1. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 01
Total Marks : 32 Max. Time : 31 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, 7, 8, 9 (3 marks 3 min.) [18, 18]
Multiple choice objective ('–1' negative marking) Q.10 (5 marks 4 min.) [5, 4]
Ques. No. 1 2 3 4 5 6 7 8 9 10 Total
Mark obtained
Comprehension (1 to 3) :
At time of methods of coordinate becomes effective in solving problems of properties of triangle. We may
choose one vertex of the triangle and one side passing through this vertex as x-axis. Thus, without loss of
generality, we can assume that every triangle ABC has a vertex B situated at B(0, 0) vertex C at (a, 0) andA
as (h, k)
1. In ABC, AC = 3, BC = 4 medianAD and BE are perpendiculars, then area of triangleABC must be equal to
(A) 7 sq. units (B*) 11 sq. units (C) 2
2 sq. units (D) none of these
2. Suppose the bisector AD of the interior angle A of ABC divide side BC into segment BD = 4, DC = 2, then
we must have
(A) b > C and C < 4 (B) 2 < b < 6 and C < 1
(C*) 2 < b < 6 and C = 2b (D) none of these
3. If altitudes CD = 7, AE = 6 and E divides BC given that
EC
BE
=
4
3
, then C must be
(A) 3
2 (B) 3
5 (C) 3 (D*)
3
4
4. Consider the straight line ax + by = c where a, b, c  R+
. This line meets the coordinate axes at 'P' and
'Q' respectively. If the area of triangle OPQ. 'O' being origin, does not depend upon a, b and c then
(A) a, b, c are in G.P. (B*) a, c, b are in G.P. (C) a, b, c are in A.P. (D) a, c, b are in A.P.
5. ABC is a right angled isosceles triangle, right angled at A(2, 1). If the equation of side BC is
2x + y = 3, then the combined equation of lines AB and AC is
(A) 3x2
– 3y2
+ 8xy + 20x + 10y + 25 = 0 (B) 3x2
– 3y2
+ 8xy – 20x – 10y + 25 = 0
(C) 3x2
– 3y2
+ 8xy + 10x + 15y + 20 = 0 (D*) None of these
6. The straight line x cos  + y sin  = 2 will touch the circle x2
+ y2
– 2x = 0 if
(A)  = n, n   (B)  = (2n + 1), n   (C*)  = 2n, n   (D) None of these
7. If the circles x2
+ y2
– 8x + 2y + 8 = 0 and x2
+ y2
– 2y – 6y + 10 – a2
= 0 have exactly two common
tangents, then
(A) 1 < |a| < 8 (B*) 2 < |a| < 8 (C) 3 < |a| < 8 (D) 4 < |a| < 8
8. Equation of the circle that cuts the circles x2
+ y2
= a2
, (x – b)2
+ y2
= a2
and x2
+ (y – c)2
= a2
orthogonally is
(A) x2
+ y2
– bx – cy – a2
= 0 (B) x2
+ y2
+ bx + cy – a2
= 0
(C) x2
+ y2
+ bx + cy + a2
= 0 (D*) x2
+ y2
– bx – cy + a2
= 0
9. A circle passes through the points A(1, 0), B(5, 0) and touches the y-axis at C(0, h). If ACB is
maximum then
(A*) h = 5 (B) h = 2 5 (C) h = 10 (D) y = 2 10
10. If Line L : (3x – 4y – 25 = 0) touches the circle S : (x2
+ y2
– 25 = 0) at P and L is common tangent of circles
S = 0 and S1
= 0 at P and S1
= 0 passes through (5, –6), then
(A*) centre of S1
= 0, 






7
36
,
7
27
(B*) length of tangent form origin to S1
= 0,
7
275
(C) centre of S1
= 0, 






7
36
,
7
27
(D) length of tangent from origin to S1
= 0 =
7
375
92

2. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
DPP No. – 02
Total Marks : 34 Max. Time : 33 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]
Assertion and Reason (no negative marking) Q.8 (3 marks 3 min.) [3, 3]
Match the Following (no negative marking) (2 × 4) Q.9 (8 marks 8 min.) [8, 8]
Ques. No. 1 2 3 4 5 6 7 8 9 Total
Mark obtained
1. The straight lines 7x – 2y + 10 = 0 and 7x + 2y – 10 = 0 forms an isosceles triangle with the line y =
2. Area of this triangle is equal to
(A)
7
15
sq. units (B)
7
10
sq. units (C*)
7
18
sq. units (D)
7
15
sq. units
2. If the straight lines ax2
+ 2hxy + by2
+ 2gx + 2fy + c = 0 intersect on the x-axis then
(A) ag = fh (B) ah = fg (C*) af = gh (D) None of these
3. If chord x cos  + y sin  = p of x2
+ y2
= a2
subtends a right angle at the origin then
(A) a2
= p2
(B*) a2
= 2p2
(C) a2
= 3p2
(D) None of these
4. The circles having radii r1
and r2
intersect orthogonaly. Length of their common chord is
(A*) 2
2
2
1
2
1
r
r
r
r
2

(B) 2
2
2
1
2
2
1
r
r
r
r
2

(C) 2
2
2
1
2
1
r
r
r
r

(D) 2
2
2
1
2
2
2
r
r
r
r
2

5. The triangle ABC is inscribed in the circle x2
+ y2
= 25 if A(3, 4), B(–4, 3) then ACB is equal to
(A)
3

(B)
2

(C*)
4

(D)
6

6. Locus of midpoint of chords of circle x2
+ y2
= a2
that subtends angle
2

at the point (0, b) is
(A) 2x2
+ 2y2
– 2bx + b2
– a2
= 0 (B*) 2x2
+ 2y2
– 2by + b2
– a2
= 0
(C) 2x2
+ 2y2
– 2bx + a2
– b2
= 0 (D) 2x2
+ y2
– 2by + a2
+ b2
= 0
7. Two circles touch x-axis and passes through  
2
,
3 and also touch y = x
3 . If r1
and r2
are radii of these
two circles then
(A*) r1
+ r2
=
3
10
(B*) r1
r2
=
3
7
(C*) |r1
– r2
| =
3
4
(D) none of these
8. Statement-1 : The joint equation of the
lines 2x – y = 5 and x – 2y = 3 is 2x2
+ 3xy – 2y2
– 11x – 7y + 15 = 0
Statement-2 : Every second degree equation ax2
+ 2hxy + by2
+ 2gx + 2fy + c = 0 always represents pair
of straight line
(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
9. Match the column
Column – I Column – II
(A) The number of common tangent of (p)
2
3
circles x2
+ y2
– 2x – y = 0 and x2
+ y2
+ 4x + 2 = 0 are
(B) If circle x2
+ y2
– ax – 2y + 1 = 0 bisects the circumference (q) 4
of x2
+ y2
– 4x – 2y + 2 = 0, then a is equal to
d
c
(simplest form),
then d – c = 0
(C) Minimum radius of the circle passing through (2, 1) and (5, 1) (r) 5
(D) Angle subtend at circumference x2
+ y2
= 25 by arc AB (s) 3
if A(3, 4) and B (–4, 3) is


, then  – 
Ans. (A)  q, (B)  r, (C)  p, (D)  s
93

3. DAILY PRACTICE PROBLEMS
Subject : Mathematics Date : DPP No. : Class : XI Course :
94
31-01-11
DPP No. – 03
Total Marks : 33 Max. Time : 31 min.
Single choice Objective ('–1' negative marking) Q.1, 4, 5, 6, 7 (3 marks 3 min.) [15, 15]
Multiple choice objective ('–1' negative marking) Q.2, 3 (5 marks 4 min.) [10, 8]
Match the Following (no negative marking) (2 × 4) Q.8 (8 marks 8 min.) [8, 8]
Ques. No. 1 2 3 4 5 6 7 8 Total
Mark obtained
1. A normal to the hyperbola
1
y
–
4
x 2
2
= 1 has equal intercepts on positive x and y - axis if normal touches the
ellipse 1
b
y
a
x
2
2
2
2

 , then a2
+ b2
=
(A) 5 (B) 25 (C) 16 (D*) None of these
2. P is a point on the parabola y2
= 16x where abscissa and ordinate are equal. Equation of a circle
passing through the focus and touching the parabola at P is :
(A) x2
+ y2
+ 52x – 48y + 160 = 0 (B*) x2
+ y2
– 4x = 0
(C) x2
+ y2
+ 4x = 0 (D*) x2
+ y2
– 52x + 8y + 152 = 0
3. If the tangents drawn from the point (0, 2) to the parabola y2
= 4ax are inclined at an angle 3/4, then the
value of a is
(A*) 2 (B*) – 2 (C) 1 (D) None of these
4. The number of focal chord(s) of length 4/7 in the parabola 7y2
= 8x is
(A) 1 (B*) 0 (C) infinite (D) none of these
5. The equation (5x – 1)2 + (5y – 2)2 = (2 – 2 + 1) (3x + 4y – 1)2 represents an ellipse if 
(A) (0, 1) (B*) (0, 2) (C) (1, 2) (D) (– 1, 0)
6. Centroid of the triangle formed by the joining feet of the normals drawn from the point (14, 7) to the parabola
y2
– 8y = 16x, is
(A) 





0
,
3
14
(B*) 





4
,
3
11
(C) 





3
4
,
3
11
(D) 





3
4
,
3
14
7. In the line 2x + y
6 = 2 touches the hyperbola x2
– 2y2
= 4. Then slope of line joining origin and point of
contact is
(A)
2
2
3
(B)
2
3
(C*) –
2
2
3
(D) –
2
3
8. Match the column
Column - I Column - II
(A) A parabola has the origin as its focus and the line x = 2 as (p) 5
the directrix. Then x-coordinate of the vertex of the parabola is
(B) If the tangents from the point (, 2) to the hyperbola
4
y
9
x 2
2
 =1 (q) 1
are at right angles, then  is equal to
(C) The sum of the squares of the perpendiculars on any (r) 3
tangent to the ellipse
16
y
25
x 2
2
 = 1 from two points on
the minor axis each at a distance 3 from the
centre is  , then sum of digit in  is
(D) Suppose F1
, F2
are the foci of the ellipse
9
x2
+
4
y2
= 1. P is (s) 2
a point on ellipse such that PF1
: PF2
= 2 : 1. Half of the area
of the triangle PF1
F2
is
Ans. (A) (q), (B)  (r), (C)  (p), (D)  (s)