of the diagonal AC is
(a + b) x + (a + b)y = 3 ab
(B) equation of the diagonal BD is u1
u4
 u2
u3
= 0
A B
C
D
u
a
x
+
b
y
=
a
b
3

u
a
x
+
b
y
=
2
a
b
4

u bx + ay = 2ab
2 
u bx + ay = ab
1 
(C) co-ordinates of the points of intersection of the
two diagonals are 








 )
b
a
(
2
ab
3
,
)
b
a
(
2
ab
3
(D) the angle between the two diagonals is /3.
DPP No. – 02
Total Marks : 25 Max. Time : 26 min.
Comprehension ('–1' negative marking) Q.1 to Q.3 (3 marks 3 min.) [9, 9]
Single choice Objective ('–1' negative marking) Q.4, 5, 6 (3 marks 3 min.) [9, 9]
Subjective Questions ('–1' negative marking) Q.7 (4 marks 5 min.) [4, 5]
Assertion and Reason (no negative marking) Q.8 (3 marks 3 min.) [3, 3]
Ques. No. 1 2 3 4 5 6 7 8 Total
Mark obtained
42 to 44

2. Comprehension (1 to 3)
Consider the triangle ABC having vertex A (1, 1) and its orthocentre is (2, 4). Also side AB & BC are
members of the family of line, ax + by + c = 0 where a, b, c are in A.P.
1. the vertex B is :
(A) (2, 1) (B) (1, –2) (C) (–1, 2) (D) None of these
2. the vertex C is :
(A) (4, 16) (B) (17, –4) (C) (4, –17) (D) (–17, 4)
3.  ABC is a :
(A) obtuse angled triangle (B) Right angled triangle
(C) Acute angled triangle (D) Equilaterial triangle
4. The family of straight lines 3(a + 1) x – 4 (a – 1) y + 3 (a + 1) = 0 for different values of 'a' passes through a
fixed point whose coordinates are
(A) (1, 0) (B) (–1, 0) (C) (–1, –1) (D) none of these
5. Let the minimum value of real quadratic expression ax2
– bx +
a
2
1
, a > 0 be y0
. If y0
occurs at x = k and
k = 2 y0
, then set of all possible values of b is
(A) {2, –1} (B) {–1, –2} (C) {2, 1} (D) {– 2, 1}
6. The area of an equilateral triangle inscribed in the circle x² + y² 2x = 0 is :
(A)
3 3
4
(B)
3 3
2
(C)
3 3
8
(D) none of these
7. Find the sum to ‘n’ terms and the sum to infinite terms of the series
terms
n
upto
...
..........
4
3
2
1
9
3
2
1
7
2
1
5
1
3
2
2
2
2
2
2
2
2
2
2










8. STATEMENT-1: If a, b, c are non-zero real numbers such that
3(a2
+ b2
+ c2
+ 1) = 2(a + b + c + ab + bc + ca), then a, b, c are in A.P. as well as in G.P.
and
STATEMENT-2: A series is in A.P. as well as in G.P. if all the terms in the series are equal and
non-zero.
(A) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C) STATEMENT-1 isTrue, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 isTrue
DPP No. – 03
Total Marks : 22 Max. Time : 23 min.
Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 6 (3 marks 3 min.) [15, 15]
Subjective Questions ('–1' negative marking) Q.5 (4 marks 5 min.) [4, 5]
Assertion and Reason (no negative marking) Q.7 (3 marks 3 min.) [3, 3]
Ques. No. 1 2 3 4 5 6 7 Total
Mark obtained
1. The equation of the circle of radius 5 in the first quadrant which touches the x-axis and the line
3 x – 4 y = 0 is :
(A) x2
+ y2
– 24 x – y – 25 = 0 (B) x2
+ y2
– 30 x – 10 y + 225 = 0
(C) x2
+ y2
– 16 x – 18 y + 64 = 0 (D) x2
+ y2
– 20 x – 12 y + 144 = 0

3. 2. A circle touches the x axis and the line 4x – 3y + 4 = 0. If centre lies in the third quadrant and on the line
x – y – 1 = 0, then the equation of the circle is
(A) 9x2
+ 9y2
+ 24x + 6y – 1 = 0 (B) 9x2
+ 9y2
+ 6x – 2xy + 1 = 0
(C) 9x2
+ 9y2
+ 6x + 24y + 1 = 0 (D) x2
+ y2
+ 2x + 3y + 1 = 0
3. If three distinct real numbers a, b, c are in G.P. and a + b + c = xb, x  R, then
(A) – 3 < x < 1 (B) x > 1 or x < – 3 (C) x < –1 or x > 3 (D) – 1 < x < 3
4. Area of the triangle formed by the x + y = 3 and angle bisectors of the pair of straight lines x2
– y2
+ 2y =
1 is
(A) 2 sq. units (B) 4 sq. units (C) 6 sq. units (D) 8 sq. units
5. Find the maximum and minimum distance of the point (2 ,  7) from the circle
x2
+ y2
 14 x  10 y  151 = 0 .
6. Consider the following statements for real values of x :
S1
: Number of circles through the three points A(3, 5), B (4, 6), C (5, 7) is 2.
S2
: |x – 2| = [– ], where [.] denotes greatest integer function, then x = 6, – 2
S3
: The image of the point (2,1) with respect to the line x + 1 = 0 is (–2 , 1)
State, in order, whether S1
, S2
, S3
are true or false
(A)TTT (B) FTF (C)TTT (D) FFF
7. STATEMENT-1: The number of integral values of  , for which the equation 7cosx + 5sinx = 2  + 1 has a
solution, is 8.
and
STATEMENT-2: The equation acos + bsin  = c has atleast one solution if | c | > 2
2
b
a  .
(A) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is a correct explanation for
STATEMENT-1
(B) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is NOT a correct explanation for
STATEMENT-1
(C) STATEMENT-1 isTrue, STATEMENT-2 is False
(D) STATEMENT-1 is False, STATEMENT-2 isTrue
Answer Keys DPP # 42
1. (A) 2. (A) 3. (B) 4. (D) 5. (D)
6. (A) (B)(C)
Answer Keys DPP # 43
1. (B) 2. (D) 3. (A) 4. (B) 5. (D)
6. (A) 7. 6
S
,
1
n
n
6
Sn 

  8. (A)
Answer Keys DPP # 44
1. (B) 2. (C) 3. (C) 4. (A) 5. max = 28, min = 2
6. (D) 7. (C)