1. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 01
1. In B-Phase complete Binomial theorem and P & C with discussion upto
27/10/10.
2. In C-Phase complete Binomial theorem and P & C with discussion upto
27/10/10 and this week Dpp no. 47 to 50.
Total Marks : 29 Max. Time : 27 min.
Single choice Objective ('–1' negative marking) Q.3, 4 (3 marks 3 min.) [6, 6]
Multiple choice objective ('–1' negative marking) Q.2, 5, 7 (5 marks 4 min.) [15, 12]
Subjective Questions ('–1' negative marking) Q.6 (4 marks 5 min.) [4, 5]
Fill in the Blanks ('–1' negative marking) Q.1 (4 marks 4 min.) [4, 4]
Ques. No. 1 2 3 4 5 6 7 Total
Mark obtained
1. The midpoint of the chord on the line 3x + 4y – 25 = 0 intercepted by the circle x2
+ y2
= 81 is .......
Ans. (3,4)
2. The centre of a circle S = 0 lies on 2x – 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2
+ y2
= 4. Then
the circle must pass through the point
(A) (1, 1) (B*) (– 1/2, 1/2)
(C) (5, 5) (D*)(–4,4)a
3. Let AB be any chord of the circle x² + y² – 2x – 6y – 6 = 0 which subtends right angle at the point (2, 4), then
the locus of the mid point of AB is
(A) x² + y² – 3x – 7y –16 = 0 (B*) x² + y² – 3x – 7y + 7 = 0
(C) x² + y² + 3x + 7y – 16 = 0 (D) x² + y² + 3x + 7y – 7 = 0
4. Locus of the center of the circle touching the angle bisectors between the pair of lines ax² + ay² + bxy = 0
(Where a, b  R) is
(A) x² – y² = 0 (B*) xy = 0 (C) x² – y² = 1 (D) None of these
5. If the angle between the pair of tangent drawn from (a, a) to the circle x² + y² – 2x – 2y – 6 = 0 lies in the
interval 







,
3
then a may be equal to
(A*) –2 (B*) 4 (C) 3 (D) 1
6. x2 + y2 + ax + by + c = 0 is the equation of a circle that bisects the circumference of the circle,
x2 + y2 + 2y – 3 = 0 and touches the bisector of the first and third quadrant at the origin. Find a + b + c.
Ans. 0
7. Consider the following statements
S1: If a  0, a, b, c  R, then roots of equation ax2
+ bx + c = 0 are complex numbers
S2 : The equation of the circle passing through the point of intersection of the circle x2 + y2 = 4 and the line
2x + y – 1 = 0 and having minimum possible radius is 5x2 + 5y2 + 4x + 9y – 5 = 0.
S3 : Vertices of a variable triangle are (3, 4), (5 cos, 5sin) and (5 sin , – 5cos). The locus of its
orthocentre is (x + y – 7)2 + (x – y + 1)2 = 100
(A*) S1 is true (B*) S2 is false (C*) S3 is true (D) S1 and S2 both are true.
48

2. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 02 Total Marks : 26 Max. Time : 26 min.
Single choice Objective ('–1' negative marking) Q.1, 3, 4, 5, 6 (3 marks 3 min.) [15, 15]
Assertion and Reason (no negative marking) Q.2 (3 marks 3 min.) [3, 3]
Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8]
Ques. No. 1 2 3 4 5 6 7 Total
Mark obtained
1. If two chords of the circle x2
+ y2
 ax  by = 0, drawn from the point P(a, b) is divided by the x axis
in the ratio 2 : 1 in the direction from the point P to the other end of the chord, then
(A*) a2
> 3 b2
(B) a2
< 3 b2
(C) a2
> 4 b2
(D) a2
< 4 b2
2. Statement-1 : Perpendicular from origin O to the line joining the points A (c cos, c sin) and
B (c cos, c sin) divides it in the ratio 1 : 1
Statement-2 : Perpendicular from opposite vertex to the base of an isosceles triangle bisects it.
(A*) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
(B) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
3. Which of the following bisects the circumference of the circle x2
+ y2
 8 x  6 y + 23 = 0 .
(A) x2
+ y2
+ 6 x + 4 y  10 = 0 (B*) x2
+ y2
 6 x  4 y + 9 = 0
(C) x2
+ y2
 6 x + 4 y + 9 = 0 (D) none of these
4. Two circles of radii 4 cms & 1 cm touch each other externally and  is the angle contained by their
direct common tangents . Then sin  equals to
(A*) 24/25 (B) 12/25 (C) 3/4 (D) none
5. Two circles of equal radius ‘ r ‘ cut orthogonally . If their centres are (2 , 3) & (5 , 6), then ‘ r ‘ is equal
to :
(A) 1 (B) 2 (C*) 3 (D) 4
6. If
6

< x <
4

and 3
n
)
..........
x
tan
x
tan
x
(tan 3
2
e 




is a root of the equation y2
– 12y + 27 = 0, then a value of
x
sin
x
cos
x
sin

is
(A)
3
1
(B*)
5
2
(C)
3
2
(D)
2
1
7. Column - I Column - II
(A) A triangle is formed by the lines whose combined (p) 0
equation is given by (x + y –9) (xy – 2y –x + 2) = 0
if the circumcentre of triangle is (h, k), then value of
|h – k| is
(B) A region in the x–y plane is bounded by the curve (q) 1
y = 36 – ²
x and the line y = 0. If the point (a, a + 2) lies
in the interior of the region, then number of possible
integral values of a is
(C) If the tangent at the point P on the x² + y² + 6x + 6y = 2 (r) 2
meets the straight line 5x – 2y + 6 = 0 at the point Q on the
y axis, then length of PQ is
(D) Number of tangent (s) which can be drawn from the point (s) 4






1
,
2
5
to the circumcircle of the triangle with vertices (1 3 )
(1, – 3 ), (3, – 3 ) is (t) 5
Ans. (A)  (q), (B)  (t), (C) (t), (D) (p)
49

3. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 03
Total Marks : 25 Max. Time : 24 min.
Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5, 6 (3 marks 3 min.) [18, 18]
Multiple choice objective ('–1' negative marking) Q.7 (5 marks 4 min.) [5, 4]
True or False (no negative marking) Q.8 (2 marks 2 min.) [2, 2]
Ques. No. 1 2 3 4 5 6 7 8 Total
Mark obtained
1. The complete set of values of ‘x’ for which the expression
















x
log
log
log
4
1
3
2
1
is defined, is :
(A*) 





4
1
,
0 (B) (0, 1) (C) 





1
,
4
1
(D) (1, )
2. n
Cr  1
+ 3 n
Cr
+ 3 n
Cr + 1
+ n
Cr + 2
is equal to:
(A) n + 2
Cr + 1
(B) n + 2
Cr + 2
(C) n + 2
Cr + 3
(D*) n + 3
Cr + 2
3. In the expansion of (1 + x)43
if the coefficients of the (2r + 1)th
and the (r + 2)th
terms are equal, then
value of r is:
(A) 12 (B) 13 (C*) 14 (D) 15
4. If in the expansion of x
x
n
3 2






 a term like x2
exists and ' n ' is a double digit number, then least
value of ' n ' is :
(A*) 10 (B) 11 (C) 12 (D) 13
5. The coefficient of x6 in {(1 + x)6 + (1 + x)7 + .......... + (1 + x)15} is-
(A*) 16c9 (B) 16c5 – 6c5 (C) 16c6 – 1 (D) none of these
6. When 1127 + 2127 is divided by 16, the remainder is
(A) 1 (B) 14 (C*) 0 (D) 2
7. Point(s) on the line x = 3 from which the tangents drawn to the circle x2
+ y2
= 8 are at right angles is/are
(A*) (3, – 7 ) (B) (3, 23 ) (C*) (3, 7 ) (D) (3, – 23 )
8. Integral part of  1997
9
2
7  is even. [True/False]
Ans. True
50